Mgchanica! Design of Process Systems Volume2 Shell-and-Tube Heat Exchangers Rotating Equipment Bins, Silos, Stacks A.Keith Escoe Gulf Publishing Company Book Division Houston, London, Paris, Tokyo llctaniul Design of Pmctss Svsterns \itme 2 SldLen*Tuh Heat Exchangers Roadng Equipnent r o Bins, Silos, Stacks Copl right @ 1986 by Gulf Publishing Company, Houston, Texas. All righrs reserved. Printed in the United States of America. This b@k. or parts thereof, may not be reproduced in any form without p.rmission of the publisher. Llbiary ol Congress Calaloging-in-Publicalion Data Escoe. A. Keith. \lechanical design of process systems. l-ocludes bibliographies and indexes. Piping and pressure vessels-v. 2. Shell-and-tube Conr€Drs: v. bear exchangers; rotating equipment; bins, silos, stacks. l. l- Ch€mical I- TirleTPI55.5.E83 plants Design and construction. 1986 660.2 ', 81 85-22005 O.ATant -562-9 (v 1) 6aaa (}ET2l)1-565-3 (v. 2) lS€fl iv Contents Foreword ........vii by John J. McKetta Preface ..........ix Chapter 5 The Engineering Mechanics of Bins, Silos, and Stacks ........1 Silo and Bin Design, I Stack Design, 8 Vortex Shedding and Frequency Responsc. Ovaling. Helical Vortex Breaker Strakes. Bin Stiffener Design. Vcssel Supports. Example 5-2: High-Pressure Flare Stack Design, 20 Effective Diameters. Section Weights-Uncorroded weight. Required t Thickness. Anchor Bolt Design. Cantilever Vibration. Static Deflection. Dynamic Deflection. Anchor Bolt Torque. Design Nozzle Loadings. Pulsation Response Spectra Induced by Reciprocating Equipment, 62 Example 6-l: Horizontal Centrifugal Pump Sysrem Design, 65 Suction Line Pressure Drop. K-Values. Discharge Line Pressure Drop. The Effects of Liquid Viscosity on Centritugal Pumps. Summary. Example 5-3: Stack Vortex Strake Design, 27 Example 5-4: Natural Frequency of Ovaling Ring Formula (Michell Formula), 28 Notation,29 References, 29 Example 6-2: Positive Displacement Pump Design,74 Suction Line Pressure Drop. K-Values. A word About Priming. Example 6-3: Centrifugal Compressor Selection, 79 Example 6-4: Installing a Compressor at Elevation, 34 Selecting the Reciprocating Compressor. ......31 Pumps, 31 Centrifugal Pumps. Hydraulic Requirements of Centrifugal Pumps. Positive Displacement Pumps. Pressure Protection for Positive Displacement Pumps. Principles of Compression. Reversible Adiabatic (lsentropic) Compression. Polytropic Compression. Isothermal Compressron. Dimensionless Reference Numbers. Centrifugal Compressors. Reciprocating Compressors. \{ulriple Staging of Reciprocating Compressors. Cas Temperature for Reciprocating Compressors. Axial Flow Compressors. Specirying Compressor Flow Conditions. Mass Flow. Actual or lnlet Volumetric Flow. Standard Volumetric Flow. Properly Specifying Compressor Flow Conditions. Piping Systems for Rotating Equipment, 60 Example 5-l: Granule Bin Design for Roofing Plant, 11 Chapter 6 Rotating Equipment Compressors,43 Example 6-5: Naphtha Pump System Design, 86 Flow from Reservoir to Naphtha Storage Tank. Naphtha Pump Hydraulics. The Maximum Capacity Condition. Reevaluation of Reservoir Line. Notation,9T References, 97 Chapter 7 The Mechanical Design of Shell-and-Tube Heat Exchangers ...... 99 Appendix A Partial Volumes and Pressure Vessel Cafcufations Fundamentals of Shell-and-Tube Heat ....,177 Partial Volume ofa Cylinder, 177 Partial Volume of a Hemispherical Head, 177 Partial Volumes of Spherically Dished Heads, 178 Partial Volumes of Elliptical Heads, 179 Partial Torispherical Heads, 181 Internal Pressure ASME Formulations with Outside Dimensions, 183 Internal Pressure ASME Formulations with Inside Dimensions, 184 Exchangers,99 Design Classifications of Heat Exchangers. Fixed Tubesheet Shell-and-Tube Heat Exchangers. U-Tube Shell-and-Tube Heat Exchangers. Floating Head Shell-and-Tube Heat Exchangers. General TEMA Exchanger Classes-R, C, and B. Basic Components of Shell-and-Tube Heat Exchangers. TEMA Formulations. ASME TUbe Joint Load Criteria. Process Evaluation of Shell-and-Tirbe Exchangers, 115 Tube Wall Temperature and Caloric Temperaturc. Overall Heat Transfer Coefficient. Fouling of Inside and Ourside Tube Surfaces. Tube Film Coefficients. Appendix B National Wind Design Standards Tube Vibrations, 139 ......... 187 Criteria for Determining Wind Speed, 187 Wind Speed Relationships, 188 ANSI A58.1-1982 Wind Categories, 189 Plate-Fin Heat Exchangers, 147 Example 7-1: Regenerated Gas Exchanger Design, 148 Tube-Side Film Coefficient. Shell-Side Film Coefficient. Shell-Side Pressure Drop. Example 7-2: Vibration Check for Regenerated Gas Exchanger, 153 Example 7-3: Chlorine Superheater Design, 154 Appendix G Properties ot Pipe Tube-Side Film Coefficient. Shell-Side Film Coefficient. Shell-Sid€ Pressure Drop. TUbe Metal Temperature. . . ..... 193 Insulation Weight Factors, 200 Weights of Piping Materials, 201 Example 7-4: Asphalt Coating Mix Heater-A Non-Newtonian Fluid Application, 160 Tube-Side Film Coefficient. Shell-Side Film Coefficient. Shell-Side Pressure Drop. Appendix D Conversion Factors Example 7-5: Zero LMTD Exchanger, 165 Notation, 165 References, 166 Chapter 8 External Loadings on Shell Structures .... . Alphabetical Conversion Factors, 226 Synchronous Speeds, 233 Temperature Conversion, 234 Altitude and Atmospheric Pressures, 235 Pressure Conversion Chart, 236 169 Lifting Lug Design, 170 Example 8-1: Lifting Lug Design and Location, 170 Notation, 175 References, 176 vl .....225 t'oreword chanics and the engineering mechanics of piping (Volume 1). The chapter on heat transfer in vessels and piping illustrates lucidly the interrelationship between process and mechanical design. Every engineer working with industrial process systems will benefit from reading this The engineer who understands the impact of process design decisions on mechanical design details is in a position to save his client or his company a lot of money. That is because the test of any process design is in how cost-effectively it yields the desired product, and how "cost" generally translates to "equipment": How much will the process require? How long will it last? How much energy will it consume per unit of product? chaDter. Although the author has made a herculean effort in covering the mechanical design of pressure vessels, heat exchangers, rotating equipment, and bins, silos and stacks (Volume 2), it is true that there are omissions. It is hoped that, as the author hints in his preface, a future volume might be added covering multiphase flow, specific cogeneration processes, turbines, and detailed piping dynamics. Still, at this writing these two volumes comprise an outstanding practical reference for chemical and mechanical engineers and a detailed instructional manual In this two-volume work on Mechanical Design of A. K. Escoe has performed a monumental service for mechanical design engineers and chemical process engineers alike. The information is Process Systems, presented in such a manner that even the neophyte engineer can grasp its full value. The author has produced an in-depth review of the way in which process design specifications are interpreted into precise equipment designs. Perhaps most valuable of all are the extensiv e worked examples throvghout the text, of actual designs that have been successfully executed in the field. The piping system is the central nervous system of a fluid flow process, and the author has treated this with proper respect in two excellent chapters on fluid me- for students. I recommend these volumes highly for each design engineer's professional library. Joe C. vtl John J. McKexa, Ph.D. , PE. of Chemical Engineering Universitv of kxas, Austin Waher Professor Dedication To the memory of my beloved parents, Aub-ri:y tt. Es- coe and Odessa Davies Escoe; and to the dedicated enei- neer, Dr. Judith Arlene Resnik, U.S. astronaut aboid the ill-fated space shuttle Challenger (Flight 51-L). v||l Preface to Volume 2 of any accepted standard or code that may govern. It is felt that this book is a valuable supplement to any standard or code used. The book is slanted toward the practices of the ASME vessel and piping codes and the TEMA standard for shell-and-tube heat exchangers. The intent is not to be heavily prejudiced toward any standard, but to discuss the issue-engineering. If one feels that a certain stan- This book's purpose is to show how to apply mechanical engineering concepts to process system design. Process systems are common to a wide variety of industries including petrochemical processing, food processing and pharmaceuticals, power generation (including cogenera- tion), ship building, and the aerospace industry. The book is based on years of proven, successful practice, and almost all of the examples described are from process systems now in operation. dard or code should be mentioned. olease remember that lhere are olhe15 who may be using different standards and it is impossible to discuss all of them. While practicality is probably its key asset, this second volume contains a unique collection of valuable information, such as a practical approach to bin and silo design as well as practical methods of controlling wind vibrations of stacks using vortex strakes; new information on nozzle loadings on compressors and turbines; comprehensive discussions and examples on sizing pumps and compressors for various process applications; expanded tube count tables for shell-andtube heat exchangers; a practical approach to design against tube bundle vibration; and a comparative synopsis of the various national wind codes. Topics included in the text are considered to be those typically encountered in engineering practice. For reasons of time and space the dynamic analyses of seismic response spectra and an extensive discussion on pulsation response spectra in piping induced by acoustic pulsation are not discussed. However, a short discussion is given on pulsation response spectra induced by acoustic pulsations. Single-phase flow is much more common in mechanical systems than two-phase flow, so because of time and space two-phase flow is not discussed. This book is not intended to be a substitute or a replacement of any accepted code or slandard. The reader is strongly encouraged to consult and be knowledgeable The reader's academic level is assumed to be a bachelor of science degree in mechanical engineering, but engineers with bachelor of science degrees in civil, chemical, electrical, or other engineering disciplines should have little difficulty with the book, provided, of course, that they have received adequate academic training or expenence. Junior or senior undergraduate engineering students should find the book a useful introduction to the application of mechanical engineering to process systems. Professors should find the book a helpful reference (and a source for potential exam problems), as well as a practi- cal textbook for junior-, senior-, or graduate-level courses in the mechanical, civil, or chemical engineering fields. The book can also be used to supplement an introductory level textbook. The French philosopher Voltaire once said, "Common sense is not very common," and unfortunately, this is somelimes the case in engineering. Common sense is often the by-product of experience, and while both are essential to sound engineering practice, neither can be Iearned from books alone. It is one ofthis book's soals to tx unite these three elements of "book learning," common sense, and experience to give the novice a better grasp of engineering principles and procedures, and serve as a practical design reference for the veteran engineer. Finally, I wish to thank Dr. John J. McKetta, professor of chemical engineering at the University of Texas at Austin, who had many helpful comments, suggestions, and words of encouragement; other engineering faculty members at the University of Texas at Austin for their comments; Albert T. Taube, P.E., who was so kind to offer helpful and useful comments while reviewing Chapter 6; and John D. Guenther, P.E., for his helpfirl critique of Chapter 7. Last, but certainly not least, I wish to express gratitude to William J. Lowe and Timothy W. Calk of Gulf Publishing Company whose hard work and patience made this book possible. A. Keith Escoe, P.E. The Engineering Mechanics of Bins, Silos, and Stacks The engineering mechanics of bins and silos differ from the mechanics of oressure vessels because solids behave differently from liquids and gases, both in storage and in flow conditions. The mechanics of stacks are almost identical to those of towers, but are somewhat simpler. An engineer has more fiexibility and approaches for solving vortex shedding around stacks than around towers, because stacks rarely have as many attached structures. 4. Dead storage-residual build-up of solids caused by the inability to exit bin. Segregation-a heterogenous solid of varying specific gravity in which the lighter particles exit the bin first, leaving behind the heavier particles. Degradation-the chemical change of solids caused by remaining in storge too long. Spoilage, caking, and oxidation are some examples. 5. 6. Solids behave differently from gases or liquids because they can transfer shear stresses without movement, SILO AND BIN DESIGN The mechanics of solid flow theory is a fairly complicated subject. The proper design of silos and bins is more than meets the untrained eye, and involves every aspect of engineering mechanics. This chapter only " sketches" methods of approaching this complex phenomenon, and refers the interested reader to literature on this specialty. The field of solids handling has been augmented the past twenty years by two researchers-Jenike and Johanson [1]. The methods presented in this chapter are largely influenced by their work. Bins and silos appear to be very simple devices, but what goes on inside is not so simple. To design an efficient bin the design engineer must understand why solids in bins do not flow (Figure 5-1): 1. Development of a rathole or stable arch that ceases flow. 2. Erratic flow-transient arches form within the solid resulting in variance of the bulk density such that flow becomes unstable. 3. Fiushing-the fluidization and flushing of powders creates erratic flow. and because of their cohesive strength, they can retain their shape under load. The shear stress transferred between the solid and the channel walls is a function of the normal pressure, w. The relationship between the two is as follows: 1t - tdttrg where {' : p: S -- w (5-l) kinematic angle of friction between the solid and the bin wall coefficient of friction between the bulk solid and the bin wall Typical values of @' are given in Table 5-1 for various solids and bin materials. This table can be used in applications where the bulk solid properties are not known (as is commonly the case). The value of @'is required by the methods presented to be a constant value so that using the table will produce a conservative design. There are two flow conditions that can occur-mass flow and funnel flow. Mass flow is a flow Dattern in which all the material in the hopper or bin is ln motion flow occurs along the bin walls. Funnel flow is a flow pattern in which the material flows primarily in the center resion of the bin. and the Mechanical Design of Process Systems NO NO FLOW FLOW FUNNEL FLOW :\ ):^.-,r. .. 1:' ,i :fr,f;:,,*::',.d r'" RATHOLE OR li"li:'.;:,.,i PIPE OEAO STORAGE Lqilii I I I -l t.-. t,; t.|..: ARCH OR DOME Funnel Flow Charactedstics 1. Material segrEgates and ratholes may be formed. 2. Flow may be erratic. 3. Low headroom. 4. Powders willflush. Figure 5-1A. Problems of flow of solids. Table 5-1 Properties of the Materiats Used in the Stacking-Out Bins [11 9r Hopper Material Iron ore Rec. 39 33 39 33 63 47 63 47 46 40 46 40 * concentrate (H2O, 1.5%) Iron ore (H2O, r0.0%) Cir.*+ Rec. Cir. Dolomite- Rec. Michigan (H2O,4.2%) Cir. Dolomite- Rec. (Moller) (H2O,8.2Va) Cir. + Rectangular opening, 4 *+ Circular openinq, 4 ft by 2.5 diam. ft. 55 lo 55 39 tb/tt3 23 190 23 25 190 141 tbfil2 585 T, fi sec calculated, lb/sec 1.25 5.50 5.7 16,7N 467 1.25 343 4.65 1.50 5.7 9.5 18,200 0.97 8,450 25 25 l4l 395 r.05 t0s 1.50 286 v.f 9,250 1.14 3.20 8.1 8,150 25 1A 105 100 229 263 t.t4 2.80 1.05 t .70 8.1 11.9 6,220 26 100 2r0 1.05 1.60 11.9 6,660 8,600 The Engineering Mechanics of Bins. Silos and Stacks arch lhickness, T Figure 5-2. Formatjon of an arch. FR€E SIJifACE srREss {q) sTiEss (L) sti€ss t laLl) CALCUIATEO S-IRESS Mass flow characteristics I 1. Material segregation problems are minimized 2. Fine Dowders deaerate 3. Material flows unilormly 4. Smooth steep hopper IALL ) Figure 5-18. Ideal flow of solids-mass flow. Figure 5-3. Stress distributions along hopper wall [1]. The strength of the solid material is the criterion for flow behavior in bins. Failure conditions ofthe solid oarticles can result in arching. no flow. piping (a hole formed in the solid formation), or limited flow Figure per wall. When the hopper angle is less than 30', the limits of radial stresses will occur in conical hoppers, as shown in Figure 5-4. Even though the hopper opening is large enough to prevent arching, mass flow piping will occur. The critical diameter at which the pipe is unstable is given by the followine: 5-2 illustrates an arch formed by a solid in a hopper. The failure of the arch will occur when the major compressive stress, R equals the unconfined yield strength, fc. lii) prevent arching, the critical dimension, B, ofthe hopper opemng must De _flJ> ' 7(1 where + m: m: ? : m) D> 4\+ ^l (5-3) (5-2) 0 for slot opening of width B 1 for circular opening of diameter B bulk density of the solid, lb/ft3 The calculated stress and radial stresses are shown in Figure 5-3. When the stresses induced between the solid particles and the hopper wall are not compatible with radial stress, a flow pattern will not develop along the hop- Figure 5-5 shows a plot ofthe piping factor, O, against the angle of internal friction, f. The limiting relations for arching and piping in Equations 5-2 and 5-3 are functions of the material yield strength, f". This parameter can be determined empirically only if the consolidating pressure ol for steady flow is known. This pressure is denoted bv or : IBQ (54) Mechanical Desisn of Process Svstems z.^ E = -to Figure 5-4. The criteria for flow when 0' < 30". o(1 where Q = d: o= + sin 6) 2sin0 mass (s-5) angle of hopper slope computed stress function along the wall Combining Equations 5-2 and 5-5 we obtain 1> t" (r + where o1lf" -)e : (s-6) flow factor of solid The critical flow factor for arching in channels represented by n: : (?J".-*, (ff) is 'e_ (1 + m)Q (s-'t) F o z Figures 5-6-5-9 show the values of ff for straightwalled converging bins with various material properties and wall slopes. These factors are presented as straight lines in the f" vs. o1 graph in Figure 5-10. The consolidating pr€SSUre 01 that the flowing solid particles exert in a vertical cylindrical channel is ot = D"yG I 30 30 40 50 60 70 ANGLE OF Ii{TERNAL FRICTON IDEGREESI,Q Figure 5-5. Piping factor, iD, versus angle of internal friction, (5-8) 6. The Engineering Mechanics of Bins, Silos and Stacks EFFECIIVE AI{GLE OF Ti|cNOfl 2O3.6070 IOEGf,EESI, E.rECrrE 6 Figure 5-6. Wall friction angle, @', versus effective angle of friction,6. ^*GLE OF FitcT|Ox roEci€Est,6 Figure 5-7. Wall friction angle, friction,0. {', versus effective angle d', versus effective angle 5 6ro EFFECTTVE AXCTE Figure 5-8. Wall friction angle, friction,6. d', versus effective angle of Of FFICTION,6 Figure 5-9. Wall friction angle, friction, d. Mechanical Design of Process Systems of the flow of solid particles. This pressure is reduced internally somewhat because as the solid particles de- I scend through the hopper, a vacuum in the void between particles develops and produces a negative gauge pressure. As the particles approach the outlet, atmospheric pressure is obtained. While the wall pressure is maximum at the bin-hopper tangent line in mass flow, it is only a fraction of a hydrostatic pressure for a liquid head equivalent to the height ofthe solid in the bin. Thus, designing solid bins for hydrostatic loads results in overdesign of the bins. As a guideline, the maximum hoop pressure at the bin-hopper tangent point is about seven times that of the pressure of the solid induced by gravity. That is, t(, = lrl E (',I F CR ot JI lrJ >l ITICAL STREI{GTH RoP(e$i{L I o trj . lrl <= ori l! = -o () F .I' -t! taE ()C z, --------)coNsoLroaTr G PRESSURE, = l6 P*:7{'y)*{H)ft q Figure 5-10. Critical values of or and f". Line A represents strength properties and Line B the constant flow factor [1]. where G is a function of the effective angle of friction, 6, and the internal angle of friction, {. This consolidating pressure, o1, provides the strength of the material that forms the pipe in the bin. Combining Equation 5-3 with 5-8 we have (+) \r./ " where "y H : : (5- 10) bulk density of the solid, lb/ft3 height that solid is stored in bin, Table 5-2 Critical Hopper Dimensions tor Material With Flow Properties Shown in Figure 5-12 [11 Critical width ot a slot opening o*o .,,,:(,1)",.""=o*o ft lor arching, ft (5-e) The value of ff is plotted against 6 and { in Figure )-l l. Figure 5-12 shows flow properties of a typical bulk solid, which are quite useful in problem solutions. Thble 5-2 lists critical hopper dimensions for the material with flow properties given in Figure 5-12. Once the problems of arching and piping are solved and the bin is designed to handle the solid mixture, the next step is to examine flow pressures induced by solid particle flow. As mentioned previously, solid particles suspended in vertical storage bins do not behave linearly, such as liquids. To a much greater extent than liquids, solids manifest shear forces between particles and on bin walls. Figure 5-13 shows typical pressure distributions for mass flow and funnel flow, and illustrates how in mass flow the pressure is maximum at the bin-hopper junction poilt. The geometric discontinuity causes an increase in flow pressure because of change in momentum Type Flat bottom or nonmass flow Freshly stored Stored for 24 hr bins 0.2 1.0 Stainless lined hopper 0* o.4 0,* 0.6 (d, = 30", 6"= 21.t Mild steel hopper (0' :3o" a' :3s") Critical diameter of a circular opening for arching, ft Flat bottom or nonmass flow Stainless lined conical hopper 0* 2.0 0.9 Mild steel conical hopper (0' : 15", d' : 35') 0.4* * 2.O** 0.4 bins (0' : 1s",0' :27") Critical dimensions 5.6 bins 7.7 + Dictated only by porticle size or dynamic conditions. +* mese ralues are the same as the flat botrom bin values because the 6' = 35" is too rough to proride of the cone when 0' : 15" steel conical hopper when walls mid flor"'along the The Engineering Mechanics of Bins, Silos and Stacks The internal pressure in Equation 5-10 can be inby the use of pneumatic air supplied to the bin. In the case of bins where funnel flow exists or for small bins with cohesive solids, supplying forced air through ducts in the bin is desirable to prevent the formation of arches and pipes within the solid itself. To compensate for the additional internal pressure, Equation 5-9 be- crease.d 60 comes e, z E P.,":77H+Pu; t40 where P";.: (s-1r ) air pressure, psig = o The use of pneumatic air in bins is often desirable and o-z in the situations where air cannot be used because of chemical interaction with the solids in a closed svstem. nitrogen is commonly used. 40 50 60 ANGLE OF FRICTION (OEGREES),6 Figure 5-11. Critical flow factor for piping. Hlso (! 6' ? 3 1oo Figure 5.12. Typical bulk solid flow properties used to determine critical dimensions for piping and arching. coNsoltDAT|NG PRESSUAE, q, Lb/Fr2 Mechanical Desisn of Process Svstems q, PSI + 0 Psl bin fu _ FUNNEL FLOW bin haf tu - F I Figure 5-13. (A) Pressure distribution for solid flow is maximum at cylinder-cone intersection primarily because of discontinuity stresses; @) The relationship between mass flow and funnel flow for conical sections. The angle of kinematic friction, d', is a function of the coefficient of friction between the solid and bin material and the compression the solid is subjected to in storage. In stacks, lining is often used where high temperatures STACK DESIGN The analyses of stacks subjected to wind and seismic response spectra are identical to those methods used for process towers discussed in Chapter 4. The differences in the two types of equipment are twofold: (1) stacks have different values for logarithmic decrement and dynamic magnification factor, and (2) the solution to problems induced by vortex shedding are different. Both of these factors are a result of stacks having simpler geometrres. The simpler geometry of the stack works for and against the engineer. The positive aspect comes as a result of the methods used to break vortex shedding-vortex breakers are much easier and more practical to install on stacks than on process towers. The negative aspect of stacks is that they do not have connected piping and structures to break up vortices and to damp wind-induced vibrations. Thus, we will focus our discussion on those aspects of wind design that are peculiar to stacks, remembering that the fundamental basis of design is the same for stacks and towers. Vorter Sheddlng and Frequency Response As explained in Chapter 4, only the fundamental mode of vibration is considered for process towers and stacks. Consequently, the Rayleigh method is applied to obtain the vibration characteristics of the stack. are encountered and carbon structural steel is the stack material. Lining must be used for temperatures in excess of 800 " F because of the danger of carbon precipitation in the steel. To avoid this and not use lining, one must use hot-rolled, high-strength low-alloy steels that have good elevated-temperature properties. Such steels are not generally pressure vessel quality and require heat treatment, such as the Cr-Mo steels described in ASTM specifications A-387 and A-542. These low-alloy steels are of structural quality, contain 0.75-1.257o chromium, and are cheaper than pressure-vessel-quality alloys. When common carbon structural steel is to be used with lining, the effect of gunite lining must be considered with the mass and stiffness to accurately determine the fundamental frequency of the stack. An approximate value of the modulus elasticity of gunite is 1.3 x 10opsi. The effect of lining in a stack must also be considered with the flexibility of the base. Table 5-3 is a list of conservative values of the logarithmic decrement and dynamic magnification factors for various soil conditions for lined and unlined stacks. For explanation and use of these values the reader is referred to Chapter 4. Ovaling When slender stacks, i.e., rings in which the thickness is small in comparison to the radius, are subjected to vortex shedding caused by air currents, the elastic strain en- The Engineering Mechanics of Bins, Silos and ergy of the cylinder is distributed in such a manner as to induce flexural and torsional modes of vibration. The ring is subjected to the following modes: 1. Extensional (axial elongation and contraction about the ring's own axis). 2. Torsional (twisting of the ring about its own axis). 3. In-plane flexural (inextensional vibrations in the 4. plane of the ring). Out-of-plane flexural (inextensional displacements in the plane of the ring). The flexural modes are generally the only modes of practical significance since the fundamental natural frequencies of the torsional and extensional modes are much greater than the fundamental natural frequencies of the flexural modes. Figure 5- l4 shows these various modes. Stacks 9 These relationships were formulated by the great pioneers Michell and Love during the nineteenth century. The reader is referred to Example 5-4 for further clarifi- cation of units. In practical stack design, because vortices form alternately on either side of the stack, the flexural frequency (ovaling frequency) given in Equation 5-13 is taken to be twice that of the vortex shedding frequency. The vortex shedding frequency is given by Equation 4-101 as -'D 0.2v (4-l0l) Now since f ,, :2f, we solve for V and obtain 60f,D (s-14) The flexural modes, in-plane and out-of-plane, are used in determining the resonance frequency of the stack caused by ovaling. Since out-of-plane flexural vibrations in which are coupled to torsional vibrations, it is the out-of-plane frequency used ro describe the vibration of the siack; however, the natural frequencies of the flexure modes in and out of the plane of the ring vary only slightly for circular cross sections. The natural frequency of the ring is critical wind velocity in which ovaling occurs. Both the vortex shedding and flexural frequencies should be evaluated at each elevation if ovaling rings are to be used. Norrnally, rhe upper third of the stack is all that is required to be investigated, based on various wind siven as , -_ I I Etn2(n2 - l), lo5 " t tpAr6t+ I + /t (s-12) The lowest flexural mode exists when n tion 5-12 reduces to " : 2 and Eoua- 4.4O9t E (5- f' l3) s: the Strouhal number (is equal to 0.2 for a wide range of Reynolds numbers). The value of V. is the tunnel tests. Now we come to the most practical aspect of stack design-how to alleviate flexural excitation. This can be done in two ways-ovaling rings or vortex strakes. Ovaling rings are used to increase the mass distributed along the tower to dampen flexural vibrations. When the flexural frequency equals twice the vortex shedding frequency, i.e., if the design wind speed range includes the critical wind velocity, V", stiffeners are added at those sections where f = 2f. The section modulus ofthe stiff- eners is given by s - (7 where V" : : o, : l): j-r H, i, t n=2 Figure 5-14. Stack mode shapes. (s-15) ,"r"0 velocity (Equation 5-14), fpm D = "rnr"u, internal stack !l \ n=l x l0 )v:DrH, investigation, diameter at elevation under ft stiffening ring spacing, ft allowable tensile stress of stack material. DSi Ovaling rings provide a redistribution of the mass of the stack, resulting in localized stiffening that tends to offset flexural frequency modes. This is particularly desirable with stacks of several diameters. However, with stacks of constant or tapering cross section the use of vortex strakes is becoming increasingly popular. 10 Mechanical Design of Process Systems Helical Vortex B?eaker Strakes a stack. The helix angle, {, should fall into the following range: For critical wind velocities less than 35 mph, dynamic stresses should be investigated. One optimum solution for such stresses in stacks has been found in wind tunnel tests and in practice to be helical vortex strakes. The application of helical vortex strakes to vertical cylindrical towers has shown remarkable results. The strakes' function is to break up vortices such that flexural frequency modes are quickly dampened. It is significant to note that adding the strakes increases drag and thus wind loading. These strakes are shown in Figure )-l). To minimize the flow-induced drag and optimize the vortex-breaking effect, the strake height, W(ft), should be in the following range: D: There are always three strakes per stack to counter the of vortices on either side of the stack. Strakes can be fabricated from a flat piece of metal, normally 3/ro-in. or 5 mm thick. Each strake is divided up into a certain number of strips, usually five to twenty alternate formation segments, depending on the length of the stack. The overall length of the individual strakes that is divided up is determined by (5-16) S:[(?rD)2+L2]oj where D = OD of stack, ft L height of tower portion straked (V: of total stack 0.09D<w<0.10D where 54'<d<58" : height), OD of stack, ft Figure 5-15 shows a helix generated on a cylinder by taking a template z'D long by L high and wrapping it around a cylinder. The length, L, of the helix is the top l/3 of the stack. Wind tunnel tests have shown that vortex breaking devices are most effective on the upper third of The number ft "S" is divided into individual strips that are cut from a larger piece of plate shown in Figure 5-16. The strips must be cut to a radius of curvatue, r, that is determined as follows: +8 a2a2 (5-17) aa2 . D- wherea: --, lt z ,L 0.090s W<0.1D d= 54o Helix angle 2rw <C358' r,r : number of revolutions around stack cylinder made by helical strake (usually <o : 1) An alternative formula, developed by Dr. Frank Morgan, and two to three percent in error of Equation 5-17, IS XW (s-18) 1-)\ \rhefe A T L I |-,D Figure 5-15. Cylindrical strake helix geometry. S, interior arc Iensth of helix = _ : ------:--------: S" exterior arc length of helix (5-le) The value Si is determined by using the outside diameter of the stack in Equation 5-15, and S" is obtained by using D * 2W in place of D in the same equation. For the most accurate results, Equation 5-16 should be used, as it is the exact radius of curvature of a helix projected on a cylinder [3]. The Engineering Mechanics of Bins, Silos and Strips are laid out, as shown in Figure 5-16, with an inner radius of curvature determined bv Eouation 5-17 and outer radius of curvature of r : r + W. it is desired that the helix be perpendicular to the centerline of the cylinder along the entire length of the helical strake shown in Figure 5-15. To obtain this each metal strip is placed in a rig shown in Figure 5-17. The rig is composed of two clamps, each 45' from the plane perpendicular to the table, or 90" offset from each othe;. O;ce the metal strip is clamped-in, a hot torch is run up and down the length of the metal strip hot-forming it to the shape formed by the clamps. The strip should not be heated any longer than necessary to hot-form. The metal strips should be the same material as the stack. The effectiveness ofthe system is not impaired by a gap of 0.005D between the helical strake and cylinder. This method leads to ease and quickness in fabricating helical vortex strakes. EXAMPLE 5.1: GRANULE BtN DEStcN FOR ROOFING PLANT Figure 5-16. Strake fabrication detail. 1t As seen in Figure 5-13b, the minimum hopper angle for mass flow is 0 :37.74'1" From Figure 5-4, 6' From Figure 5-5, <D : l0 = 0, which implies that we will not have piping forrning in the bin 6=70' For a circular opening, m = 1 s'(l + sin 6) ^ (5-5) zslnd From Figure 5-6, ff : 1.6 ff=(l+m)Q Q: or Twelve granule bins are to be designed to provide granules for the manufacture of roofing shingles of Example 3-6. Each bin is to contain 10.02 tons of sranules. yielding 120.24 lons rolal capacity for all twe'ive bins. The client desires to use an existins steel frame that limits the bin to a rectangular shapJwith an off-centered opening as shown in Figure 5-18. From this figure we consider the first criterion in bin design-to satisfu flow conditions such that the granules wili move. Stacks : 1= : o1 : B =). = (s-7) 0.80 7BQ 90 lb/ft3 0.667 ft (90)(0.667)(0.80) : 43.6, tbrtU From Figure 5-12, f" : s0 lb/fC Figure 5-17. Clamping each strip on 45 degree offsets and hot forming with torch obtains desired geometry. Mechanical Design of Process Systems 12 l--j*---l E ,.T ;l t;;lr\l tl \ 1 /\ I Figure 5-18. Granule bin silo. : In this problem, a 12.625 ft and b = 4.00 pressure at the bottom of the plate is Thus, the critical arching dimension is B= r(l f{o ' + m) Since 0.278 the bin -' (90X2) :0.278 (5-2) ft ft < 0.667 ft = 8 in. archins will not form sure distribution exerted on the bin walls is taken to be a simple hydrostatic load. The bin walls are fixed on three ends and free on the top edge. The solution for the maxi- mum stress is given by uno F : orPb at x = 0, z : a b 0 : t : 4.000 12.625 *r :0.030 Vz = 0.032 The maximum stress occurs at the bottom side at z:0 (5-21) : 12.625 ft: plate thickness, in. x= 0 and /<.)n\ 151.50 in. For 5.4-516 Gr. 55, o4 : 13,700 psi. Solving for t in Equation 5-20 we have r: /v,pu'\o' l__-l reaction force exerted on the plate edge normal to the plate surface, lb/in. load per unit area, psi p,r (5-20) where Vr, V2, 01, and 02 are in Figure 5-19 P z,ur _ _ vrPb2 *1!o' unoF orPbatx +a.z b = = = = ' ifu > borz:0.4bif a'( b : (n.6zs)ttffi : From Figure 5-19 we obtain the following: b F eo* The in After flow criteria have been met, we proceed to the structural design of the bin. The allowable stress used in the case of bin design is the ASME allowable, since the granule weight forms a pressure distribution, thus making the bin walls pressurized components. For simplicity and ease in calculations, the solid pres- : v{bt : P ft. 1:l ko.o:o)(z.ssr) I .\ tn' r:,eoo (rsr.sofin.'lo, --lb- | I :0.627 in. The Engineering Mechanics of Bins, Silos and Stacks The stress at mid-plane is "" z , : b a t2 : , 12.625 4.O At x = 0, z :b = 12.625 ft 4.734 psi _ lro.orzlr+.rl+rr rs r. sor'lo ' = 0.502 in. Selecting SA-516 Gr. 70, . Deflections of bin plate" v,Pb2 0.4b, P _ [ro.o:otr z. 13 oat: ae1)fl51.50),lo I (0.00020)(7.891) ',Jb- 1+t.oy in., Dlb ln. 17,500 5 -- 0.557 in. at bottom edge _lto.ozzx+.tt+xrsr.sor,lo' _= 0.446 in. ar z = 5.050 fr D : flexural rigidity of plate Et3 12(1 - v'?) o 16 I Figure 5-19. Rectangular flat plate solutions. 14 D Mechanical Design of Process Systems (30.0 > 12(1 106x0.562)r - 0.311 :48: .b49.25J in which, w :7.4565 x 10-o in. Bin Stilfener Design To reduce bin plate thickness, stiffeners can be used with thinner plate. A thinner bin plate makes fabrication simpler because a thinner plate is easier to weld and is cheaper. With stiffeners, each enclosed area is analyzed as a flat plate with three edges fixed and one edge simply -b = Atx = u,z t supported. The stress in the plate is given by the following: (0.004x7.891)(48.0), w_ ob Ph2 = 't,'l:-: and ^Ph2 : *,5o' and F t- 481 ,649.253 w= 1.4913 x Itr l0-1 in. For a e/ro-in. plate deflections are negligible and no stiffeners are required for this plate thickness. " F- QrPb at x = 0. z = 0 - 02Pb ur * : tJ. z'0.4b \5-22) (5-23) where V1, V2, 01, and 02 are shown in Figure 5-20 .09 .o8 .o7 .05 .o4 Figure 5-20. Rectangular flat plate solutions. The Engineering Mechanics of Bins, Silos and Stacks : P: t: F reaction force exerted on the plate edge normal to the plate surface, lb/in. load per unit area, psi plate thickness, in. rhI P = 90--l f 2.625 fcl : :8.0 ft, a/b : 0.50. From Figure 5-20 we obtain Vr = 0.064. Thus, from Equation 5-22 we have _ :_ o.", (0.064x 7.891)(96)2 _ 11 r (0140 = JJ.009.228 psi > al)owable Consider b : 4.0 ft, a/b = 1.0. From Figure 5-20 we have i{'' : 0.192 and from Equation 5-22, o^, : 24,756.921 psi > allowable : Similarly, considering b o-"- : 11,475.865 psi < 2.0 ft, : 17,364.2?9 psi - 3.5O) -(rq) 4.036 psi allowable = < 5-21 hold, using Figure 5-18. By iteration we obtain : 6.458 ft, P - 4.036 psi, a/b = 0.619, Vr :0.091 o^":15,643 psi o 17,500 psi b and Since the maximum stress is less than the allowable for the top portion, no third stiffener is required. First Stiffener Design a = 4 ft-o in.: b : 2 ft-8 in. a/b:#:t.roo 17,500 psi ofb : By a process of iteration we obtain a value in., in which o^, (2.667 The top portion ofthe bin is now a plate with three sides fixed and the top edge free. Thus, Equations 5-20 and First Stiffener Consider b - 15 /'-TR 2 ft lt Pt 8 | | I I l. tco fi l' ,H1 17,500 psi allowable /r )ll \q--7891 psi | Thus, we place the first stiffener 2 ft 8 in. above the bottom seam, 'Yr = 0.383 v ffi UV u, Second Stiffener At 2 ft 8 in. the maximum pressure exerted on the bin wall is rh P - e0; / rf': 2.62s - 2.667\ ft ln;-l Consider b = 4.0 ft. a/b : \ = 1.0 in which Vr 6.224 psi : 0.192 from Figure 5-19. Thus, o-", ='o'n',)lu:?.',!'08)2 (0. 141) : I STIFFENER 19.s26.e psi > R : .yrpb : (.383)(7.891X32.0) :96.712lbhn. : w 17.500 psi By a process of iteration we arrive at b = 3 which o-"" : 17,502 psi ft I in. in Third Stiffener At the new elevation, 6.167 ft above the bottom seam, we obtain the maximum pressure exerted on the wall. With plate pushing uniformly on stiffener, the latter will be analyzed as a fixed end beam with uniform loading. 96.712 lb/in 16 Mechanical Design of Process Systems w/ w: : (96.712X48) (4'92 - M-^. M - ^-; W=wf 24 M.*: 4,642.18 tb 181x48 0) 24 : = 9.284.36r in.-rb , _- (8,532.384) in.Jb (0.54) in. _ ., ".,, ,l?soo rbfinj 773.697 ft-Ib rtun I For design purposes select a design stress of o : 0.37 in.a t/+-in. thick, (9,284.361) inlb(.49) in. : 17,000 lb/in.'? .zr :0.39 = P -'yD From data provided by the client, P = 400 lb/ft'z tion point. Using a factor of 7 we have 0.268 in.a at junc- P = 7(a00) = 2,800 lb/ft2 in.a Therefore, 3-in. x 2-in. x t/+-in. 4 is sufficient Stiffener at Junction Point ot Bin Hoop Force x2-h. a o 17,000 psi. I:M"g I of : Therefore, Ztlz-in. x 2-in. With a factor of safety of 2. This would give a yield stress of 34,000 psi, which is conservative. Select a 3-in. x z-in. x tl4-in. 4 Select a 2rl2-in. I ' 'ol Rs1?.3E4in.-rb A-","". = '266 '1921(48 I:M"q Mc , @ >< tla-in. 4 is sufficient P : 2,800 rb/rt (r-lq) = re.zt44 psi UseP = 20 psi For bottom plate, a:4 ft-0 in.: : 0'383 R : (0.383X20.0X32.0) b:2 ft-8 in., a/b = 1.500 rr = 245. r20 lbl in. w, w = (245.t20X48.0) M.*: =-: 1.+ Second Stiffener Design M _ ( I 1.765.760X48) : A_.-'-- P = 6.224 psi a: 4ft-}in.;b : 3 tt-6 By linear interpolation, 1t R: pr-". = in.; a/b =!:3.5 : 4 slj.520 injb t.t+l 88.879 lb/in. {: w = (88.879) lb/in.(4E.0) rn. : 11.765.760 Ib Select a 3rl2 in. x 3 in. x tla in. 4 :9.349 (0.340)(6.224) lbl\n.2(42.0) in. w 1"t = ,266 .192 lb I.in : (23,531.520X0.79) _ 1.094 in.a 17,000 I = 1.3 in.a for section Therefore, 3rlz-in. x 3-in. long side facing bin x r/+-in. r is sufficient with The Engineering Mechanics of Bins, Silos and Stacks Bottom Portion of Bin 0. | 825(6.31 3X50.928)' - Bottom portion of bin will be approximated with four tdangular plates welded together, as shown in Figure 5-18. '-'----''' (0.438)2 Therefore, use 716 in. f, for bottom plates Bending Stress in Bottom Portion *ll11 ->l Ptt I ll-tl ll --'l' Y Pr = 7.891 lb/in.2 pz : e0 lb/n3(16.50 ft) : J [-]q144 10.313 psi --tt t La- t-ll It- At an angle ot90o-0:37.7474, P: 10.313 sin 37 .747" = 6.313 psi CROSS SECTION CUT AT MIDPLANE OF TEIANGLE By linear interpolation, B' :9.3659 o:412 o= It; -il rJ 1$ -_tt =o.rszs 0.1825Pa'z ,, qan , P = 6.313 psi on triangular plate m.l8r5x6.rl3x5o.%y - \l 17.s00 = u.4rJ rn. A with t:3/E in., ,'" -_ 0.1825(6.113)(50.928), (0it5,- : 21249.532 38,000 : : - area of triangte = Ia'20'lro.z*> = \21 : 1,497 .589 in.2 = F : (6.3 13) lb/in.,(I,497.589) in.2 : at3 : (4.244)(12)13 : 16.916 in. M, : F(a/3) : 160,495.84 in.-lb s?? nci YJ' -= ,t '''-",4q -J- : 38,000 psi 55.92% of minimum yield Mc % yield, : with rhe in. 21249.532 70,000 f, , : t0.40 ftj ot A For SA-516 Gr. 70, minimum yield % yreld From previous information, = l/,JWPSl 30.36% of ultimate yield I thJ r/{O Otl\3 r:-=-:[,007.49Er l,/. Iz 9,454.279 lb 17 Mechanical Design of Process Systems 18 ,^ 50.928 atJ:_=lD.y/orn. For three horizontal plates, 3 ( 160,495.84)(16.976). o"u (1r,007.498X : (r2.62s itx8.0 rt1 = '2 17,500 psi 1!30-1f - z,3ts.22JIb or for three plates, ,_ ' - (160.495.84) in.-lb (16.976r (r 1,00?/98xr?J00) Therefore, tlrc in. t_ in. _ .,.,,,, i"rlb/i"r - " "'-' m. wt : 6,945.669 lb is sufficient. i:\\:-j Vessel Supports Consider all trusses as pin connected. Side Truss For simplicity and to keep things conservative, let us analyze the internal plate to determine if we need any supports on inside of structure. weighr of internal load w rblfr t: 3/8 : (t20.24) lz'z+o v\ 'on'I ,on / : 269,337 .60 tb End Truss For two outside plates, in.; wt : (12.625)(8.0)(0.375)(1,14)(.283) wto'.r : : 1,543.482 Ib 3,086.964 lb For two side plates, Wtt"d ftXt) : (1s 1.s0)(192)(0.s63) wt: : = 6,173.9r, tO For each bin, 16,362.0 in.3 ro*r 2(3,086.964) Under Bins-4 Triangular Plates Weight of steel (Wt): (12.625 ftx16.0 : A 0.283 lb/in.3 (16,362.0)(0.283) : 4,630.446 tb /a qor \ - 4 l- '"'l A.244\tt44\ wt of \21 each bin - = 5.990.355 in.1 of metal (5.990.355)(.283) = 1.695.270 lb The Engineering Mechanics of Bins. Silos and Number of Bins : as continuous beams in the longitudinal and lateral direc- : 13,562.164 lb Empty weight of structure : : = Wt of granules Total wt loaded w - : wL: lzsss.+rglli [+.olrt : so,g73.ozo ro lt: : 4 4.0 ft RA : : Ro : 911,210.313 lb/in. rur Y, w . (9 .210.313r lb E in. : 174,952,380.1 lb (174952'380 1)(192) 8" : 0.393 wt = RB: Ll43 wf: 303'739 771 .. 75.934.r93 lb/rt 4.0 Rc Considering the plate in Figure 5-18, M- FoR EACH spAN 303,'736.7711b Total number of internal plates Total length tions. 4,630.446 lb + 6,945.669 lb + 3,086.964 lb + 6,173.928 lb + 13,562.164 tb 34 ,399 .r7 | Ib 269,337 .60 : 19 The frame structure shown in Fieure 5-18 is analvzed 8 Therefore, Wtrorur Sacks 1. 143(30,373 .676) = 11,936.3tt ,O = 34,117.rt b : 0.928(30,373.676) : wf: 1.143(30,373.676) :34,717.rt 0.928 wf 1.143 0.393(30,373.676) 28,186.77t tb rO Solr ing for reacrion\ in lateral plate 92.1 ,n. FOR EACH SPAN WL= 30.373.676 lb = 4 rqx x\7 r)l,n -rh Therefore, bin must have internal supports under botaom. Number of vertical supports =9=R: = Number of ioint suDDorts F tol 716 ?71 : --"' _-:j____: : IJ 303 33,748.530 tb : 9 tl 20,249.118 lb '73-6'771 9 v.* : V-* : 0.607(30,373.676) tb 18,436.821 lb RB =;6 (10.373.676X2) = 37,967.0q5 Ra = ft. = lb 11,390.129 lb Design each support column for 37,967.095Ib srde saructure = 38,000 lb The bin structural detail is shown in Figure 5-21. 20 Mechanical Design of Process Systems BIN JUNCTURE DEIAIL STIFFENER DETAIL Figuie 5-21. Bin struclural frame detail. EXAIIPLE 5-2: HIGH.PBESSURE FLARE STACK DESIGN Add 12 in. for platforms and 12 in. for ladders. A high-pressure flare stack shown in Figure 5-22 is to be designed and construcred to the following specificatrons: Base diameter : l0 ft Height from bottom of steel base to tip of flare stack ft Gas pressure in stack = 2 psig Gas temperature = 100oF Design wind velocity = 100 mph Maximum gas flow rate 300 MMscfd Earthquake design : : World Mercali 6-7 Effectlve Diameters : 200 Add 4-2-in. d lines. 2-in. g dia. line D : (3.375X4) D"^""., : DB : Dc : De : : + 2.3'75 in.-Add : = 2(12) 42 + 37.50 : 79.50 in. 90 + 37.50 = 127.50 in. 120 + t/z 13.50 in. 13.50 37.50 : 37.50 in. 157.50 in. in. insulation The Engineering Mechanics of Bins, Silos and Stack Height (fD Wind Pressure P, (rb/ftr) w = B x De x Wind Load Pz (5,270.98X110.5 26 : to6)(!f)tz6):20415 30-40 33 : ro.olffit:3):25e.88 40-74 38 : toor(lle)o 74-76.5 44 : too(l#J(44):34650 '16.5-125 44 : 0-30 125 48 : 28o.so = t0.6tl'-'""1t48t = \ 12 / 306.00 159-t74 r: so\ : ro.orfifJt+t): 48 866.25 + 2.5) + x (90.0 + (13,604.25)(24.2s + 2.5) + (2,862.0) (10,404.0)(65.5 + 2.5) + 2.5) :2ee.2s ,0.u,(]?Za)r*) /r 159 Moment lb/tt reo.8o 51 PSF 174-200 : 51 <o.orit#)or) = 202.'73 48 Wind Load 159 PSF Moment s.270.98 (s,270.98)(13.0 + l5 .0) + (2, 862.00) 2,862.00 llrl \21 44 PSF 169,052.44 ft-lb (5,270.98)(28.0 + 34-0) +- (') ! __! 86rn) 38 PSF r0,404.00 x (7.5 + 34.0) + (1 o,404 .0) I34.01 \) I 622,44r. 76 ft-lb (5,270.98)(62.0 + 48.5) + ,rO-l 30_ _t -l ;1. 33 PSF (2,862.0) 26 PSr t3,6U.25 x (41.5 + + 48.s) + (10,404.0x17.0 + (13.604.25) 48.5) /an s\ | -'l = 1.851.388.35 \2l fr-lb Figure 5-22. High-pressure flare stack; unless otherwise indicated, all dimensions in feet, design wind speed 100 mph. : 22 Mechanical Design of Process Systems Wind Load For Section D (5,270.98)(113.0 + + 34.0) (2,862.0) x (92.5 + 34.0) + (10,404.0X68.0 + 34.0) + x .25 + 34.0) + x (126.50 + (r3 ,6O4.2s)(60.7 x (35.25 + 10.0) I + (2,862.0) 102.0 + + r0.0) /,,r.0\ + 30.0) + (13,6M.25)(70.7 x (45.25 + 30.0) + (10,174.5)(27.0 + 30.0) 30.0) + : s, r:t,+rr.zo 0.56 t" E y '.E:29 : 30,000 psi x o.oo5 > o.oo425 (0.56X0.005)(29.0 x 109 0.004(29.0 x 109/(30,000)l + 90.00 o. = 20,021.918 psi !: d (0.500 rt-ru - 0.12s) = 0.009 Section Weights-Uncorroded Weight - d (1 + 0.004 E/y) ' : t"_(0.625-0.125) :0.006 wr = ' o l25) 16,684.932 psi Section Allowable Shell Buckling Stress 109 o. = 30.032.877 psi (6,142.50) i3o'oJ 0.00425 For Section A 5 + 30.0) + (866.25) + - 120 d (2,862.0) (136.50 + 30.0) + (10,404.0X112.0 + 30.0) (2,598.80)(s.0 x > For Section B l+-lt '\2 x + (0750 : (10,174.5) :3,672,858.86 6,142.50 !: d li (2.s98.80) + o.oo6 For Section C 5 + 10.0) + (866.25) x (r7.0 + t0.0) r (5,270.98X157.0 120 (0.56)(0.006x29.0 3,228,045.06 ft-lb + 10.0) + (10,404.0)( - 0 125) : o, : 10.0) (0'875 "" _ tl + (0.004x29.0 x 109(30,000)] : 20,02i.918 psi (866.25) \'2 * d - .-. - /:+.0\ + 34) + 00.174.5) l:-jj: I (5,270.98X147.0 2,598.80 + (13,604.25)(26.'75 13 A (0.2833) '' j: (37.0)( 12) 'n. ',[l/€)'-litt\'l', [\, / \2 I ) 8,199.69 lb Section B 106 psi; wr - (02813) { rzoo,rz,' " [(T)' = 45,340.61 lb (*, )']'"' The Engineering Mechanics of Bins, Silos and Sacks Section Section C wr (ry ro]l_., - (0.2833); (44.0X12)'n.n [('r), [\, | \ 2 l) : 42,029.09 lb 'n (16)(42 .0)(169 ,0s2 .44)(12) rl (42 + @D2l(1.2.0 + 41.0X30,032,877)(1.0) 8,199.69 + r(42.0 + 41.0X30 ,o32.877)(l .0) Section D t. wt = (0.2833) in. --ll(30.0)(r2) : Total " : : Mr r(D"'?+Dr'?)@"+D)oE r(D. + D)oE oe : 18.25F](120.0 + I 1 8.25X14, 182. : A." - (16)(120.OXs, 138,419.76)(12) (1 , OK for buckling l2o + 2(2.50): =; 125.00 : Wn - l?!'e!6 58 - 76,84r.ros lb *,- = ottl24(125.00) 24 '']!;01?,tu' Section D + [ Total tension in each bolt Thickness 16 D" r[(120)'? in. Try 24-11+-rn. d anchor bolts dec t 1/z Anchol Bolt Design 128,966.580 lb Required in. = 0.052 [(9' - (r94,)]'" 33,397 .r9 tb wt A : 19X1.0) 40,000 psi 76'841 109 = |.921 in.2 < 40.0(n l3/+ 1.980 in.'] in. dia, 8-thread series 128,966.580 + 118.25X14,182.19)(1.0) in. + 7r in. [ , OK for buckling r(120.0 t, : 0.381 Check [/av\ : t-wl t\d/ I ^AR:No, 1 Section C r1r20)'? + r(120.0 + , = 0.245 in. - rl + (24) 95,569.39 I 18.5)(16,684.932X1.0) Ar = t/q iI^. 'll_ , OK for buckling Bearins pressure + (16)(90.0X1.8s1.388.35)(l2l (88.75f1(90.0 + 88.7s)(20,021.918)(1.0) 53,540.300 r(90.0 + 88.75)(20,021.918)(1.0) t, = 0.183 in. .r :/s-in. [ , OK for buckling 1.913 in.'? 48(s, ^' Section B (90), (4X12X5,138,419.76) (12s.50) (16)(120.0X3,672,858. 86)(12) (1 18.5F1(120.0 + I I 8.5)(16,684.932)(1.0) 1.980 in.'? = P-- = 48Y + W :i- 7rl:in. nDu' j r Drj " r38.419.76) : Base fl psi < Fb ;e t28.966.58 7r( : thickness, T1 t" : " (;oiltJ 128,e66.58] (40,000) r( 125.00)'/(7.50) Pt :7\3.734 Tr < - 125.00X7.50) 1.33(900) : : 1,197 psi compression =B* C : Z3tqin. I + thickness Zttcin. : 5.5o 24 Mechanical Design of Process Systems = Te (5.50r After one iteration, Il,lr r l rarl "t = 1.800 in. l:j;;:;=l I zu.uuj I l''' -'' :0.151 1 K: [ :twu) o [:1zo.r+r.roenorl'' [4(20.000)el [ 4(20.000X5.5) I 1+ (61,789.8ss) (10x1,096.373) After six iterations, K:0.178 B.ownell and Young Base d Bolt circle P Base 4 :di : f, f"-Eq = n E' -- Method 125.00 in. lo(1.096.373) = fc,-o,.area, (1.0e6.373) 125.00 130.00 130.00 : 212.50\: (7.00) 2(7 1 16.00 130.00 in. 116.s0 1t. : : 7.00 in. K= 1,000; = I L4 : (1,200) \r/2 I ^" JI. - ^1^-l : : 1,106.925 psi [ 2(0.333x125.00) + (5.138.419.76) r,=- ' [46.,rr'l,,rr.*, I t,26t. sto)1"' - ,.'' "' [:rt ,o"ooo I 2.181 in. (without gussets) lr( ""-" h = -r 1.588; C, = 2.316 z:0431l. - 00l .,"\ ll25 (128.966.58){0.r''' 12 / 559,723.403 A z'd = ,..,, f,'s, gusset spacing is 7.00 1.980 in.2 (12) ?r( 125.00) t2 n b "' = 32.725 in.. | = A = 5.00 in. O\ 5.00 32.'125 From tble 4-8, using linear interpolations, My: - O.467fcrt2 My= 0.467 (1,268.836)(5 - r,- _ l(oJ{l+.6rr.oou)l = - U.UOI ln. : t 6l,789.855 20.000 '00f :14'813.660 in.-lb 2.10g in. I t = use 2rls in base Brownell and Young External Chair Design Fc t: : = I 0.333 0.782 : 7.001 2(0.333X12s.00) K = 0.333; c"= For t",^ ,"8)(t25.0) + 1.268.836 psi - Using 24 gusset j t0,963.73 : with fc,"., fc(Bc) : 559,'723.403 7.00 - 0.061 + 128,966.58 : 6.939 in. : 688,689 983 688,689.983 rcr6.e3e - (10)(0.06rI ($Q)<r.sasr = r 5.00 22 b : gusset spacing 1,096.373 For |ta-in.O bolts, = 32.725 in. t 15 : e -:" 2 t.375 in. The Engineering Mechanics of Bins, Silos and Stacks : : PB \r. max. bolt load on upwind side fsAB - 2r.708.185[ 4r t = lr/+ fw : 1.33'yn(0.55), for wind or earthquake 21,708.185 lb fw: * (t + 0.30),n Izrs.ool I [z'(L375)J ,l I : i.33(20,000X0.55) Weld size = 14,639.99 5 154 1)1 --- = 0.396 -.'14,630.00 3,612.549 ir..-lb or .' _ [{6x3612.549)lr" _, t 15,000 I = : = (10,963.73)(1.980) in. in. f, "^. 0.396 '2 for compression ring = 0.198+ Va in. minimum weld each side Cantilevel Vibration '. Calculation of Gusset f, Thickness for Compression Rings : (,aJo o . (,$n', = 5 860 rt Corroded Stack weisht r,2 [ = 4qr2-r2 =]. t2 ,= :0 [ereL, ] withk=%(1.250)=0.469 *,^ : 6nluurf(,sl - (91 :6,16'".ze4tb *," : <arr oezrl(r1)' - (r91 :36,323217 r35 in. h:G+H I21h n. :9 + lt/+ in. i h 12.500 r 0.135 P 2t/c in- tb = l2tlz in. *,:,ounn Bolr Load lttt rl(?l- (rtl]I|l: 35,o6oe6o,b 23,905.217 tb 101,457.688 lb 18,oo0rtr-Ptt- htP I,500 18,000(5.00)t63 - Lc :0 (12.500),(21.708.185) _ 1,500 qt - q= 0.24ltS 0.40 in. r/z-in. f, 5.00: 13.0 = U.UtJ < trl 0 = (200X5.8601 LD,2= 4!4:1688= ft U.5 14.773 < 2r) Therefore, vibration analysis r,?as, be performed. - 0.025:0 = 8.00 + r^ rlnn L 200 (21,708. 185)k, _ : Wa is OK Skirt-to-Base Ring Weld ': - ,: (#ft)* (";)'0u." r:a.+ ro.76x r2)] , _ [r+xs. r-[ --;6 20"0)!-l t r28.966.58 "(t20-00) : 101,457.688 lb, : 193.50 - lr.O * ff : r'v)) ft 1.648( 193.501 L? 5r(ET, = o.gaOx:sJt-lItc t.648 I : t: ,uB = )'tv+ tzl L" = 200 0.511 cps vc :3fDrr:3(0.s11X5.860) : 8.983 mph seconds 26 V:o v* Mechanical Design of Process Systems : 100 mph : (roo) r- (*J'"' : k_ L..Ws _ fu 13 1. 165(1.3) : 193.50)1t 0 l5 mph 170.5 (0.0077X5.860)5(29.0 ( x _ ( 2 : "f it{zs.zts), - \ /. (34.71 (0.207X5. 86oX x x t :6047 -' 106)0 5)2 5 (1.760) = 3.520 / ss cps \-/l , lfl in.a : / 77,307.326 6.047 cps 10 ft, 6o(to0l-- 0.2(66) : 2t,:2.640 < \/ss.zs + o.zs\ < f'" -_ 7.58(0.625X29.0 x lfff5 _ = a)\).^< 1.320 cps 4.252 At bottom section, in] f,' _ 7.58(0.751(2?.0 x t06)05 60(10.01 = 5.102 cps i,:o2t66t=1.320cos '10 8EI 8(29.0 60(7 At 120-in. dia : 0.523 in. P"D,(LF(12)j - _ 7.58(0.5x29.0 ' 10 , '=: \'oo/\ 34."111 ir. -. D.= t.: " 2f,:2 0.107 psf 0,,,) * (,z,|(?..,") i+r \/ +r r o.zs r: : - 0.r25) + (,$,o.uro : ," = (_..)(? * :35.285 in. 0.2v 0.2\66, :D=(35;=r'l/rcPS /.f 1.0X0.00238X 1.467P(8.983,, (,$,o.to vortex shedding frequency f _ 0.2(66) _ | %n 2 , = . t, At 90-in. dia : 7.5 ft, Static Deflection ^ ^ Y.-{.,o- 20.826 cps 2f"=7.54t Therefore, the stack is free from cantilever vibration. tt.467V : 106) t.457.688.) 115 :0.002 < 0-l-]06t 60(3.50F 13r.165 mph Maximum gust velocity : 0.0077D,5E 7 58(0'3zs-iq9 l93.so)4(t2f 106)(77 ,307 .326) = 0.164 in. 2f,:2.640 . t.rO, Therefore, stack is free from ovaling vibration. Dynamic Deflection Using a magnification lactor of 30. 6 : 0.164 (30) : 4.915 in., which is permissible Ovaling Vibration Natural frequency of free ring ''^ 7.58r.(E)o 5 :t AIICHOR BOLT TOFOUE Anchor bolt torque on stack bolts is handled exactly like tower anchor bolts as discussed in Chapter 4. Using Equation 4-66 and considering lubricated bolts we have T:CDFi where the uplift load on each bolt, F, is 6oD2 At 42-in. dia : 3.50 ft, (4-66) -t,: r2) ,2a1us.0ot 4(5, r38,4r9.76X r0r,457.688 a : tt't6t 'tztD The Engineering Mechanics of Bins, Silos and Stacks .\hich results in a required bolt torque of r: (0. rs) (r.75)(77 ALL MATERIAL TO BE SA-285 _C ,987 .312) = 20.471.67 in.lb = 1.706 ft-lb Use 1,706 ft-lb torque with lubricant grease Fel-Pro C- or equivalent. The skirt base and anchor bolt detail for the stack is hown in Figure 5-23. 5,A,, Design Summary Static wind shear at base = 22,355.110 \b Static wind moment at base = 1,299,115.509 ft-lb Dynamic wind shear at base = 22,844.841 lb Dynamic wind moment at base = 1,308,916.974 ft-lb Total deflection at top of original tower 4.418 in. Total deflection at top of modified tower 5.898 in. Base plate thickness:2lle-in. plate Compression plate: 1l/4-in. plate : : trL_u--l ffi ALL WELD SIZES 16) l:/+-in. anchor bolts Required anchor bolt torque: 1,710 ft-lb Total operating weight = 128,966.580 lb , IN INCHES EXAMPLE 5.3: STAGK VORTEX STRAKE DESIGN An exhaust stack 126 ft tall is to be Drovided with heli.'al vortex strakes. The length of the stack to be straked is the top portion 31 ft 6 in. long. Cornpute the radius of iurvature of the strake to be cut from flat olate. Referring to Figure 5-15 we have the following:- D:ODofstack:7ft4in. L:31 ft 6 in. D 7.333 : J.DO/ .i = _ = _ L _31.5 : 2ro 2rtl) zl-tci I .t a-tgg-'et. a THBEAo sERtEs BoLTS TO STRADDLE CEI.ITERLINES BOLTS t{ \ou, +b2 _ _ a2cu2 _ _ (3.66'7)2(r)2 - --;F- := (5-17) + (5.013F (356?X1t10.521 ft Figure 5-23. High-pressure flare stack base support detail. 28 Mechanical Design of Process Systems Check BASE PLA?E - 3/16r Using the approximate Morgan equation we have, Si : : interior arc length [(rDJ'? + 52:exterior arc length = : 41.637 ft L2]0 5 : 39.025 ft [[?r(8.667)]'? + (31.5)'?105 STRIPS CUT FRO}I x:9:t?'o,T:r.nt s. (s-1e) BASE PLATE 41.637 r \w : ._________ (5-lg) (0 667) r - |937)(0 - 9.966 ft = 9 ft i t.594 in. 0.937 10.521 - 9.966 _ va e:,rof = = 5.276Eo errol ff t 0.5ft + 0,66?ft = 11.-2. The final product is shown in Figure 5-24. EXAMPLE 5.4: NATURAL FREOUENCY OF OVALING HING FORIIULA IMICHELL FORUULA} To use the Michell equation (5-12) dimensional analysis must be applied to obtain Equation 5-13. The original Michell equation is as follows: f. '' = , I rtJrJ - 'J].--.-(n'. +l+/) -. (5-12) 2"Y PAf -r/ where p :0.283 lb/in.3 for A: (t) in. x steel (1) in. f : in.a E : lb/in.2 I - T-; . per unit lenpth ofring. t2 z : in.' l/r for steel 386 lb.-in. rgl I z7f 'i-c' (0.283) -.l!l E - : 4.409r Ir ---- Vt1 1 in.2 1(36)r(in4) 1 in.a (5.333) (5-13) Figure 5-24. Manufactured strake elements. The Engineering Mechanics of Bins, Silos and : : a: B: D: A cross-sectional area of stack, in.2 anchor bolt area, in.2 stack radius = D/2, ft critical arching parameter, dimensionless critical diameter at which piping is unstable, di- mensionless; internal stack diameter (Equation 5-15), ft; outside diameter of stack (Equation 5-16), ft; dynamic magnification factor (Thble 5JI E = modulus of elasticity. psi : material yield strength, psi ff: critical flow factor for arching in channels, dimensionless f, : natural frequency of a ring, Hz f" = stack vortex shedding frequency, Hz G : consolidation particle parameter (Equation 5-8), dimensionless H : height that solid is stored in bin, ft H, : stiffening ring spacing, ft I = moment of inertia of stack cross section, in.a L : height of tower portion straked, ft m : geometric parameter for arching (Equation 5-2), dimensionless n : flexural mode (Equation 5-12), dimensionless P"1. = air pressure (Equation 5-11), psig Pn** : maximum hoop pressure at bin-hopper tangent point, psi r : outside radius of stack (Equation 5-12), ft; nf. S= Low Oamping 6D HiBh Greek St/mbols : bulk density of solid. lb/ftl 6 = logarithmic decrement, dimensionless 7 Damping = : modetutelt stiff soil; aormol spreadfooting or pile sup- port soft soil; foundation on highlJ stressed Iriction piles perpendicular to stack centerline (Figure 5-14), : d' : dr : ot : or : p : interior arc length of helix (Equation 5-18), ft : exterior arc length of helix (Equation 5-18), ft S. = section modulus of stiffeners (Equation 5-15), ft' t : shell thickness of stack, in. V = wind velocity, ft/min V" : critical wind velocity in which ovaling occurs (Equation 5-14), fum w : width of strake, ft; normal pressure applied on mode shapes relating translational displacements about the x, y and z axes, respectively 30 6 : piping factor, dimensionless 0_: ungle of hopper slope, degrees 0 : modal shape relating to rotation about an axis Si 7.1 90 0.052 60 0.105 tural Itame support. Average Dampin? So ]) Average High Damping 6D6D Damping 2" gunite lining 0.070 45 0.100 31 0.300 10 9 4" gunite lining 0.117 27 0.r25 25 0.360 Inw Danping = rocky, very stiff soil; Iow-stressed pile suppon, or struc' ft bin walls by solid (Equation 5-1), psi 0.035 Unlined Stacks Lined Stacks dius of curvature of vortex strake (Equation 517), ft over-all length of vortex strake (Equation 5-16), XI 29 Table 5-3 Conservative Values for Logarithmic Decrement and Dynamic Magnification Factor tor Various Stacks NOTATION AB Stacks dimensionless coefficient of friction between the bulk solid and the bin wall (Equation 5-1), dimensionless kinematic angle of friction between the solid and the bin wall, degrees consolidating pressure for steady flow (Equation 5-4\, tbflft2 allowable tensile stress of stack material, psi number of revolutions around stack made by a helical strake, dimensionless REFERENCES 1. Jenike, A. W., Johanson, J. R., and Carson, J. W, Storage and Flow of Solids, American Institute of Chemical Engineers, New York, New York, 1981. 2 . Blevins , R. D . , Formulas For Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York. NY. 1979 3. Thomas, G. B., Calculus and Analytic Geometry, Addison-Wesley Publishing Co., Inc., Third Edition, 1960. Rotating Equipment Not all PD pumps are purely rotary or reciprocating, but we will focus our attention on these types. PD pumps, by Fluid movers and their use are vital to the process industries. This chapter focuses on two basic typespumps and compressors. The sizing of these units and their interaction with the other components of a process definition, deliver fluids at a rate proportional to the speed of the pump action and this rate is independent of the pressure differential across the pump. For this reason means must be provided to limit the discharge pressure and this will be discussed under the section of positivedisplacement pumps. Typical rotary positive-displace- system are discussed. This chapter does not address the detailed mechanical design of sophisticated equipment, such as turbine blade design and gas dynamics in a turbine. That type of material is a separate field of study and lies outside this text's objective of examining how to select and apply rotary bquipment to process systems. For further reading, see the bibliography at the end of the book. ment pumps include screw, gear, vane, cam, and lobe. Reciprocating positive-displacement pumps include piston, plunger, and diaphragm. Selecting the type of pump to use is a function of the service to be handled. Sometimes, the selection is obvious; for example, if you wanted to pump molasses, you would choose a positive-displacement pump. In the situation where neither a standard type of pump is used for the service, nor is it obvious what type to use, a centrifu- PUIIPS As the primary movers of liquids, pumps come in gal pump is always considered first. The reason for considering a centrifugal pump initially is because of its low initial cost, economical cost of maintenance, wide range of materials of construction, and relatively large clearances. Factors to be considered in selecting a pump are many types and an understanding of the various kinds is essential in successfully applying them to process systems. Pumps are used to transfer liquids from one point to another. They basically fall under two categories-centrifugal and positive-displacement. The centrifugal pump gets its name from the fact that the pump's impeller im- as follows: 1. Efficiency parts kinetic energy to the liquid with centrifugal force acquired by the impeller's rotation. This simple mechanism allows the centrifugal pump to be practical for high capacity, at low to medium heads. The aspect of low to medium heads will be discussed shortly. Typical centrifugal pumps include mixed flow, propeller, peripheral, and turbine. Positive-displacement (PD) pumps trap a quantity of liquid and force it out of the cavity against the pressure of the discharge by means of rotary or reciprocating action. Ideally, a PD pump will produce whatever head is impressed on it by the system restrictions to the flow. 2. Net positive suction head (NPSH) required by pump 3. Operating costs 4. Shaft speed 5. Magnitude of clearances 6. Materials of construction 7. Fluid service to be handled 8. Availability and delivery time of pump The type of pump to be used for a specified service or duty can be selected from Figure 6-1. This figure clearly indicates how different pumps have overlapping charac- 31 Mechanical Design of Process Systems 10 ro- F o I J I 234 -l 5 Figure 6-1. Pump selection guide. teristics. Depending on the relative importance of the previously cited criteria, a certain type of pump will be selected. Figure 6-1 will help the reader determine from a quick glance what type(s) of pump(s) will be required. Gentrifugal Pumps Centrifugal pumps are the most widely used because of their wide operating range and the reasons previously cited. These pumps come in a vadety of types, depend- ing on the type of impeller, casing, stuffing box, and bearings. These components are shown in Figure 6-2. The radial type impeller is by far the most common centrifugal pump in the process industries. The flow is directed by the impeller imparting motion on the fluid, driving the fluid to the periphery of the impeller. This allows the velocity head to be converted mostly to pressure head in the volute. The mixed flow pump impeller consists of vanes doubly curved or screw-shaped so that the impeller moves the fluid by both centrifugal and pushing action. The result is a discharge of axial and radial flows. The axial flow pump impeller develops head by a lifr ing or pushing hydrodynamic action that results in totally axial flow on discharse. The impeller is hydrodynamically balanced to ensure minimal vibration. The casings can come in a variety of designs, but are either vertically or horizontally split. A vertical-split casing implies that the casing is bolted together along a vertical plane. Similarly, a horizontally split casing is bolted or connected along a horizontal plane. The advantage of the vertical split casing is that the pump is supported along the shaft allowing for thermal movements without causing shaft misalignment. Packing and seals on the shaft are the most common of failure for a pump. In low-pressure applications, soft or metallic packing will suffice in a stuffing box. In most low-pressure applications, a single seal will usually suffice. When pressures exceed about 50 psig and there can be no tolerance for leakage, a double seal is utilized. These seals come in various configurationstandem. bellows. and face-to-face. source When process conditions get severe enough, a double inside-outside seal, where part of the seal is outside the stuffing box, is used. The disadvantage of this type of seal is that not all stuffing box arrangements allow such a configuration. For proper cooling and lubrication the seal must be supplied with a fluid, called a seal flush. Figure 6-3 shows such a system. G:oup ll and lll Standard Pumps Group I Standard Pump Materials Common io all Alloys Unless otherwise Noted Parl No. Malerial Parl 104 lmoeller Gasket' 107 Rear Cover Plate Gasket* Durabla 108 Bearing Housing Adapler Casl lron 109 Bearinq flousrno Fool 111 Gland Studs or 112 Sealcaqe'(E) PTFE 113 Molded Rino Packinq'rE) Kevay'il 114 Inboard 0ellector PTFE 115 Casino Studs/Hex Nuls 118 Inboard 119 Bearina Housing Cast lron 120 Inboard Eearinq' Sleel 121 0utboard Bearino' Steel 122 0ilSlinoer Steel 123 Bearino Cover Cast lron 124 Bearing LockNut Steel 125 Bearin0 Lockwash€r Steel 126 Beaino Cover Gasket Cork 127 Bearino Shim' 129 outboard 130 Shall Couolino Kev 131 Beanno Housrng Adapler' 132 Soherical Washer lor Foot Steel 133 Trico 0iler (nol shown) Steel-Plaslic 134 Bearinq Housino Venled Drarn Plu0 Plastic 136 Cao Screw for Foot Steel 138 Cap Screws 139 Machine Eolts lor Bearing Housrng 140 CaD F Casl lron 3M S.S./303 S.S anqe Studs with Hex Nuts 304 S.S./316 S.S.10 TFSB 0ilSeal' Steel oilseal' Screws TFSR Steel 0" Binq SBR lor Eearinq cover iorAdarterto Steel Steel Cover 'Pafls 10rtra'y sl0ck.d by cLsrome.lor e4erqenc/ rs 'Ppd "Trrd.name ol lnternanonal Nrrel Coooanv (A)Nor avarable In Recessed h0eller pumps (BlNor avr'abre In Seri Pnmno oumoe (Cr \or rva ubre on 4x3 LS.loii 4d US I3 o' 614 US l3A rcast sleel suotntuledr Sleel (E) Used n Packed PonPs only {t) Trtanrum Dumos havs GraJor rmpell€. oaskels Cdro,r b a reo'9ercd lraoe name or un'on Carbrde Coro0 anon lGr Allov rs B7 Sio. Duclilp lron rnd Crlbon Sleel oumos {H) Icd€name ol E Duponl deNamoors & ComDafiy Inc I {01Jackeled cover oral€s are carhon sre€l Figure 6-2. Centdfugal pump components. (Courtesy of the Duriron Company.) Mechanical Design oI Process Syslems A seal flush configuration. (Courtesy Durametallic CorDoration.) Figure 6-3. The various types of seals are shown in Figure 6-4. The pump manufacturer should be relied upon for the choice of seals. Sealing technology is a subject vast enough to encompass this book and the reader is referred to Buchter [1] for additional sources. Bearings, like seals, are for the most part the main responsibility of the pump manufacturer. In all situations, the bearings should be of the outboard type (not subjected to the process fluid), unless situations prevent this type of arrangement. Hydraulic Bequirements of Centrifugal Pumps In this section the reader will find it advantageous to refer to Chapter 1 . The most important hydraulic parameter in pump selection is the net positive suction head (NPSH), which is the total pressure at the pump suction point minus the vapor pressure of the liquid at the pumping temperature. NPSH is the energy that forces the liquid into the pump, and is expressed in foot-pounds of energy per pound of mass (normally referred to as feet of head) or pounds per square inch of absolute pressure. When values of pressure are expressed in feet of liquid, the theoretical height to which a liquid can be lifted at any temperatnre is the difference between the atmospheric pressure and the vapor pressure of the liquid at that temperature. Figure 6-5 helps simplify the calculation of the NPSH. of the In selecting a pump the engineer must refer to the performance curves the pump manufacturer prepares for each model ofpump. Most performance curves are plots of flow capacity (gpm) of water versus break horsepower or total dynamic head in feet. Such a curve is shown in the examples that follow. As seen, the efficiency curves are plotted with various lines indicating impeller size and the NPSH required at various points. In reading the performance curves, it is emphasized that the extreme right side of the curve should be avoided, because the capacity and head change abruptly. Pumps are normally selected to operate in the area of high efficiency. The danger in selecting a pump on the extreme left is that at low flows the pump horsepower overheats the liquid. If low rates carmot be avoided, a by-pass may be required to prevent vaporization and subsequent pump damage. Thus, vaporization of the pumped liquid can occur two ways: (1) the NPSH required is not being met and cavitation occurs in the liquid causing vapor bubbles that can severely damage the impeller or (2) the pump horsepower overheats the pumped liquid, forming vapor bubbles that can (and normally will) damage the pump. Excess heat resulting in pumping a fluid can be avoided by determining t}re minimum flow required to allow proper heat dissipation. At low flow rates or shutoff conditions, heat is transferred to the liquid contained in the pump casing at a rate representing the power losses of the pump. The power loss is the difference between the brake horsepower consumed and the water horsepower developed. The remnant energy in the pump bearinss and that lost to convection to the outside atmo- h O l-o :. 9? ;7 3.: E> .9+ 9@ E.) I q= oii ! 36 Mechanical Design of Process Systems Pump Hydraulic Design Calculation Sheet Liquid Viscosity at P.I (Pumping Temp.) Vapor pressure at PT Sp. gr. (7) at PT. Flow at ambient temD. Operating flow at PT. Design flow at PT. psra gpm gpm gpm _ Suction Discharge Source'pressure psra Terminal pressure psia Static psi psi psra Static (head)(lift) APr discharge Piping system Other Discharge press. Suction press, psl (+ headx- lifi) = - APr line loss Suction pressure - Vapor pressure psra psra NPSH avail NPSH avail NPSH req'd - ft ft [,lin NPSH avail > NPSH req'd + 2 'lnilial press., e.9., ATM or O - unp at Duty condition (gpmXTDHXr) _ ono" _ psi psi psia psia TDH TDH psra leet fl @ Onp at Maximum Capacity 66o.," = (3,e60Xr) Condition (gpm)CrDHXr) (3,960Xri) TDH = total dynamic head TDH = discharge press. - suction press. 4 = pump efficiency, PT. = o/o pumping temperature Figure 6-5, Pump hydraulic design calculation sheet. sphere is negligible. The temperature rise per minute is computed by the following relation: 42.2(bhp,") W*Cp where At : bhp," : W* : Co : (6-1) temperature rise per minute, oF/min 6.u1" horsepower at shut-off weight of liquid in pump, lb specific heat of liquid in pump which is the power required if the desired head at the required capacity could be produced with zero losses. For water flowing through the pump, conditions become stabilized and the temperature rise is determined by the following: ". _ (bhp - whp) 2,545 m where 2,545 : ir : (64) Btu equivalent of I hp-hr mass flow rate- lb/hr- The break horsepower of the pump is given by .. OH"y bhp = -,::--r J,vou4 Another variant of Equation 6-4 that relates the tem(6-2) = : flow rate, gpm H = total head, ft where Q "v q = = ^ ^o(;-,) specific gravity pump efficiency (fraction) ': QHI 3,960 (6-5) In Equations 64 and 6-5 the compressibility of water is The water horsepower is given by who Derature rise to the total head is (6-3) neglected. To prevent overheating of the pumped liquid, a bypass piping arrangement is used to have the pump operating at full capacity. Such an arrangement is shown in Figure 6-6. It is always desirable to pass the bypass liquid Rotating through an intercooler to cool the fluid before it enters rhe pump suction port. Under no circumstances should the bypass line connect directly from the pump discharge to the pump suction. So faq we have not considered the pumping of viscous liquids. For a liquid that has viscosity greater than about 10 cp, a viscosity correction must be made, because the pump motor must work harder to pump the fluid. All pump manufacturers' pump performance curves are based on pumping water. To correct for the pumped liquid's viscosity, Figures 6-7 and 6-8 are used to approximate the equivalent water performance. The figures, developed by the Hydrauiic Institute, are used by entering the bottom with the viscous flow rate (gpm), moving vertically upward to the desired viscous head (head per stage for multistage pumps), then moving horizontally to the left or right to the viscosity line, and proceeding vertically upward to the correction-factor curves for the head and capacity. The equivalent water-performance values are then obtained by dividing the viscousperformance values by the correction values. Thus, the pump selection can be made on those ratings established for water. The efficiency of the viscous liquid pumping conditions can be calculated using the efficiency correction factor multiplied by the pump efficiency for water. In this manner the viscous performance of the pump can be determined using the manufacturers' performance curves, which are always based on pumping water. This procedure is illustrated in the examples later in this chapter. Positive Displacement (PDl Pumps Positive displacement (PD) pumps are usually selected after it has been determined that a centrifugal design can- Equipment 37 not meet the requirements. Thus, PD pumps are used where centrifugals cannot operate-under low NPSH requirements or handling a highly viscous liquid. There are several types of PD pumps, as previously mentioned, and their positive attributes are that they at relatively high efficiencies when pumping viscous liquids. Operate under low NPSH conditions and produce high suction lifts. Operate with high heads at a wide range of capacities . Have a wide speed range, which is limited by the liq- 1. Operate 2. 3 . 4. uid's viscosity. inherently self-priming. 5. Are Selecting the fype of rotary pump is primarily a function of cost and the particular requirements that are to be met. 1. Vane ptmps-normally have a capacity up to about 380 gpm and operate by trapping liquid within vane differential pressures, usually at around 50 psig. The practical limit on viscosity is approximately 100,000 SSU. Vane pumps are subject to wear and should not be used with a liquid that has poor lubricating quali- ties. 2- Gear pumps-normally are used up to about 1,000 gpm and can handle liquids with viscosities up to 5 x 106 SSU. These pumps operate at approximately 1,200 rpm with liquids of 10 to 500 SSU viscosity (see Figure 6-9). It is desirable to have internal timing gears and bearings since only one shaft sealing area is required. A variant of a gear pump is shown in Fieure 6-10. INT€RCOOLEA Figure 6-6. Excessive heat build-up is often caused by operat- ing pumps at reduced flow rates. To prevent overheating the pumped liquid, it is advisable to pass the liquid through an intercooler before it enters the pump suction port. Mechanical Design of Process Systems l 00 .90 .ao .70 o .60 z .50 _40 .30 .20 ."n, B S9 .icF CP .\$ ?p r_': \9, rd ^ 3cP '6 g 1s" Hp Zro o!o -co g vrscoslTY-ssu '. s u";*t* s g;*1" I 15 20 25 30 40 CAPACITY.GALLONS PER I\4INUTE 50 (At 60 bEP) Figure 6-7. Performance correction chart for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.) Rotating Equipment ol fil -l v, l( o F () [>l z2l ogl trol HEI !t ol 8el >l FI gl o-l 5l gt <l FI :l tuI o-l rr lrl I :l<l lrl -l I 4 6 CAPACITY 810 IN lOO 15 GPM Flgure 6-8, Ferformance correction chart for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.) 39 Mechanical Design of Process Systems Figure 6-9. This drawing of a rotary gear pump illustrates the positive-displacement principle. The fluid is captured in the gear teeth and displaced to the suction port. The crescent acts as a seal between the suction and discharge ports. An application of this type of pump is illustrated in Example 6-2. Figure 6-10. The internal bearing gear pump is a variant of the rotary gear pump in Figure 6-9. (Courtesy of Worthington 3. Friction head-the pressure (psi) required to overcome frictional resistance of a piping system. Velocity head-expressed in psi, see Chapter 1. Tbtal suction /r/-the total pressure below atmospheric (in Hg or psi) at the pump suction port during pump operation and equals the following: Screw pumps-these pumps, depicted in Figure 6- 11, are used where large flow capacities, 4,000 gpm and 3,000 psi, are required. Screw pumps can handle vis107 SSU and have bearing and cosities up to 10 x timing gear requirements sirnilar to gear pumps. Screw pumps come in various designs, and one type, shown in Figure 6-12, can handle highly viscous, non-Newtonian fluids such as glues, molasses, tar, asphalt, and wastewater with ease. Positive displacement ( PD) pumps come in a vast variety and you should refer to the manufacturers' literature to best determine the selection of the particular pump to be used. However, PD pumps are sized very much like centrifugal pumps, and the calculation sheet in Figure 6-5 can safely be used for sizing either type. Pump sizing is focused upon here to illustrate the various ways in which a pump may be specified. Figure Gl3 shows various installations for a pump. Some properties and characteristics illustrated in Figure 6- 13 are lfi-the vertical distance in feet (expressed in psi) between the liquid level ofthe liquid to be pumped and the centerline of the pump suction port when the pump is located above the liquid level of the ' liquid to be pumped. Static suction head-the vertical distance in feet (expressed in psi) between the liquid level ofthe liquid to be pumped and the centerline of the pump suction port when the pump is located below the liquid level of the liquid to be pumped. Static suction Pumps, Mccraw Edison ComPanY.) 1. Static suction lift plus the frictional head, or head minus the static suction head (only if the frictional head is greater than the static suction 2. Frictional head). Total suction head-the total pressure (psi) above atmospheric at the pump suction port when the pump is operating and is equal to the static suction head minus the frictional head . Static discharge head-expressed in psi, is the vertical distance in feet between the centerline of the pump and the point of liquid discharge. Total discharge head (TOH)-the sum of the frictional head in the discharge line (discharge frictional head) and the static discharge head. Tbtal static head-the difference between the static discharge head and the static suction head or the difference between the static suction lift and the static discharge head. Toial dynamic head-the sum of the total discharge head and the total suction lift or the difference between the total discharge head and the total suction head' E -o E.i aa E i E 35 Et= ,^.c! '6'y P:; q .= .:.. -o 'T 0) o ! 9q) .E CDY) (.)c, ,*(5 .g E r].1 o 3t* ; i: AE F.q .?3H ;6o b5 9E o.; -o :", \ d 9 o.: i!-P I E.EE oo 6-E9g ao E';e qIb !E9 s g 3 = il -oo EE3 dz =E ;-F B o- - bX- € .=o $Egq 'EE P H:1 :..6 9? E= =.!ebo ;. o t! - .F c s 9! b;d 9=Y"t o I cg .2 o E:0i (sYE:,il E Xe.d" : r ".! 33 r_d ?E 49 &: E06: r * xE ;i P: EP I ! (L =;= 6-d PU(J thJ rDt 5.s,b F>\ DDq O x rE F ='; I ai dE 6 crt gl'" dd E 'i-oi E= =; F d) Mechanical Design of Process Systems Figure 6-12. A cavity screw pump is ideal for handling higbly viscous non-Newtonian liquids. (Courtesy of Moyno@ Industrial Products, Fluids Handling Division, Robbins and Meyers, Inc.) t|'r$|lhF..Dl$hra When using PD pumps where a suction lift is required, remember that the theoretical height to which a liquid can be lifted at any temperature is the difference between atmospheric pressure and the vapor pressure of the liquid at that temperature, when both values of pressure are expressed in feet of liquid. However, the suction lift practical for actual pumping installations is somewhat less than the theoretical value. Figure 6-14 shows the theoretical and practical suction lifts for water. Also, remember that the higher the installation is above sea level, the lower the vapor pressure, and the lower the maximum suction lift. Application of PD pumps to practical installations is given in the examples. The unit conversions included in Appendix D are helpful in pump calculations. Pressure Protection For PD Pumps By definition, a positive-displacement pump transfers at a rate proportional to the speed of displacing action and this rate of transfer is independent of the pressure differential across the pump. Thus, means must be provided to limit the pressure and the pump discharge side should the discharge piping become restricted or blocked. There are various methods used to prevent overpres- fluid sure: 1. Install a relief valve at the discharge of the pump with the relief valve discharge being piped back to the pump inlet in which an intercooler is placed in the line. Such a configuration is shown in Figure 6-15. In Figure 6-13. The principal parameters of pump selection. (Courtesy of Viking Pump Division, Houdaille Industries, Inc. ) such an arrangement a temperature sensor device is placed at the pump discharge to detect excessive temperatures. The intercooler, or heat exchanger, is used to cool the pumping fluid. Normally, temperature becomes a problem when the instantaneous discharge and inlet flows are equal. Gear and multiplex Rotating Equipment (plunger, diaphragm, and piston) pumps are examples of such pumps in which this situation occasionally de- 2. velops. Place a pressure switch in the discharge side of the pump piping, interlocked to shut off the pump driver. Since pressure switch set points are not as reliable as relief valves, a relief valve must be added to the discharge piping and set at a pressure slightly greater than the pressure switch to ensure adequate protection. The relief valve would be piped-up similarly to that shown in Figure 6-15. 3. Install a torque{imiting device in the pump driver when a relief is not practical, such as slurry service. A torque{imiting device can come in the forms of a shear-pin or torque limiting coupling. These devices Figure 6-14. The theoretical and maximum recommended lift for water at various temperatures, 'F. (Courtesy of Viking Pump Division, Houdaille Industries, Inc.) suction have advantages other than protecting the system against overpressure; they protect the pump against foreign material or whenever the pumped fluid might tend to solidify. Overpressure protection is essential in positive-dis- placement pumps. Relief valves applied should be added to the discharge piping itself, because built-in relief valves on the pump that are not removable for testing are undependable. COMPRESSORS The three types of compressors used in the process industries are centrifugal, reciprocating, and axial flow compressors. Like pumps, depending on the application, the type of compressor is roughly a function of the gas capacity, action, and discharge pressure. Figure 6-16 shows the operating ranges of the three basic types of compressors. As clearly shown, one type of compressor, despite its disadvantages or advantages compared to other types, is usually the obvious choice. Reciprocating compressors are normally used when a relatively low flow rate is required, but high discharge pressures are expected. This situation is common in the gas processing industry where high discharge pressures are needed for process conditions. The need and use of reciprocating compressors is unavoidable in many process system applications. Centrifugal compressors are the most common typ€ in hydrocarbon processing plants and are to some extent the workhorse of chemical process compression needs. There are four basic advantages a centrifugal compressor has over a reciprocating compressor: 1. Lower initial capital investment. The cost advantage is increased as the power demand is increased. (B) Figure 6-15, A temperature switch can be used in lieu of an intercooler (heat exchanger) in which the switch can shut off the pump driver when liquid temperatures become excessive as in (A) or can be used with an intercooler in (B) to divert flow through the exchanger. In either case, a pressure safety valve should be used on discharge. (B) assumes the suction temperature is constant. To prevent overheating on low flow rate conditions, a flow switch is often used. 44 Mechanical Design of Process Systems 2. Lower Princlples of Compresslon 3. The general gas law that applies to all gases can be written in several forms: 4. operating and maintenance cost. The operating and maintenance cost of a centrifugal is approximately one-third that of a reciprocating compressor. Compactness of size. Centrifugals occupy less space and make much less noise. Simplicity of piping. Reciprocating compressors can cause severe pulsation shock response in piping systems. The cost in preventing the effects of pulsation in piping systems can entail many hours of engineering and a healthy capital investment for either analog or digital simulation tests. Centrifugals do not have this problem. Axial-flow compressorc operate at greater capacities Axialflow compressors are governed by the same formulas that apply to centrifugals. The axial units are more efficient than the centrifugals, but the latter have a much wider operating range. Axials are used primarily for and are often used in series with centrifugal units. PV = zmRt (6-6) zmRt (6-7) mw : PV: zM.Rt (6-8) zRt (6-e) where clean gases such as air, because they are much more susceptibie to corrosion, erosion, and deposits than centrifusals. : V: z: R: R: P absolute pressure, psra volume of gas, ft3 : compressibility factor for real gases (z 1 for a perfect gas) R/mw gas constant of the particular gas universal gas constant 1,545 ft-lbr/lb. : t= m= : : v: mw mole - : 'R absolute temperature, mass of gas, lb- 'R : 'F + 459.7 molecular weight of gas number of moles of gas m/mw specific volume of gas, ft3llb. : Mo A very important gas property is the specific heat ratio, k. This property is determined from the following: .c"c" K=---j= c" where C, Cp cP : 1.986 (6-10) specific heat at constant volume, Btu/lb.-mole- = 4.97 Btu/lb,-mole-"F for ideal monatomic gases = specific heat at constant pressure, Btu/lb,-mole- : s - 7.00 Btu/lb.-mole-"F for most diatomic gases Reverslble Adiabatlc (lsentropic) Compression a The reversible adiabatic (isentropic) compression of o an ideal gas is obtained when no heat is added to, or removed from, the gas during compression. The process is reversible when no friction exists. The formulations differ for a perfect gas versus a real gas. 6 Perfect Gas INLET FLOW,ACF souRcE:DriroPLot{ t2l Flgure 6-16, Approximate ranges of application for cating, centrifugal, and axial-flow compressors recipro- [2]. PrV,K : (z PtYtx ! : l&F tr \Pr/ : 1) (6-11) (6-12) Rotating Equipment Real Gas (z P1V17 t' t' : * 1) : gas flow rate in standard cubic feet per minute of gas (60"F, 14.7 psia) P, : absolute pressure at suction, psia Pd: absolute pressure at discharge, psia t. : absolute temperature at suction, oR where Q (6-13) P2V2'y lP:l " (6-14) \Pr/ _2"*24 : mean comoressibilitv factor where. for any system of units : : : -y : t: P absolute pressure V k volume or specific volume, v specific heat ratio isentropic exponent for real gases, Co/Cu absolute temperature z. za : : compressibility factor at suction compressibility factor at discharge For a gas capacity of Q : 100 scfm, Equation 6-16 becomes subscripts spectively I and 2 denote inlet and discharge conditions, re- [,,,-, To determine the exponent, T, real gas properties must k-r kt be used. These properties can be obtained from gas property charts and used in the following formulation: r / \'l I-I-y =*l'*,lSll [ \atloj (6-15) JCp where J : mechanical equivalent of heat : '778 ft.-lbrl Btu /,el : ll-l d[,l p \ rate of change of compressibility facror. z. with respect to the required temperature. t. along a constant pressure, P. path To determine a mean value of the isentropic exponent for a real gas, ?, over a compression range, Equation 615 must be solved by iteration. In Equation 6-15 if we have a perfect gas in which 4" : : ? 'v=k For a compression ratio PzlPr < 2.0, mately equal to k for most real gases. t [, ], \k/t t (6-17) qn : : mechanical efficiency the ratio of the actual horsepower delivered to the gas to the brake horseDower. or shp bhp : : (6-18) overall adiabatic efficiency the ratio of the isentropic horsepower, hpr, for a stage of compression to the brak€ horsepower, or hD" is approxi For isentropic compression of an ideal gas the theoretical horsepower requirement is as follows: hp':ffi|('iJ'*-', -'l['',J' adiabatic efficiency the isentropic horsepower, hp1, delivered by the actual horsepower delivered to the gas, or hpr 4,o JCP I gnp '''' R k-1 l\P,/ In applying these formulations that deal with the isentropic compression of an ideal gas, efficiency factors must be defined in order to apply the equations to real world compressors. These efficiencies are as follows: l=l =0andz:1.0 then Equation 6-15 becomes ], h._ =6.42llPdl k _rl{r,l_ -l\520/- (6-19) bhp In defining the horsepower input for a single stage of . compression, utilize the overall efficiencv as follows: 6'6, bhP=*=ffi[(,t-']F;'{*) \ k /r (6-20) Mechanical Design of Process Systems For bhp at 100 scfm, Equation 6-20 becomes J The isentropic energy transmitted to the compressed gas in ftJb/lb- of gas represents the adiabatic head, or t \t ,[,,*-, I - 'la \mw/ \K- r/ [\Ps/ ",: llsl{IlllSlT I (6-2r) The compressor driver horsepower (bhp or ghp) is related to the adiabatic head by the following: ghp: bhp : (6-22) 33,000a" frfl, (6-23) 33.0001"" where rir : mass PlVtn = where n: (6-26) flow rate of the gas, lb./min The adiabatic efficiency can be defined in terms of the polytropic efficiency by the following: PrYro (6-27) the polytropic exponent, n + I orn +k Expressing Equation 6-27 in terms of temperature and pressure we have t' /p,\? t' -- \P,/ The value gas ;H" constant When Equation 6-26 is expressed between the initial and final conditions we have bhp=ffiH=-'l'H \-o /1 : PV' (6-28) ofn depends on whether the gas is a perfect (z: l) or a real gas (z * 1) as previously dis- cussed. For a perfect gas the relationship between adiabatic and polytropic efficiencies is given by Equation 6-24. Similarly, the polytropic exponent, n, for a perfect gas is related to the polytropic efficiency and adiabatic exponent. k. as follows: n-1 k-l n lll (6-29) \4el k-1 _R (6-30) JCo (6-24) sincek: Equation 6-24 is discussed in more detail below. For a single stage of compression, neglecting any changes in potential and kinetic energy, the temperature change from the inlet and discharge is given by Af : r. - r : 6.33(2,547bhp - q) (6-2s) QCo where q : total heat energy lost to the surroundings or to any available cooling water or cooling jackets. This value does not include thermal enersv for intercoolers or aftercoolers. For a multistage compressor, Equations 6-20 through 6-25 must be applied separately for each stage. Polytropic Compression ColC" The relationship between the polytropic efficiency and adiabatic (isentropic) efficiency of a perfect gas is shown in Figure 6-17. The polytropic efficiency, 4p. is usually determined by the compressor manufacturer using either an old design or testing a new design. The polyropic exponent, n, for a real gas is determined from real gas properties or with using real gas data and using the following expression: n- I n [z+ t l_tl /a'\] _t_ JCo lqo \at/l Equation 6-31 is identical to Equation 6-15 except that the isentropic exponent for a real gas, 7, is replaced by the polytropic exponent, n, and the compressibility factor for real gases, z, is divided by the polytropic efficrency, ?p. This type of compression occurs when a gas is reversibly compressed along a path that is defined by the followins relation: (6-31) Similarly to Equation 6-15, Equation 6-31 must be solved by iteration for a mean value of the polytropic exponent, n, over a compression range. Rotating 6A 70 72 74 ciency for a perfect gas (Z lp In Equation 6-31, if we have l3l : ouno z \r/p *'ffilett'le = I fora perfect sas then, JCp4p , /r \ K l-l @32) \4pl For most real gases below a compression ratio of approximately 2, then n = 1). '' (,C,tffi (6.33) For ghp at 100 scfm, n-l:j-:= n 47 Figure 6-17. The relationship between the polytropic efficiency and the adiabatic effi- 767880 POLYTROPIC EFFTCTENCY Equipment - I _k n ll\ 'K l-l 1 ,no (il t=l : k /t[tfl H!-1J_j1?L \;/\ _ (,$,,, H,6.34, ] The equations for polltropic head are similar to those for adiabatic head. Equation 6-21. Thus. \ql The basic horsepower and head expressions for polycompression are similar to those for isothermal compression, Equation 6-20. Thus, we have fopic FJ . : (.*_)t^J IH(l ,] " (6-35) 48 Mechanical Design of Process Systems If the polytropic head is known, the compressor horsepower (ghp or bhp) can be obtained from the following: bhp : ehp : mil (6-36) 33,000a* riH bhp t, = i&)H \P,/ (6-38) values): /\ I lk-ll . y v (6-3e) ./ - -t----t -4p\ K / \p : k-l (6-40) k Normally, the value of ?e is estimated from data supplied by the manufacturer. For initial or preliminary values of the polytropic efficiency, 10, Figure 6-17 may be used. lsothelmal Gompression This compression occurs when the temperature of the gas being compressed remains constant during compression. For a perfect gas in which z 1.0 and (AzlAip 0 we have : P1V1 : : (6-41) P2V2, OI PV : (6-42) constant The theoretical horsepower developed during a reversible isothermal compression process is ho,:atz " 8.1l0hl&) \P,/ (644) 7h where : Ia : isothermal efficiency 4, overall efficiency : Itlln F) . hp, hpr tlfl- tl:. (64s) Equations 6-35 through 6-38 are used separately for each stage of a multistage compressor. Equations 6-38 and 6-39 can be used to calculate the polytropic efficiency directly (provided t, ta, P,, P6 and k are known wnere _ : overall polytropic efficiency : IpI. The outlet and inlet temperatures for polytropic compression are related by the following expression: ! not achieved, because the heat of compression causes the gas to exceed the inlet temperature. The actual performance of a real compressor can be evaluated by the following: (6-37) 33,00040 where 4oo Equation 6-43 assumes that the heat of compression is fully removed by cooling. In practice this is (6-43) After applying Equation 644 and determining the brake horsepower (bhp) for a single stage of compression, the discharge temperature can be determined by Equation 6-25. Dimensionless Reference Numbels In sizing and selecting the type of pump or compressor to be used, a logical correlation is often desirable. The following dimensionless parameters apply to pumps and compressors and are the specific speed and specific di ameter, as defined as follows: N : ' N(Q)o 5 (6-46) H0.75 : specific speed, dimensionless N = speed, rpm Q : capacity of flow rate, ft3lsec H : head, ft-lbrilb. where N, ^ "": where D. : D: H: D(H)o 25 e* (6-47) specific diameter, dimensionless diameter of impeller ot rotor, ft head, ft-lbr/lb. Figure 6-18 shows the dimensionless parameters as originally presented by Balje [3]. This figure is the graphical combination of Equations 6-46 and 647. Past experience often dictates what type of pump or compressor is to be used and in cases of uncertainty or new applications, this figure will be useful in equipment selection. Figure 6-18 must be applied to each stage separately, as each impeller or stage must be chosen with each separate inlet capacity or head for that stage. Rotating Equipment ^. 10 E G I 4 =N '/q/Ha1 D,= DHltalJT' /V O D = Speed, rpm = Flow, fr3/s = lmpeller diameter, 0.3 0.6 ft 30 1 60 Specific speed, r00 3m 6m 1,000 3,0()() 10,000 4 Figure 6-18. The initial selection ofa single-stage compressor is made using the specific speed and specific diameter parameters t3l. Gentffugal Gompressors The centrifugal compressor powered the first turbojetpowered aircraft and is still used today injet engines as a supercharger. The main advantage of the centrifugal compressor is that it produces a large pressure ratio for a single stage of compression, and is easily manufactured. Its advantages over the reciprocating design were cited previously. Most centrifugal compressors are designed so that the gas enters the impeller axially-parallel to the rotating shaft-as shown in Figure 6-19. The gas flow is then changed to the radial direction and is accelerated in a peripheral direction as it moves along the impeller. As the gas exits the impeller, it enters a stationary diffuser where the gas velocity is reduced. This process is repeated at each stage on multistage compressors. Most of the pressure increase in the gas occurs in the impeller and the greatest pressure drop occurs in the diffuser. In multistage compressors, cooling the gas between stages is quite common and many such compressors have water-cooled separators or diaphragms. The polytropic relations, Equations 6-26 through 640, are usually preferred for centrifugal compressor calculations. Figure 6-20 shows why with a schematic plot of the centrifugal compression process on a temperatureentropy graph. Using the adiabatic (isentropic) process, the actual discharge temperature is underestimated Figure 6-t9A. Centrifugal compressor-single-stage. (Courtesy of Dresser Industries, Inc., Roots Blower Operation.) 50 Mechanical Design of Process Sysrems Changing the speed of a centrifugal compressor involves the "affinity laws," which apply to single-stage compressors, multistage compressors when each stage is considered separately, and to multistage machines over a narrow speed range representing no more thm a 15% change in speed. These laws are stated as follows: 1. The developed head (feet) varies to the square of the speeo. 2. 3. The required power varies to the cube of the speed. The capacity (cfm) varies to the speed. Figure 6-21 shows the effect of varying centrifugal compressor speed. In centrifugal compressors a phenomenon known as surge occurs when the compressor capacity is lower than a specific flow rate. This specific flow rate is shown in Figne 6-22 as the "surge limit." The phenomenon of surging is manifested by cyclic vibration of gas flow, which can even result in reversal of flow direction, power requirement, and discharge pressure. The phenomenon normally is associated with excess noise and 1 2. 3 4 5 6 7 8. Nozzte 9. Shaft Cover 10. Oi Fterainer Sub Cov€rSeclion 11 BeartngSrand Bearing Stand Cap l2 Coupting End Beanng SteelShim 13 tmpelerEnd Bearino r'rus Bed nq 4. Or'Ferar-e. -!run Ho-s nq 5eal t5 Sa.t Spaci.g Fing 16 Votute Discharge Casing 17 Intetsection j8. impe|er j9. clideVane Housing ZO. In er Nozzte 21 cuideVane 22 curoevaneLrtdop moe er End ptdl; 23 24. Intet Wearing Fing Figure 6-198. Cross-section of a single-stage centrifugal of Dresser Industries, Inc., Roots compressor. (Courtesy Blower ODeration.) (ideal). Since the polytropic compression process, by definition, is the path connecting the inlet and actual discharge conditions, the polytropic formulations are preferred by compressor manufacturers. This factor becomes extremely important in sizing intercoolers, since using the adiabatic discharge temperature would result in undersizing the cooler. The larger the compression ratio of the machine, the more severe the mistake ofundersizing the cooler becomes. Gas inlet conditions can change and when they do they affect a centrifugal compressor differently frorn a positive-displacement compressor, such as a reciprocating machine. Table 6-1 lists the effects of changing inlet parameters on a centilugal compressor operating at a constant volumetric flow rate and a constant sDeed. Atidd: t2t-tl At*,-r=t2-tl ENTROPY s Figure 6-20. Centrifugal compression process. Rotating Equipment /. :.1 9 t .46 il /. ,lPji: ;.J 2 t{l I k' "y { lsr N t\\ 3A\ a\ 1\ I t; (Vtt I s,l t[t ) >-Kl J;Al un 4 d .t AI *f \\N \E.I NN \'lN \'l N /s A ll N; \ w:, I I .1 '=\\ E E ${ \l il .lI\ 'I sI aE:93Bs3B9BEig9S3P3e9 lstu Stnsslud 1N3?8ld !3/VlodtsuoH R lNlltld ! 8 L 61 I \ \ I = c 5T--r-t N \ ii",-l oU; I ?; 3;t \ 3io- \\ 83q33P339 3Sll ]Unss!rd 1i!ltld !3NrOd3S!08 1tt3U3C ga. _11 -t ;L al,l L ,/a =rl l I I I .J .J :- |t\ 3\ \ t\ :9 \ \ \l \ >, 3 E33P cY3ll I rillu ld 9833P33 t3fl0dlst0lt 1r!llttd ;-n <E .ti ry'E oa. < Or^ =E ltY 5l Mechanical Design of Process Systems 52 Table 6-1 E tects ot Varying Various Inlet Parameters on a Centrilugal Compressor Increasing lncreasing Increasing Increaslng value ot Inlet lnlet Molecular Weight Polytropic n or Pressure of Gas Adiabatic k Pressure Differential Deateases Decreases Decreases Decreases Decreases Decreases Constant Decreases Compression Ratio Inlet Density Discharge Pressure Discharge Temperature Power Required Head Developed Mass Flow Rate r20 COMPRESSOR CHARACTERISTI( I B I , I s80 7 I ... I 460 c0MPn€ss0F SURGE LIM 40 I] I I t t0 0 D 0 r0 20 30 40 50 60 70 80 90 too tn PERCENT CAPACITY Figure 6-22, Pressure vs. capacity for a constant-speed centrifugal compressor [4]. vibration of the compressor and sometimes the compressor piping. Normal surge limits are 40% to 90% of rhe design point, with the higher range (close to 90Vo) being associated with multistage mach ines. Controlling surge in centrifugal compressors is more difficult than in centrifugal pumps, but the following factors ease the problem considerably: 1. Throttling at the discharge flange. 2. Throttling Increases Increases Increases Increases Increases Increases Constant Increases Decreases Decreases Constant Decreases Increases Constant Constant Constant J. Using a variable speed driver, usually accomplished CONSTIiIT SPEED 0 o. Increases Constant Increases Increases Constant Increases Constant Increases at the inlet flange, which is usually more efficient than throttling at the discharge flange. by the turbine driver. 4. Bypassing or blowing off excess gas to avoid surge. These steps will help in alleviating surge problems, but if a variable rate operation is required, the compressor manufacturer should be consulted. Antisurge devices can be incorporated into compressor systems. For nontoxic or inexpensive gases the compressor discharge can be vented to the atmosphere as shown in Figure 6-23. For expensive or toxic gases an automatic anti-surge system can be installed as shown in Figure 6-24. In this type of arrangement a heat exchanger is placed in the system to remove the heat of compression from the vented discharge gas to prevent a loss of compressor performance caused by the temperature rise above the design value at the inlet. Compressor manufacturers use standard cubic (scfm) feet to speciry compressor performance, just as pump manufacturers use water to determine pump performance. The manner in which scfm and altitude correction is handled is discussed later. Impellers are critical in the selection of centrifugal compressors. The three basic types of impellers for centrifugal compressors are shown in Figure 6-25. The conventional closed impeller shown in Figure 6-25 is used for adiabatic heads up to approximately 12,000 ft-lbri lb-. The open, radial-bladed impeller shown in Figure 6-25 develops more head with the same impeller diameter and shaft speed. The open inducer impeller can produce heads up to 20,000 ft-lbrnb*. Whenever the head requirement becomes too great for a single impeller, then one must think in terms of multistage compressors. Each stage of compression of a multistage compressor is treated as a single stage compressor and the same formulations hold. Rotating Equipment Reciprocatlng Compressofs cle. Figure 6-26 shows the reciprocating compressor cycle. This cycle involves this displacement of gas, These compressors normally are sized according to the adiabatic expressions of Equations 6-11 through 6-25. Normal practice in calculations for reciprocating compressors is to use the adiabatic exponent, k = Cp/C,, then adjust the results according to the specific compressor design and configuration. The parameters that affect the compressor horsepower, cylinder capacity, and discharge temperature are length of stroke, shaft rotation hence the classification of a reciprocating compressor as a positive displacement type of unit. The compressor is speed, cooling efficiency, and fixed clearance of cylinders. All of these parameters vary for each given application, but have the same basic cylinder design and cy- drscharge unable to exhaust all gas from the cylinders and the residual gas remaining in the compressor at discharge conditions expands to inlet conditions. This phenomenon is shown in Figve 6-27 . The clearance voiume is usually set by the compressor manufacturer and is specified to match the specified capacity with the standard size compressor unit. Power consumption is not affected by the clearance volume or the volumetric efficiency. The use of "clearance pockets" is used in some compressors to vary the volumetric efficiency. These clearance pockets can be sized to affect the capacity of the compressor, as in Figure 6-28. Power consumption at reduced flow rates is minimized by use of capacity control. The use of a clearance pocket (additional clearance volume) reduces the volumetric efficiency of the compressor, because the re-expanding gas fills most of the cylinder, and the suction valve opens further in the stroke. This mechanism is economical, because the energy expended in gas compression is retrieved in expansion. The clearance pocket is separated from the cylinder by a stop valve. Figure 6-28 shows how varying the cylinder clearance affects the numeric value of the volumetric efficiency at constant compression ratio. The volumetric efficiency for a reciprocating compressor is given by: inlet actual capacity piston displacement Figure 6-23. Manual surge control system for centdfugal (6-48) comPressor. The parameters that affect the volumetric efficiency are as follows: l. flow monitor 2. 3. centrifugal compressor Figure 6-24. Automatic surge control with recirculating bypass. The ratio ofa relative clearance volume, e, which is the ratio of clearance to theoretical displacement expressed as percent. The compression ratio, C., of discharge to inlet pressure. The various exponents of the polytropic curve of reexpansion. Such a curve is shown in Figure 6-29. Here the cylinder is normally cooled by a water jacket or surrounding air. The small volurne of gas that remains in the clearance volume expands and contracts with a cooling surface. Consequently, the re-expansion curve (curve 3-4) is initially steeper than the adiabatic curve (curve 1-2). With continuing expansion ofthe gas, the gas temperature falls below that of the piston and walls, and heat is transferred from these surfaces to the gas. Thus, the exponent of the re-expansion curve (curve 3-4) is variable. For reexpansion oflower compression ratios, Chlumsky [5] Mechanical Design of Process Systems OPEN BACKWARD.BLADED IMPELLER OPEN RADIAL-BLADED IMPELLER CLOSED BACKWARD.BLADED IMPELLER '120 BACKWARD LEANING B LADED IMPELLER e 63 RADIAL BLADED IMPELLER si 100 80 60 (PARAMETER- s % SPEED) (PARAMETER. % SPEED) 40 149 120 EH o o"o, -4, ?E 40 60 B0 100 120 qoRATEO INLET VOLUME BACKWARD LEANING IMPELLER AOJUSTABLE IN LET GU IDE 3 1?O q E 100 E c' ao E BLADED IMPELLER s ADJUSTABLE ol s l ll opi-l RADIAL IN LET GUIDE V WIDE VANES UIDE VAN ES G T 100 100 Vcc g'g .-B d> ro ao so s9 40 20 40 60 80 100 oToFATED INLET VOLUME 120 20 40 60 BO 100 obFATLO l\-ET 120 VOIUMF Figure 6-25. Basic types of impellers for centrifugal compressors. (Courtesy of Dresser Industries, Inc., Roots Blower Operauon.) Rotating Equipment ; P2 = receiver pressure P1 = inlet pressure Compression Stages: O = start @ = comPression @ = discharge @ = expansion O = intake -tl @@ Figure 6-26. Reciprocating compressor cycle. o/o Clearance = Clearance volume (100) Volume Figute 6-27. The effect of clearance capacity. 55 Mechanical Design of Process Systems Clearance volume tts l{ts F 6. It rsl<\ | rls lrlo 115 I 100 o/o Piston DisDlacement Figure 6-28. A clearance pocket (additional clearance volume) reduces the volumetric efficiency of the compressor because the re-expanding gas fills most of the cylinder, and the suction valve opens further in the stroke. | CLEARAT{CE :C 0O5L + O.Smn, WHENE L=STHOKE L-ETGTH voLuME -.---------+ sourcE : cH urMsl(Y l5l Figure 6-29. A pressure-volume diagram of a compresor with clearance (zero flow resistances) [51. Rotating Equipment recommends fof compression ratios of appfoximately 2; the re-expansion may be approximated as an adia- batic process. For the volume, Va-the volume to which the gas expands during the pressure drop from P2 to Pr-we have the expression ., : ". .. /pl, (64e) "" \p,/ For compression ratios of 4 and higher, the re-expansion cannot be considered as an adiabatic process. For these compression ratios the polytropic exponent m (where m denotes the difference between the re-expan- PV' (constant) and the compression PVn (constant). 1.25. For diatomic gases, m The value of the polltropic curve exponent, m, varies sion : with pressure. Chlumsky [5] recommends for a com- pression ratio of 3:4 the following values of m be used: Substituting Equation 6-49 into the expression for volumetric efficiency, we have First stage Second stage ,lt - v"+v"-v4 - -----------=;-- Third stage Fourth stage Fifth and further 'u'(*o]' - stages m:l 20 m : 1.25 m: 1.30 m = 1.35 m:k or These values are given at different pressure levels, as ex- -t -.[(,*i - where e = *vp: (6-50) .utio of the clearance volume. Vo. to the volume swept by the piston stroke. v" ?" = #vp: V^ expression for volumelric efficiency. Equation 6-48, the ratio of gas volume pumped to the volume swept by the piston (compressor displacement) Figure 6-30 shows the graphical solutions of Equation G50 for various compression ratios and exponents of the polytropic curve of re-expansion and clearance values. 34 _L- I9n ist in multistage compressors with the suction of the first stage at atmospheric pressure. The volumetric efficiency for a perfect gas (z = 1), not realistic, is given by 4,r:100-c(cRr/k-1) where 4,, : theoretical volumetric efficiency The volumeuic efficiency for a perfect gas (z with realistic effects. 4":100-cR - c(cR'/k - l) Cs : compression ratio : PzlPr 1@Z 80 c Figure 6-30. Curves for determining volumetric efficiency [5]. (6-s l) : 1) (6-s2) 58 Mechanical Design of Process Systems The difference between Equation 6-52 and Equation 6-51 is that the theoretical volumetric efficiency should be reduced by a value equal to the compression ratio to obtain an actual value for a perfect gas. This is a factor that has been determined from field experience. For a real lv: 100 gas (z * 22: _ cr _ c1(cR)i" _ (6-53) I rnlet and discharge compressibility factors, respec- tively As stated previously, reciprocating compressors follow the expressions for an adiabatic process. The work required for the adiabatic compression of a perfect gas (z : 1) is found by the following expression: w: 1. Operating at high speeds, they can be coupled 1) with realistic effects, where zt, dency has been to increase the cylinder size using a smaller number of cylinders. Multistage reciprocating compressors have the following advantages: PV (-o_JhtJ= 2. 3. fluctuation of torque. The more cylinders, the less the fluctuation of torque. 4. Starting multistage compressors is easier because they have small moving masses and thus can be driven by electric motors with less inertia torque and lighter construction. 5. Variations of pressure and flow velocity in the intercooler or oil separator are less, thus making these 6. -'] (6-54) 7. 6-16 or bv the followine: : u [ll,I- . rl'l [,, * ,l 33.ooo k-l [\Pr/ \ 2., / (P Vrrr44 For an ideal where ga's, 21 P1, Pz : : parts smaller. Machines of various capacities can be manufactured using identical parts, making interchangeability efficrent, The theoretical horsepower may be found by Equation 6o. di rectly at high shaft speeds thus utilizing cheap electric motors. Better balance of inertia forces. The mass of the flywheel, which rotates at high speeds, can be made smaller, resulting in a smaller (6-5s) 22 inlet and discharge pressures, respectively, Multistage compressors are better suited to automatic operation. Gas Temperature for Reciprocating Compressoas The discharge temperature of a positive displacement compressor, a class of which the reciprocating is included, can be predicted by the following expression: psia Vl, V2 = ir et and discharge gas flow rates, respec- tively, acfm In Equation 6-55, the theoretical horsepower may be varied by the following parameters: l 2. 3. 4. lncreasing Increasing Increasing slon rate, Increasing the compression ratio, Cp the specific heat ratio, k the inlet pressure at a constant compresthe actual inlet volume (nat standard vol- ume). Multiple Staging of Reciprocatang Compressors Multiple staging is the compression of a gas from one pressure to another involving more than one step. Each step acts in series with the others and entails a basic machine element. In multiple staging of reciprocating compressors, increasing the cylinder size is less expensive than increasing the number of cylinders, thus the ten- ,r /P'\? t-\Pj (6-56) where t : absolute temperature for any system P = absolute pressure for any system : 1, 2 : k Cp/C', adiabatic exponent inlet and discharge conditions, respectively Axial Flow Gompressors In axial flow compressors, the flow enters the unit oarallel to the axis ofthe shaft and the flow direction esientially remains unchanged from the inlet to the exit of the unit. Airfoil blades are located on the rotor shaft, varying in pitch and size according to the flow conditions. The gas passes through the airfoil blades in an axial direction. Axial flow compressors are used for applications of about 25,000 cfm upward. The formulas for centrifugal compressors apply to axial flow machines. Axial flow compressors can handle greater capacities, which is the primary reason why they have replaced centrifugal com- Rotating Equipment pressors in aircraft gas turbine units. The characteristic curve (head versus flow) for an axial flow compressor is much steeper than for a centrifugal compressor and the surge limit is a function ofdesign capacity. Contrary to a centrifugal compressor, the required horsepower for an axial flow compressor at constant speed and pressure decreases with increased flow Axial flow compressors are not as common in the process industries as centrifugal or reciprocating types of machines. Fans and Blowers Fans and blowers are basically compressors. They fall under two types of compressors-centrifugal and axial flow. If one understands the basics of centrifugal or axial tlow compressors, fans and blowers come easy, for they are less complicated than compressors. Specifying Gompressor Flow Gondltlons Specifying compressor flow conditions is a major source of confusion in applying compressors to process sl stems. There are three basic ways to specify compres- :or flow conditions: l. flow-define the mass flow rate of the gas, Ib./ in the English system and kg/hr-m in the Sl/metric. 3. Actual, or inlet, volume flow-volumetric flow rate of the gas at the inlet conditions, expressed as acfm or icfm in the English system and m3/hr in the SI and MKGFS systems. -1. Standard volumetric flow-the volumetric flow rate of the gas at the inlet conditions expressed in terms of standard cubic feet of gas per minute (scfm) or millions of standard cubic feet of gas per day (MMscfd) in the English system and m3/hr in the SI and MKGFS systems. Mass Iass Flow The method of defining the mass flow rate of the gas h terms of the inlet conditions of the comoressor is far ored by many and is mandatory in calculating gas propenies between stages. Mass flow rate ,?2uJt be specified as either dry gas or wet gas. Ifthe gas, for example, conrains water vapor, this could drastically change the compressor design. One of the problems of using mass flow is not speciffing the flow conditions as a dry gas, which ir reality is a two-phase or multiphase flow. Another disadvantage to using mass flow is that it does not allow one to appreciate the physical size of the sysrcm. An intuitive feel for any system is essential to its successful desisn. Actual or Inlet Volumetric Flow Actual flow rate conditions at the inlet to the compressor is denoted as acfm or icfm-acfm meaning actual cubic feet per minute and icfm meaning inlet cubic feet per minute. The disadvantage to specifying acfm is in the internal components ofthe compressor, e.g., a sideJoad refriger- ation compressor, or in a multistage compressor. In a multistage compressor the previous stage's discharge temperature is a function of the previous stage's compression efficiency, and mass flow rates are better for such conditions. Acfm is best for plotting compressor performance curves, because the impeller is sensitive only to the actual volumetric flow and is insensitive to the gas state conditions. Mass flow and acfm volumetric flow should be used because mass flow is invaluable in communicating with tle compressor manufacturer and in dealing with internal machine flow conditions, and acftn is essential in getting a feel for the physical size ofthe system. The use of mass flow and acftn should counter the disadvantages of both approaches. In computing pressure drop through connecting piping systems to compressors, it is imperative that acfm be used to avoid any confusion in designing the piping systems. Standard Volumetric FIow Specifying gas conditions in terms of standard volumetric flow is done extensively throughout industry. The gas flow conditions are based on standard inlet condi- tions-pressure, molecular weight, temperature, and compressibility-all based on "standard" conditions. Thus, the standard specific volume is constant being that u.,. : "'+J'': constanr (6-57) where z.,a : compressibility factor at standard conditions R: universal gas constant, which is a function of the molecular weight of the gas : P$d : tsld temperature at standard conditions pressure at standard conditions Volume flow is expressed as Q,ta : mV,ro (6-s8) where the standard volumetric flow is directly proportional to the mass flow rate. 60 Mechanical Design of Process Systems As with using mass flow, when using standard flow conditions one cannot appreciate the physical size of the system. And worse still, using scfm does not provide any of the advantages of using either mass flow or acfm. To specify something as "standard" one thing is essential, that all parties agree on what is "standard." Unfortunately, this is not the case with using scfm, as the following "standards" cited by Lapina [6] indicate: The specific volume, V, may be determined by sas\ / ' \ v = z /rl::_:l I::-::l mw / \ where, as before, mw scfm (6-61) \1,14Pl : molecular weight (379.46)mh : (6-62) 60 Metric system English system 1. P",a : 14.7 psia t'ta : 60'F 2. P,u : 14.7 psia t"a:70"F 3. Pd : 14.7 psia t.to : 32'F 1 2. P",a = where mh 101.3 k?a : 0'C P"a : 101.3 kPa t,ra and tsa:15'C rir = moles/hour = (rfi)(mw) (6-63) and finally, aclm: qs _ = [(MMscrdx106)1 1,0 Thus, what is considered "standard," as Lapina [6] writes, varies from industry to industry and engineer to engineer. In the net result what is often gained is confu- where sion. tion) conditions. lie nu)1/f*l*)|/t) t--aOoz, t \-pJ\460 + -' rJ\il .""_*, subscript, s, denotes properties at the inlet (or suc- Equation 6-64 may be expressed as follows: e.=acrm=*-tltjHP*.,-J Properly Specifying Gompressor Flow Gonditions To properly size or select a compressor, the capacityno matter how it is given-must be converted to the inlet conditions. To do this the following expressions are used: (6-6s) where the scfm is based on a dry gas. To convert the standard volumetric flow to mass the following relations are used: flow English system: PrVr tflt _ P2V2 tzzz (6-66) V: P: where t: z : volurne absolute pressure absolute Sl/metric system: Iemperalure compressibility factor rir In Equation 6-59, if z and t acfm : where e_ = rirV ri : V p : : mass scfm fP"o \zd ' ro'\ (6-61) R.td t.ld/ 1.0 for a perfect gas, and P are at standard conditions, then : : : "' p flow rate, lb./min specific volume, ft3llb,,, density, lb./fC PIPING SYSTEilS FOR ROTATING EQUIPMENT (6-60.) For rotary equipment to be functional and contribute to the process system, it must be connected to the system with piping. The science of connecting piping systems to rotary equipment is a relatively new field and has drawn Rotating Equipment the stalwarts of academe to join with industry in solving problems of piping and equipment. The two problems focused upon here are nozzle loadings and pulsation response spectra distributed to the attached piping system by reciprocating machines. Table 6-2 Typical Manufacturer Allowables lor Nozzle Loadings tor Inline PumPs Nozzle Loadings In earlier years various rotating equipment manufacturers would define allowable nozzle loadings as "zero force and zero moments." Such statements were not only ludicrous, but showed how little confidence some rotary equipment manufacturers had in their products. Ultimately, the pipe stress engineer was left to use his (or her) sole judgment to determine if the piping loads were substantial enough to damage the attached equipment. There are several standards for handling nozzle loadings on rotating equipment, and probably the best known are those of NEMA (National Electrical Manufacturers -{ssociation). NEMA provides guidelines for nozzle Ioadings for steam turbines for mechanical drive service. Unfortunately, its guidelines are appiied to every prece of rotating equipment by eager customers and engineering contractors. For example, what is valid for steam turbines is not valid for inline pumps. Because steam turbines are more fragile than most types o[ rotary equipment, using the NEMA standard produces over-conservative designs for most types of rotary equipment. The American Petroleum Institute (API) also has standards for rotating equipment: API 611-General-Purpose Steam Turbines For Refinery Service; API 612Special-Purpose Steam Turbines For Refinery Service; ,\PI 617-Centrifugal Compressors For General Refinery Services; and API 618-Reciprocating Compressors tor General Refinery Service. Applying API standards to nozzle loadings on rotating equipment leads to the argument in which rotating equiprnent specialists claim that the API standards are only intended for procurement purposes, and the pipe stress engineers, having no other guidelines to follow, assert that the API standards are what is to be used in practice. The best criterion for judging nozzle loadings is experience with a given piece of equipment. For example, my several years of practical experience with turbo expanders dictate they can withstand three times the nozzle loadings allowed by NEMA (remember-only for steam turbines!) .{lowables for inline pumps, as above, did not exist a tew years ago. Such pumps were regarded as piping components, e.g., valves, and allowables were considered unnecessary. But "thinning-up" casings to reduce naterial and costs makes such allowables possible, alrhoush controversiai at times. PUUP SIZB ( in) Fa lb Mi= ! Mo= Fo 2x3x6 4000 50 00 4000 3x4x6 6000 60 00 5000 2x3xo 4000 5000 4000 3x4xB 5000 6000 5000 4x6xg 6000 7000 6000 4x6xl0 5000 7000 5000 6x8x! 0 8000 9000 8000 6x6x20 500 0 6000 5000 | 0x1 0x20 800 0 9000 6 12x12x20 r 2000 F *Miao * !{oact 1to,n", F" Mi.o Lo -tb t-1 13000 Li 000 10000 2.g Hhere, F = resultant of actual force applied,lb Mh. u.tuut bending monent on suction nozzle,ft-1b Mou;, actual b€nding nonent on discharge noz2Ie,ft-1b 62 Mechanical Design of Process Systems There are three basic options to solving nozzle loadings on rotating equipment. 1. A detailed finite element study of the equipment. Destructive testing of the equipment. 2. 3. Close interface between the rotating equipment manufacturer and the piping stress engineer. The problem with finite element analyses is who is going to pay for it-the client, the engineering contractor, or the rotating equipment manufacturer? Next, can the rotating equipment manufacturer disclose proprietary information often required in finite element analyses? Destructive testing poses the same question, who will pay for it? The third option-the pipe stress engineer conferring with the equipment manufacturer-is perhaps the most viable of the three, because if the NEMA and API criteria cannot be met, then the rotating equipment manufacturer can at least expect extra loadings and can design for it, if time permits. Thus, the rotary equipment vendor working as a team with the piping stress engineer(s) can help to alleviate most nozzle loading problems. NEMA and API standards are very safe and a piece of equipment that meets their requirements should not have any nozzle loading problems, such as leaks. The problem comes in modular skid construction, where the values provided by the standards are very conservative. Manufacturers often give allowable values for their equipment, and Table 6-2 presents some typical ones. A generalized standard taken from several pump manufacturers' allowable standards is shown in Fieure 6-31. Reasonable nozzle loadings for turbo expandJrs worked out by the author and several turbo expander manufacturers are listed in Table 6-3. Neither Thble 6-2 nor Table 6-3 should be substituted for the manufacturer's allowables, if the vendor has his own. However, the information can be a valuable tool. Rules of thumb often are not only invalid but are often based on special situations that may not be true for every case. One must be extra careful in piping steam turbines, be- cause these units are usually fragile. Example 2-2 in Chapter 2 illustrates a piping arrangement connected to a steam turbine. If expansion joints are allowed, the configuration shown in Figure 6-32 is ideal. PULSATION BESPONSE SPECTRA INDUCED BY RECIPROCATING EOUIPI'ENT Reciprocating machinery often induces pulsation response spectra in attached piping systems. This subject alone is comprehensive to fill several volumes, so we will just outline the problem here. Mno =\fif,,T Mfi Mfl MF" =..ffi*r N/-t+Tlg MFN = greater of Mpo & Mp", where Mso & resultant moments applied at nozzles MRO = resultant bending moment about DM, DM,{ .-.-L FFs = = F"-(0") + = F"y(d") + + M"y+ FDy(dD) + l\4"y tr\arr 12 t\-a i, LtAr'.-"t_ | lL,/..r,r[Fs2" + F!, + F!.]o5 Fno = [F2o* + FBy + FB FD,(dD) = greater of MDy + 110.5. )l ; FzD.]o 5 FRs or l\iDy FFD *&*^!!'*ffi. z.o Figure 6-31. Generalization of forces, moments, and allowable nozzle loadings. - MRs are Rotating Equipment Table 6-3 Reasonable Turbo Expander Nozzle Loadings Nozzle Size (in 4 6 8 10 '|., t4 l6 Nozzle Size (in 4 6 8 10 2,436 3,654 4,870 M, 3,383 4,474 5,074 6,710 6,7& 8,947 6,088 7 ,306 8,524 8,455 10,146 11,838 I 1,184 9,730 l3,513 t7 ,870 2,436 3,654 4,870 4,474 6,088 11,184 M, g9 l too 1 974 1,948 1,948 I,948 ) q)) 1,624 5q1 3,896 2,436 7 )47 3,246 4,869 ?OO too |,623 , 1,948 2,272 aa \ La \ so5 5,189 5,189 &9 r too 1,299 9',14 1,948 1,948 1 t <o7 3,246 3,895 ) 3,895 5 R4? 6,817 7 ,784 d n{q 4,871 5,683 6,486 13,421 15,658 F, 1 too 1,623 t <o7 3,246 ,) <o? 3,246 1,948 1,624 3,383 5,074 3,896 2,436 a )L1 4,869 4,059 5,843 6,817 4,87r ,784 6,486 8,455 10,146 11,838 13,513 I O)) 6,7& 6,710 8,947 ,306 13,42r 8,524 15,658 9,730 r7 ,810 5,189 3,895 A \A\ 5,189 648 972 l,080 F, 1,080 |,659 2,699 r,620 2,488 1,620 2,429 2,699 1,620 4,U9 4,O49 4,147 6,220 10 |,296 |,620 2,160 2,699 3,318 4,147 4,049 10,367 L,944 4,976 4,859 6,748 8,098 6,748 12 2,160 2,699 ? )10 2,268 3,779 3,779 5,806 9,448 50? 4,3t9 4,319 10,798 10,798 4,859 r2,147 12,t47 16,588 18,661 100 4,859 < ?oo 13,497 13,497 20,735 6,486 6,486 6,63s 7 ,464 8,294 9,964 5,669 6,479 7 ,289 8,099 8,098 9,448 12,M\ t4 16,216 16,216 24,912 12 t4 l6 |,948 1 11) t so{ 3,895 4,545 Nozzle Size (an 6 8 l6 l8 20 24 , ') cll5 3,240 3,892 < 1r10 7 5,683 l tlo 9,730 s ?oo 7 s lqq 8,294 14,514 Mechanical Desisn of Process Svstems 64 Table 6-3 (continued) Compressor Discharqe Nozzle Size (in.) 4 6 8 l0 1'' 14 16 18 F, F, 650 |,444 i 974 2,165 2,888 3,610 , 1,300 1,624 I q4q ) , 4 )74 sqq ? ol o PG: lA: G: HEJ: GEJ: 111 Fz Fs M, rqq 2,048 3,072 4,097 5,121 1,624 , 2,436 ? 1,949 soo 3,249 3,899 { n{l 4,548 6,486 5,198 5,838 Planar Guide IntermediateAnchot Guide Hinge Expansion Joint Gimbal Expansion Joint Figure 6-32. An expansion joint arrangement ideal for steam turbines where nozzle loadings must be kept low (almost always the case with steam turbines) and the use of expansion joints is practical. (Courtesy of Pathway Bellows, Inc.) Currently, two methods are used to predict pulsation problems: (a) modeling the system on an analog computer and (b) simulating it on a digital computer. Basically, the piping system is modeled with support and soil stiffness vaiues input at every pipe support as discussed in Chapter 2. Then the system is excited with various forcing functions that represent the reciprocating machine or machines. The piping supports are moved 6,145 ,169 8,193 7 9,202 7 )49. \ My M' Mp 165 3,W7 4,046 6,016 6,070 8,093 t4q 4 at) 4,060 4,872 5,684 A1L 7,5r9 10,116 6,496 '7 a'7q 9,023 t0,527 12,139 6,496 8,662 12,030 14,162 16,185 9,730 13,514 l8, '7 1a-l 181 around, deleted, or added to decrease the amplitudes generated by the forcing functions. This analysis can be done on either an analog or digital computer. There are two methods available on existing computer software that can help head off pulsation problems. These methods arc modal ertaction analysis and time spectra (time history) analysis. Modal extraction is computing the natural frequency of the piping system, after modeling the pipe support and soil stiffness values, and comparing this frequency to that of the shaft speed of the equipment. Time spectra analysis is a transient analysis that basically does exactly what modal extraction does except on a transient basis for every time interval over a specified period of time. In other words, we compute the system's natural frequency for every second over a period of one hour. Over the period of one hour we excite the system with a forcing function that accurately defines the rotating equipment. Figure 6-33 shows a piping system excited by pulsations from a reciprocating machine. A complete investigation of the pulsation frequencies and surge capacity is normally required, which involves the compressor bottles (surge drums), compressor suction header, and suction compressor bottle, the discharge header, and discharge compressor bottle. Two companies are engaged separately in investigating these problems-Southern Gas Association's compressor analog computer at Southwest Research Institute and the Structural Dynamics Research Corporation (SDRC). The compressor bottle (or surge drum) acts as a pulsation dampener. A typical bottle is shown in Figure 6-34. The compressor bottle acts as an acoustic filter designed for all frequencies induced as the reciprocating engine speed varies. The compressor bottle cannot damp out all frequencies, but should store energy generated from the various frequencies and reduce them to produce a relatively smooth and continu- Rotating EquiPment Figure 6-33. Piping system excited by pulsations from a reciprocating machrne' ous operation. Sizing the compressor bottles should be done by a specialist who has worked in this field for several years. In the days before analog and digital simulations, pulsation Droblems were solved (and still are) with orifice plates. These plates were placed in the piping system and the orifice diimeter was approximately 0.53 times the internal diameter of the pipe. These plates' distributed throughout the piping system, acted as pulsation dampeners. Although orifice plates produce huge pressure drops, they are effective in many installations. EXAMPLE 6-1: HORIZONTAL' CENTRIFUGAL PUIIP SYSTEM DESIGN A food processing plant is having a cooking kettle installed to process molasses into refined syrup for breakfast foods. A horizontal centrifugal pump is to be installed next to a fuel tank to supply fuel oil to a burner in rhe cooking kettle. The fuel oil tank is to have a 50 psig Figure 6-34. Typical pulsation bottle (or drum) configurations that act as pulsation dampeners. nitrogen pad because the tank cannot be raised for higher head at the pump. The cooking kettle is 200 ft downstream and 15 ft above the discharge flange of the pump. desired to select and size the burner feed pump shown in Figure 6-35. The discharge pressure at the burner end is to be 40 psig. It is Suction Llne Pressure DloP Fluid : tuel oil TemDerature : 90'F Pressure = 50 psig p 54.725 lb^lft3 : p: 139.53 cp : (139.53)(6.72 x 10-a) : lb./ft-sec e : 0.0018 L:1.0ft Suction line = 3 "dSch 40, Di : 3.068 in Q : 150 gpm 0.094 Mechanical Design of Process Systems cooking kettle Figure 6-35. Hot-oil pump piping scheme for Example 6-1. fuel tank 3" x 1tlz" burner feed pump (r5o)sar lrj, ll]]ry\ s€c/ min \7.479 gal/ \60 (7.393) in.: I t n'in.r/) Entrance and l-3-in.d 90" = 6.51I ft/sec exit: K:1.78 std ell 1-3-in.d gate valve : K : 0.30 : K : 0.14 \-.. * \1,14 l3 068li.,o.srr, rt (s4.72s)l9r N.-=DVP-\ 12l r sec lh ft' - From Equation 1-4 we compute the frictional pressure drop as follows: nur., r0.094;-1\ * r.leY '' : ILL \D -'l- I2e, n-sec With NR" ao, : 969.1, the flow is laminar. From Equation 1-6b we compute the friction factor as follows: 6L 6A f=j_: N*" 969.1 oo, - fro.ooorrts.oorrtzr,,.rrl t (3.068) I :0.066 rsa.72sr K.Values (Velocity Heads) Referring to Figures 1-7 and 1-11 we have the following: llr(6.511)? tt2 ftr zr:z.zr Ap1 : L524 psr sec2 n-111 sec'-ln I\144'o',,l in.2/ Rotating Equipment o,,:[ry.0"'] Discharge Line Pressure DroP The conditions are the same as the suction line except for the following: @.64D'?#Hh) ts+.zzs1$ Line size = 2-in. Schedule 40 for which Di For 1l/z-in. d pump discharge, .";;;m[ : (150)#[+r-J(#,J 2.067 ^."^ -'-Apr = 23.642 : fr-lb. ^. -' sec2lbr 2.982 Psi fr : sec K-Values lor 2-in. Portion 2-2-in.-std90' elbows = K = 0.40 For 2-in. S/40 discharge line, exit:K:1.0 EK: r4o L-200ft -^r,r ^ ^. For 2-in. d S/40 pipe, t, ., ,.oOl 06zr -. -l th. 'il r14.343).. _ft2 I tfr: t [{0.044)r200.0X [-o rS+.225r I .z \raa in.,] fr-lh (ry) - (14.343)A(54.72rk S€C'-lD1 =r/.lR? A* = (o.os+) -.1!. n-sec 63.72 psi : too high-choose a 1 r/z-in. x 3-in' diftuser With 3-in.d Sch 40 PiPe, 64 64 " Nr"_ 1,438.3 _^^^^ (lso)sa, L+fu)(,**) (7.3e3) in.2 (r- K-Values for 11/2-in. Portion : : K 0.78 Entrance From Thble 1-7, for a 2-\t. E*: L : r". x lll2-in. diftuser, K : 0.055 o.srt = [('-ryt tz - l\ I |I @ :0.037 Nt" sec *--L) K-Values for 3-in. d PiPe 2-2-in.-std 90" elbow 3.0 in., d ft =K= 0.54 Dr: t.so exit:K:1.00 1.610 in. e3.642t L,ro.rrr, '- 10.094;.'"' tt-sec hl tt'l = l1!4lr r.zzo.s Nn" : \l2 l I (6.511) a,so.tts, l!: sec (0.094);lb' I n-sec 6A f: - Nn" = 0.066 : 969.125 Mechanical Design oI Process Systems 68 ^_t ^pf_[ (0.066x200.0)(12) (3.068) (s4.7zs)t#(6.51rF + g (,* *-) fr-lh SeC'-lDr Apr : 13.309 psi = use 3-in. { S/40 pipe New K-Values for 1r/2-in. Pipe : Entrance K From Table l-7 K 0.337 : E*: : 0.78 , for a 3-in. x fluid being handled should be Newtonian. Gels, slurries, asphalt, and other non-Newtonian fluids should not be considered with these charts. In handling such fluids a positive-displacement pump is usually required. (Example 6-2 is an illustration of how to handle such a liquid.) To use Figure 6-39 we must convert the absolute viscosity io kinematic viscosity. This is done as follows: use the charts, the r.54] : w: p 139.53 cp at 90'F 54.725 lb/ft3 io.oooozog\tu-r.. (139.53)cpl . --"1 ;;--(32.17) -ij-i:!-. lllz-in. diffuser, rr-lh \ rcp / r(' r.ttt rDr-sec' th 154.'725)= L : 3.0 in.: d : 1.6i0 in. Nn.:1,720.5;f=0.037 rt" z : f12 0.0017-:sec ..^.: ji1Ii0., L (1.610) '-'"rll lQ or ll lh fr2 / rfr? I ,I \s4.125)'+ (23.642f ::- 0.0017 fr-1h )/1t tr " '"m 0.0000107639 Irr V-- | '" sec? \ 144 in.2/ sec'-lDl : sec centistokes i: sec v: 159 .261 centistokes 3.912 Psi Total pressure loss in discharge linc 13.309 3.912 = 17.221 psi Using Table l-8 we make the viscosity conversion from centistoke to SSU as follows: Using the pump manufacturer's curve in Figure 6-36, we can enter data on the Hydraulic Design Calculation Sheet in Figure 6-37 to size the pump. 0.226r-::::=v Apr - - The Effects of Laquad Viscosity on Gentrifugal Pumps From the previous analysis and Figure 6-36 we know the hydraulic performance required of the pump. Before the actual horsepower requirement for the motor and the impeller size can be determined, the viscosity effects of the liquid being handled must be considered. One requirement of a centrifugal pump is that the handled liquid be relatively clean of suspended particles. Obviously, for the same size pump and motor a highly viscous liquid will tax the unit more than would a low viscous liquid. Thus, the viscosity is an important property that affects the horsepower of the pump motor. To account for this, the Hydraulic Institute has prepared charts shown in Figures 6-38 and 6-39 for determining viscosity effects. To rq5 t - 704.695t t : 706 SSU t2 862.832 = 0 Now, looking at Figure 6-39 we see that for 150 gpm, : 82 feet, and 706 SSU we obtain the following coefficients: TDH Cr:056 Ce:090 x Q^*, where QNw is the water capacity at which maximum efficiency is obtained Cu = 0.90 for 1.0 The corrected flow rate becomes ^ Qc = sDm"i... :-: = LO U.YU 150 166.61 = 167 spm Rotating EquiPment O o @ (o <o {) 5lL a 69 70 Mechanical Design of Process Systems Pump Hydraulic Design Calculation Sheet Liquid fuel oil Viscosity at PT. (Pumping Temp.) Vapor pressure at Sp. gr. (.y) at PT. Flow at ambient Operating flow at Design flow at 139.53 0.010 PT temp. PI PT. cp psra o.477 150 150 150 _ Suction Source pressure Static head - APr, line loss Suction pressure - Vapor pressure NPSH avail NPSH avail Discharge 64.7 1.9 1.52 65.08 = = _ gpm gpm gpm - 0.01 65.07 171 t Terminal pressure Static head psia psia psia Piping system Other Discharge press. Suction press. = - - ft ft NPSH req'd = psra psi psi 71-38 psia '1.9 psl 17.221 psi psl 96.201 psia 3'1.12 psra psra 82.017 feet APr discharge = TDH = bhp at Duty Condition =ffi DnpD = = 515hP=5v+hP bhp at Back-Pressure Condition or'c* = Sffi = *AlrffiB = 3.7o6hp - 4hpwithwater Figure 6-37. Pump hydraulic design calculation sheet for Example 6-1. centrifugal pump with a l0-hp motor and a 5-in. impeller. In selecting a centrifugal pump it is desirable for the The total dynamic head becomes Hc TNH R' = 'i-" =;:91. LH U.YU = 9l fr Now, referring to the manufacturer's curve in Figure 6-40, for Qc : 167 gpm and TDH : 91 ft, we determine the pump efficiency as n:63% The NPSH required = 8 ft To correct the efficiency for viscosity we have r" : !C,t = (63%)(0.56) = 35.28% efficiency The brake horsepower for pumping the liquid is bho,,," QHl- = 3,960 4. (167)19l)10.877) (3,960X0.153) - 9.53 ho Referring to Thble 6-4, we see that the next larger mo- tor size is a 10 hp rnotor, thus we select a 3 x lllz-in. required flow rate to fall in the middle of the pump curve. Avoid extreme sides of the manufacturer's performance curves. Select an impeller that is at least two sizes below the largest size available for the pump, because if greater head is later required, e.g. , if additional piping is added to the system, changing impellers is much cheaper and expedient than purchasing a new pump. In the final analysis the design engineer must not forget the potential problem of back pressure that the pump could be exposed to under varying conditions. For example, if the discharge line contained a bypass valve that diverted flow to either the cooking kettle or to a reservoir that collected water, the reservoir would be used if and when the pump and piping system are cleaned with water or a cleaning agent. In this situation the pump would have to be sized for handling water or whatever cleaning is to be used. When the bypass valve is shut off, closing the discharge piping connecting the pump to the cooking kettle, the flow conditions are changed, resulting in a lower TDH. With the same size impeller, as the TDH lowers- the flow rate increases as the curve shifts Rotating Equipment 300 26 150 1(n 80 60 40 30 20 15 10 8 10,000 8,000 6,000 '4,000 3,000 tO 15 20 25 30 40 50 60 70 80 90 100 CAPACITY-GALLONS PER MINUTE Figure 6-3g. Viscosity corrections for capacities of 100 gpm or less (Courtesy of the Hydraulic Institute, Cleveland Ohio.) 72 Mechanical Design of Process Systems i F> *.2 ;t ?E P,Z E< o6 ; Figure 6-39. Performance correction chaft for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.) Rotating Equipment Table 6-4 NEMA Frame Dimensions ___o Ir r--i F- E =q- E -->l H-SIZE HOLE Source: Goulds Pumps, Inc. 74 Mechanical Design of Process Systems to the right in Figure 6-40. Since the impeller does not change, more horsepower is required for the lower TDH. This condition is known as the break horseoower (bhp) required at the end of the pump curve. or maximum flow capacity condition. In our case we have a minimum TDH of approximately 45 feet in which the bhp becomes ' bhp = {llE(s){l 0) 3.960(0.46) : 3.706 or 4 hp with water Thus, we see that our 10-hp motor is sufficient against back pressure. Often, the water condition requires more horsepower, and thus a larger motot than the process liquid condition. The design engineer must be always cognizant of any other fluid that the specified pump may have to handle. : N*" : DVP '4 {lP}n : \tzl (3.78r) a sectes.soer k n" (0.630)- _lb. ' ft-sec 193. t 16 From Equation 1-6b we compute the friction factor as f: -:- Nn" = 0.332 K.Values (Velocity Headsl for Suction Line Referring to Figures 1-7 and 1-11 we have the followtns: En'irance andexit K 1.0 + 0.78 1.78 : 2-4-in. plug valves : : : K: 2(18X0.017) 1-4-in.-90" standard elbow EXAUPLE 6.2: POSITIVE DISPLACEIIENT PUMP DESIGN A positive-displacement pump is required to transfer a adhesive coating mix from a storage tank to a bin in which the mix is dropped onto a nylon sheet (see Example 3-6). The adhesive coating mix adheres the particles together to form roofing shingles. First, we must perform a fluid analysis of the system shown in Figure 6-41. ft-sec (_ri' )tr_ry sec min \7.479 gat/ \60 (t2.73)h.2H*l : :30(0.017):0.510 \-r : 3.781 ftlsec 2.9O2 velocirv From Equation 1-4 we compute the frictional pressure droo as follows: r2) * a.M8l oo, [<o.zs:xgo.ox L (3.068) I k (6.5ilr g fr-Ih mix p : 95.909 lb*/fc :400'F Temperature L : 11.0 ft Pressure = 20 psig a : 150 gpm Suction line = 4 in. Schedule 40 + Dr = 4.026 in. e : 0.0018 p : 938.08 cp = (938.08)(6.72 x 10-4) :0.6:0 lb' 0.612 heads Suctaon Line Pressure Drop Fluid = coating : K LtK (e5.eoe) (rso) sar : Apr : J F-!-,- SeC'-lD1 40.822 psi Referring to the pump hydraulic calculation sheet, Figure 6-42, we summarize our results. From this we compute a total dynamic head (TDH) of 93.76 feet. Past experience indicates that a rotary gear pump of the type shown in Figure 6-43 is excellent for handling high viscosity liquids. The pump manufacturer has the performance curves rated in terms of kinematic viscosity in SSU. Now converting our viscosity to SSU's we have Ssu : ll(.1,]1 635) (938.08X4.635) w/g 195.9091 l-l \ 32.2 l = 1.459.78 SSU L) o o o ro q o r) o to N o o GI o lo o o o to (o o lt ir o o o o o izu(o!@sl- a z E 75 Mechanical Design of Process Systems //t ir Rotating Equipment Pump Hydraulic Design Calculation Sheet mtx adhesive Liquid VG;o;itrt PJ. (Pumping Temp.) 938 \/.^^r at PT qn ^;aee,,ra /_ I .r PT ^r rioriat ihbient temo. Operating flow at 08 cp .1.537 PSla - not lEn j:X PT. {^n,.r PT YI: 150 Suction - APr line loss Suction pressure - = 4.0 psi 2.O psi Static tift - aPr discharge Piping system Other Discharge press. Suction press. psia 8.70 psra Vapor pressure = NPSH avail NPSH avail NPSH req'd Terminal pressure psia 14.7 Source* pressure Static + (headlift) 8.70 psia 6-90 ft ft ri na = - TDH TDH = = 16.70 2g.g1- = = = psia psl 13.74 psi psi 53.75 psia -8.70 psia 67.58 psia feet 2+2=4ltrcqulred lrin NPSH avail > NPSH req'd + 2 lt (oom)ffDHX'v) .. bnp"c = :(38;bX4- bhp at Duty Condition nr"^ _ * (150X67.58X1.537) = n = (3,960Xrr) (3,s60X10) (gpm)CrDHXr) 3g.g4o/o TDH = total dynamic head TDH = discharge press. - suction press 4 = pump efficiency, bhp at Maximum Capacity Condition o/o Figure 6-42. Pump hydraulic design calculation sheet for Example 6-2. We now refer to the manufacturer's performance curves which, in this case, are rated to the viscosity of the service fluid. The closest curve is that shown in Figure 6-41. As a starting point, it is always desirable to start at the middle of the curve. Extreme ends of any pump performance curve should be avoided, as the pump's performance varies significantly at either end of the curve. Thus, we select a very common speed for this type of pump-155 rpm. Now for 150 gpm and 62.45 psi TDH, we find that we need approximately an 1l-hp motor. Solving for the pump efficiency we have bhp = Q(rDH)"y (6-2) (3,960)rt Thus, we have (150X93.76X 1.537) ,, _ ' (3,960)(10) : 0.496 or 49.6% This efficiency rating is quite common with a rotary gear pump handling a highly viscous liquid. Now, refer- ring to Table 6-4 one can observe the classifications of electric motors. From Figure 6-44 we see that the viscosity of our fluid, 1,460 SSU, is about mid-way between the two curves shown. Thus. the required horsepower is between 8 hp and l0 hp. Looking at Thble 6-4 we see that electric motors are lUz hp and 10 hp. To meet our requirements, we select a lO-hp motor, because 7llz hp is too small. Notice that the pump has built-in jacketed enclosures to match the piping, which is hot-oii traced, to keep the fluid in the piping and pump liquid. These jacketed systems are discussed in Chapter 3. In this problem we have a suction lift on the suction side of the pump. It is important to remember that the theoretical height to which a liquid can be lifted at any specified temperature is the atmospheric pressure at the installation site minus the vapor pressure of the liquid at the specified temperature minus the friction loss in the piping. The theoretical and maximum suction lift for water is shown for various temperatures in Figure 6-14. For non-volatile liquids, the maximum allowable suction lift should never exceed 15 in. Hg (7.4 psia) under ideal conditions. For volatile liquids, the maximum allowable Mechanical Design of Process Systems Complete jacketing ol casing, head and rotor bearing sleeve for heating or cooling liquids. Hich ten Dronze for long, rugged service. on head for handling hot liquids. Figure 6-43. The type of gear rotary pump selected in Example 6-2. (Courtesy of Viking Pump Division, Houdaille Industries, Inc.) Rotating Equipment Figure 6-44. Rotary gear pump performance curve. (Courtesy of Viking Pump Division, Houdaille Industries, Inc ) suction lift should never exceed 10 in. Hg. If these val- ues are exceeded, then the suction source should be pres- surized with a neutral gas (inert nitrogen) to offset any pressure that may fall below the vapor pressure of the liquid. At the liquid vapor pressure, vaporization occurs, resulting in possible cavitation and pump damage. A Word About Prlming A positive-displacement pump, like the rotary gear pump in this example. must be primed when pumping low viscosity liquids. This is done by a vacuum device or by using a foot valve. Also, with a low viscous liquid, the fluid drains back to the suction when the pump is idle. For a viscous liquid, like the one in this example, the liquid is retained in the rotary gear clearances and thus acts as a seal when the pump is restarted. However, before restarting the pump, the liquid being pumped should be introduced through the discharge side of the pump to lubricate the rotating components. Since the coating mix is not a clean service, a centrifugal pump is impractical because it cannot handle a nonNewtonian fluid containing suspended particles. EXAilPLE 6-3: CENTRIFUGAL COiIPRESSOR SELECTION A centrifugal compressor is to be specified for a gas plant, which is at sea level. The unit is to compress 3,000 lb./min of gas mixture at 50 psia at 60'F to 150 psia. The gas mixture is composed of 40% ptopane,3O% ethane, and 30% methane. The reduced pressure, P", the reduced temperature, L, the molecular weight, and the specific heat of the mixture is determined as shown in Table 6-5. Using the data in the table we calculate the ratio of specific heats for the mixture as follows: c-. cp. - 1.986 13.08 13.08 - 1.986 (6-10) = 1.18 The compressibility factor for the mixture is determined from the reduced pressure and reduced tempera- ture. Thus. Mechanical Design of Process Systems 80 Table &5 Tabulation of Gas Mixture Properties Mol Gas Propane Ethane Methane o/o P" (psia) t" ("R) Pc 40 44.t0 616 666 .64 246.q 30 30 30.07 708 668 550 9.O2 212.40 343 4.81 31.47 20Q.40 16.07 17 Gas Mixture 659.20 266.40 165.00 102.90 534.30 6.86 3.68 2.54 13.08 Table 6-6 16l Typical Centrifugal Compressor Frame Data* Nominal Nominal Nominal Nominal Nominal lnlet Volume Flow ffi (icfm) Frame (m3/h) l,000-7,000 B 6,000- 18,000 13,000-31,000 D E F *Wite 23,000-44,000 c 33 ,000- 65 ,000 48,000-100,000 this table is based on P .D 50 a (lt-lbl/lbm) 1,700-12,000 10,000-31,000 10,000 10,000 22,000-53,000 39,000-75,000 56,000-110,000 r0,000 82,000- 170,000 534.30 : 4.97 3 : : rp^ : 10,000 ft-lbfnb. 76% |,370 150 50 (6-14) (6-61 - 460.) 1O,339.276 icfm (or acfm at the inlet) 7,700 rpm 54 an, machinery duplicating this table woud be purely coincidenml. t1 Using Table 6-6 from Lapina [6], we find our unit to he a Frame B with nominal values to be as follows: N" 914 1,120 Thus, we have Now from Eouation 6-32 we have n-r /r- r\ T=\-o 1" From above, kr Hp" 44 factor - ,mRt, ----" V: (mw)Pi : 30 36 406 584 : - Y l6 (mm) l), we can use Assuming that we have a perfect gas (z Equation 6-14 to find the average discharge temperature. Using Equation 6-6 the inlet volumetric flow is (0.972x3,000)( l.545x60 (144)(31.47Xs0) 78 78 ^'' P, Pr : 0.972: inlet compressibility ,, 77 77 30 (in, l l,000 7 ,700 5,900 4,900 4,000 3,300 76 76 30 30 30 30 30 lmpeller Oiameter Metric English Computing the compression ratio we have Now from Figure 6-45, we have zr (%) Speed (rpm) (k.Nm/kg) survey of currently available equipment, the instance of :0.076 60 + 460 Rotaiional Efficiency 10,000 10,000 10,000 659.20 t Polytropic ltp' : l'18 = 0'76 Thus, 18\ l0 r0.i6l u.18/ - 0.116 Rotating t? = 0116 tr(C " : (60 + 460X3.0) zz : 0'93 or t, : 590.68'R : v-22 =zt 130.68'F Now, the average compressibility for the gas mixture must be obtained. From above the inlet compressibility, zr : 81 Using the compression ratio and pressure ratio we determine the outlet compressibility factor from the compressibility charts in Appendix E. Thus, from which n-I Equipment ! zz _0.972 + 0.93 _ 0.95 In determining the polytropic head we use Equation 633, where 0.972 Compression ratio, p- rc^r,=:j: P, '-" 150 659.20 = Pz=Pa O.228 of specific heat, k, is k = 1.18 = inlet conditions, which is an approximation. Thus, and the average ratio Temperature ratio, ' = (-*-) (*,{,) [[&J-"*-" -'],u ,_, _tz_560.68 _ r trR,2-L-534-30-'"^< f- compressibility tactor, Z = 1.00 PV/RT \-- ---1 ------J NS \ N \s iK (\ S \ \-"%_ = 0.94 \*r-1 \l I Y x \ '1 0 -tl = riP{ N ilxl/- -x -0.85 BO \t 'oS = 2.00 1.60 401 -t -'---- x 'r;{ I --> = >< \ ii( 0.60 (6-33) >i *al \"'r \ \ 0.92 \ 0.91 0.01 0.02 0.03 0.04 0.05 0.06 reduced pressure, Pr 0.07 0.08 0.09 Figure 6-45. Compressibility curves for very low values of reduced pressure. (Reprinted by 0.10 permission of Chemicql Engineering, McGraw-Hill Company, July 1954.) a2 Mechanical Design of Process Systems from which r: H= Thus, [(t't31srq'01 (8.62r) r(3.0f ,,6 - *- ='ni?l lo' - r] 29,913.143 ft-lbr/lb. N:N"l ' by II : maximum polytropic head per stage, (see Figures 6-46 and 6-47) tttm'ntl I ^ [t26. L krzrrr I L( = ft-lb/lb. ^" r.t: tzo. r lt: r .+zr I )(0.972)(520t | . t8 P,r (6-69) 7 l3l rpm rir H. ' 33,000 : (3,000)(29.913) 4o (33,000X0.76) 3,578.11 hp Using Table 6-7 to determine the mechanical losses, we find that 1.377 : Il,:-"'' rqqrr lo' | r t.ooox r)l The required shaft power is L. : From Figure 6-46, He. (6-10) I \Ho. N.J Lr Using Table 6-5, we have 0 I u ..P \05 N = r7 TOOr (6-68) -q where Ho. 3 The required rpm is The required number of compressor stages is determined : N., '.H- 2.ite = 11,000 ft-lbfnb. (0.02sx3s78.11) (P.rL"*r : P.r + L. : : 99.453 3,578.11 12,000 11,000 10,000 6: I limit for miled yield 9,000 slress mpeIers 8.000 I lNTuw ltl I 7,000 6.000 E 5,000 4,000 3,000 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 0 Figure 6-46. Maximum polytropic head per stage-English system [6]. L., ta + 89.453 :3,667.563hp Rotating EquiPment trl Eru =32 ot 928 u=@ v krzlTt ttl - I'n,J,,'*Lon"N slress impellers Ezc e20 o .- 16 5rz 'i^ 't.0 1.l 1.2 1.4 1.5 1.6 1.7 1.8 1.9 0 Figure 6-47. Maximum polytropic head per stage-metric system [6]' Table 6-7 [61 as a Losses Approximate Mechanical Percery Mechanical Losses, Metric (kw) English (hp) 3 0-2,500 0-3,000 2.5 2 2,500-5,000 5,000-7,500 3,000-6,000 6,000-10,000 10,000+ L,'n (ohl 1.5 7,500+ nents.Thistablewitt'howewr'ensurethatmechanicollossesareconsideredandtiea uselul valuas for estittutinS purposes. The discharge temperature becomes tz = rr(C (" ')/" = (520X3.0)0.r'6 : 590.68'R tz:130.68'F This example demonstrates how centrifugal compressors are estimated. The reader should be cautioned as when to use inlet values for the values of k and z. The value of k will decrease during the compressron process and calculations for the polytropic head and discharge temperature should be made with average values of k, including single stage compressors. Compressor manu- facturers use the inlet values at each stage of compression, but the inlet values for each stage wi1l be different. In calculating the polytropic head, the inlet value of k can be used to achieve an approximate value of the head with some error, because the polytropic head is insensil). tive to the value of k and thus n/(n - The discharge temperature is much more dependent on the value of k. Using the inlet value of k will yield a conservative value of the discharge temperature, generally 25-50'F in extreme cases. For a more detailed discussion of the specification and design of centrifugal compressors, the interested reader is referred to Lapina [6]. Mechanical Design of Process Systems 84 EXAMPLE 6-4: INSTALLING A COMPRESSOR AT ELEVATION 8p00 A reciprocating air compressor is to be installed in a food processing plant, which is at an elevation of 6,562 feet. The desired capacity is 33.3 m3/min. The machine to be used is to be refitted and is of Polish make. From an elevation-barometric conversion chart, such as Figure 6-48, we determine that the atmospheric pressure at the site location is 11.53 psia. The compressor is to compress the air to 7 atmospheres, or 102.87 psia. Now, r' /^- ^. . rP\ ",1 : v : 33.3 rmtn l3s.314 \ m"i 2,000 t4 t3 t? tl Alfr o3ph.ric Pn33ur., lb./sq. in. Figure 6-48. Atmospheric and barometric pressures at various altitudes [7]. I.175.96 cfm Compression ratio: For a multiple stage unit, the compression ratio is Pr = 11.53 psia Pi : 102.87 psia C- : t02 I g l.)J : Cnr = 8.92 > 6. thus requiring Crz LD '', : iP. wnere D. With an intercooler, you must consider the gas pressure drop across it. The minimum horsepower is developed when the ratios of compression are equal in all cylinders. The ideal case is with no intercoolins in which Ludwig [7] suggests Pr P2 P3 _ Pa2_ -z p. cD'.J (6-71) : --:l Dl ^n Pn-r Po3_ p: rol P, P" D1 'o.-l Thus, for two stages, and with intercooling, Po1 (6-73) p. two-stage compresslon Pr=Pr=&:...: - CR3 :.-":[bJ /P. Pr. n -P__,'-4- 4-' (6-'72) where subscripts 1,2,3, ..., n subscript d prime : : (') : \0.5 t_,21 LRI : LR2 : l;l \r (6-74) l,r gas conditions across a cylinder in which I represents the first stage, 2 represents the second stage, etc. Thus, the compression ratio per stage is approximately interstage discharge pressure condition, directly at the cylinder represents the actual pressure to the suction of the succeeding cylinder, which and for the CR:(8.92)05=2.99 Pr : Pdr first stage, 11.53 psia : (2.99x11.53) + rs the interstage discharge subscript f: condition that is reduced bY pressure drop over the intercooler system final discharge pressure from a multistage machine 5 i = 36.94 psia For second stage, Por = (2.99r(11.53) - i: 31.97 psia Rotating EquiPment : Pr 102 87 Psia The discharge temperature the first stage is by Equation 6-5s ta, : bho ' = l ','lu" / \ l.u x '=. -. 11.203,486.3721 l (69.6) Total horsepower : = ttFJ? for k= tu, : (85 : 287 94"F 83 763 hp + 83.763 182.669 or 183 hp 98.906 Equation 6-75 is based on a given compression ratio, Cp, 6rake horsepower/ 106 ft3ld at 14.4 psia and suction ternperature. F,s is a constant which is a factor for the specific gravity of the gas. 1.406, + = 460)(2.99)0'?8e ='147.94"R or tnt 60 based on the discharge temperature from the intercooler. The intercooler cools the air to 90'R which is the suction 54f : tr2 : tiiR"G tvr = (90 + 460)(2.99)0 287 : 48r 46r 754.80'R pressor size is to use the "horsepower per million" iurves depicted in Figure 6-49. The "horsepower per million" ii the bhp/MMcfd and is used to determine the horsepower per stage by the following relation: rr:#:b(MMcrd)F,, (*) = (r.r75.e6){60x24) : I,421,068.508 : (6e.6) = ('-lr;(14_:#. J ( Hi+Hfl : ll- /,,/' "'l I 30 l- 28f 26 lllllll Ratios below 1-4 are subiect v manufacturer foa best dala. ttttttl l- 24Y 22u lo signiticanl etror, consult the 1.5 1.6 1.7 1.9 1.9 2.0 2.1 2.2 2.3 2.4 2.5 Ratio of comPression Figure 6-49. Power requirements for reciprocatmg compressors. (Courtesy of Ingersoll-Rand Company.) q: e8.eo6 hp /,, ..\ t.421.068.s08\j-r:) :1,203,486.372 3o 7/., 69.6 ' For the second stage, MMcfd : 36 (6-75) where F"n is determined in Figure 6-50, converting the acfm to MMcfd we have t 40l*l 9 i.?_ 2 Ml A reliable and quick method to approximate the com- z . $ o2l For the first stage, F., '14.4 psia 50|.- Selecting the Reciprocating Gompressor bhp to Gas ref( 1 294.80"F MMcrd ( 521 intake I temperature to the second stage. Thus kz l: ical efiiciency, 95j 58fiMechan through valv€ Gas vek 561- :3,000 f 'city | (APl equat( rfll The discharge temperature for the second stage is I 1f9_!Jl) _ touo uu / 0.60 1.5 2.0 2.5 3.0 Ratio of compr€ssion, Figure 6-50. Horsepower correction factors for specific grav- ity [8]. 86 Mechanical Design of Process Systems Next, the cylinders must be sized. This can only be done after the interstage temperatures and pressure are defined . Because of the clearance required to allow operation and permit the provision of passages, the piston does not sweep the entire volume of the cylinder. Thus, the actual cylinder capacity is lower than the displacement of the cylinder. Relating this in terms volumetric efficiency we have o (6-i6t LD where 4" Q Cp : : : volumetric efficiencY capacity at inlet conditions, acfm cylinder displacement, ft3/min, where = I4*l I \121 """ \ 144",)E'|" where L = : A"" : ,46" N: A of (6-77) piston stroke, in. ar€r of head end of piston, in.2 area ofcrank end piston (,46" minus the area the piston rod), in.2 of Ipm where - .. [eU:l I zdtzs I C" Cp : : (6-78) cylinder clearance compression ratio ratio of specific heats colllpr€ssibility factors at the suction and discharge conditions, respectively. k= 2., za = For our machine we have the following design: L = 220 mm : in. 9.661 - 500 rpm Dr : 500 mm : : For the second stage, piston rod diameter o,. = piston stroke : : " (";t")' 10e.563 in.2 convenient formula recommended by Neerken [8] is n. = o.si ,2.]2t )lr uu'),roo, .."\= lrogL:t44 : 1,512.514 ft3lmin l\t2 I _ 60 mm : 2.362 in. roe.563 in.? *(.9)' ,n., : 105.181 in.'z + ro5.r8r 'l c":l 10e.563 r44 {gjutl ,roo, l\ t2 I : 538.165 ft3/min The volumetric efficiency is approximated by Equation 6-76 as n, = o.si - (0.lr)[(2 ee)'i - r] = 0.81i :8t.iEa This analysis is only a preliminary estimate of what the compressor design is to be, although in this example, data is drawn from an existing unit. The actual selection of a compressor can only be accomplished using the manufacturer's data on such items as piston displacement and the volumetric efficiencies of the cylinders. The manufacturer's data should always be used before attempting a final design. The actual unit in this example is similar to the one shown in Figure 6-51 . A more detailed discussion on how to specifr and design reciprocating compressors is given by Chlumsky t5l. N 19.685 in. = diameter of first stage cylinder Dz : 300 mm = 11 .81 1 in. : diameter of second stage cylinder For the first stage, : = 65 mm /r o <rs\t r l'- """1 = 304.341 in.2 - &. : \21 304.34r /r sso\' - " \;) = A cosmetic manufacturer of women's lipstick contracted a chemical company to formulate a chemical that satisfies certain specifications. The chemical process engineers determined that piston rod diameter A,- = EXAMPLE 6.5: NAPHTHA PUMP SYSTEiI DESIGN 2.559 in. 2ee. re8 in.' a light cut of naphtha would make an excellent base for the lipstick. The pump in this application can also be used to supply the naphtha to a small chemical company nearby for manufacturing paint thinner. This second application is called the "maximum capacity condition" and will be discussed after the pump is sized for the first application. The pump must be sized for both cases. Figure 6-51. Two-stage reciprocating compressor with a shell and tube intercooler. The first stage is achieved with the vertical .yiinder and the seconl stagi with tiie horizontal cylinder. Pistons of the first stage are aluminum and the second stage are cast iion. (Courtesy of Zaklady Budowy Maszyn, Aparatury im Szadkowskiego, Poland ) In the first case, a rail switcher transports the naphtha to the chemical plant from a nearby refinery The plant only needs to send one 50,000-gallon railroad tank -car once every four months to meet the cosmetic manufacturer's needs. The light naphtha cut is 68"API. The task is to design a pump and hydraulic system that will store and transport the naphtha according to the configuration shown in Figure 6-52. The reservoir is large enough to consider the fluid as having a constant head. The plant manager estimates that the naphtha head required is 12 feet, but wants to have it resulting in a colorless liquid. Next, the naphtha is processed through an activated charcoal filter to remove the fuel odor. Finally, the finished process liquid is loaded into the 50,000-gallon tank car. In the petrochemical industry, the specific gravity of petroleum is given in terms of hydrometer termed 'API. The relation for API is as follows: "4p1 = (6-79) ^tp 7w evaluated. The basic process involves the naphtha passing throush a scrubber that contains caustic soda (NaOH). The ciustic soda removes the straw color in the naphtha, 141.5:131.5 where : l* : .yo the specific gravity of the petroleum product at 60"F the specific gravity of water at 60"F Mechanical Design of Process Systems 88 NLL = normal liquid level 9" g', g', $+-Llj g',g',2,-O,g', 9" 5',-O"r _L Figure 6-52. Pump-piping scheme of light naphlha cut used 10 manufacture women's lipstick. (Example 6-5). 'API, temperature is given of in Figure 6-53. For our case 68oAPI, using Equation 6-79, we have The Flow from the Reservoir to Naphtha Storage llank ro:141 5: 7* 199.5 in which 7o : of liquid is The relationship between the o.zo9 (0.709)(62.4)lb/ft3 : 44.26lbifC at 60'F The maximum pumping temperature is controlled at 90'F. The coldest pumping temperature is at 34'F Since the density is higher at the lower temperature, that is the one used for frictional pressure drop calculations. Thus, referring to Figure 6-53 "Yp : 0'13 45.55 Dresslon: o : rr.os o'(\)" (6-79) The velocity heads on the line from point @ to point @ are as follows: and p: The reservoir is of such large magnitude that the head considered constant, because the railroad switch engine delivers the naphtha regularly to the plant. The flow rate from the reservoir to the storage tank in gallons per minute is determined from the following ex- lb/ff Values of f1 are determined from Figure 1-7. Rotating Equipment Entrance:K:0.78:0.78 18 fr : 18(0.017X2) : 0.612 2-4-in. plug valve: K : Q : 1e.65(4.026) APr Exit:K:1.00:1.00 sr- : LtK 2.392 : [rrrt*J" 177.2 12 x= 38 sec p 3.900 psi 10.5 psi nitrogen pad ) 10.5 psi 6.60 psi = 20.308 ft : ft 12.35 psi - : 1.223 psi I l. 127 psi > 10.5 psi The new flow rate is (1!4|-(a.a67;x A(45.ss)k = lb. 2.640 - : : Adding an additional 26 ft of head we have ft :::- DVp < x + 3.90 0.0884 ft, -. l\Re : ft of naphtha head = (12X0.325) psi This pressure differential will cause the naphtha to be forced back into the reservoir. The number of feet required to deliver the liquid to the tank will now be determined. Since we already have 12 ft in the tank, then wm o 4.46'1 1.223 Ot' 3.90 psi 4 lb./ft-hrl : lb^ 'a = r. r co'\ [2 lcp / z.u ft-hr : : I I hr ft-hr \3,600 Q : 1e.6s(4.026) (#r)0' : 315.317 gpm I sec/ f l rnin I \oo r""/ 93,088 0.0884 ft, Using Np" to check the friction factor, r-05: (rgl* (1-6a) Nr": \ul -2r"r.[+. rt=*) (7.e48rx tb = '7 .948 sec a r" : secr+s.ss1$ - - ft-hr lt* -"*n \:.ooo 165,633 \ sec/ 2.51 (93,088)(0.17875) f: Applying Equation l-6a, r.-"1 0.03198 ft aP. = l(o.o3l9x1o5.83) Now, t-- ,,, 4.026 t12J l- x.l4I | 16 I aP,' = ILL +H t.t \s \ || (1-4) t(Hft I (4s.5s)k $.46if ##j fr-lh SeC"-lDf f: + 0.0319 2.3921 | I -n 'Etc o,,: [rr1*opu"' * r.,nl - rrelr' ft-lb. SeC'-lOf AP1 : 38 ft 3.364 Or' - APr 8.486 psi < = 12.35 psi - 3.864 psi 10.5 psi pad Select a 6-in. { fi -:- Sch 40 pipe : 8.486 psi 90 Mechanical Design of Process Systems To determine the flow rate we must consider what the system is to service. Plant operations dictate that the loading of the tank car must not take longer than four and one-half hours. The rail tank car capacity is 50,000 gallons. We select 4.35 hours, which yields a flow rate of Repeating the hydraulic analysis we have 2-6-in. e : { plug valve: 1e.6s(6.065) (, K Entrance and exit: K 18 fr 18(0.015) : : or--)" = : : Dr : 1.78 0.27 z.oso s9.990 eat 513.107 gpm - \ 12,----7------ -- re | .57 0D(#(*J - a4 1'79 0L') - (0.0884) : []-::Yl(a.8a)(a5.55) N*"=''-'; f:0.01803 t : r 2.6401 rll ssxs zot'?\r++/ ^.^lt+s - ffiAPr:l l(0.0r803x105.83) -r, ^-.U)Urz\rz'z APr = re2 spm will size a centrifugal pump 192 gpm, ,r, lll t*tr-oj Ir r with 192 gpm capacity. For sec 19'ut\,r.rouo, rr ne : We fr 5.700-- 0.2006 hrs {+!!) \60 min/ 4.35 l6.o6sl I I \-rzl I f+ I : 0.032 (from Equation 1-6a) ./ r\ l.---. tt'd'*l@ r 38 ft - APr : 12.35 psi - 0.930 psi : 11.42 psi > 10.5 pst So there is 0.92 psi (11.42 - 10.50) net positive pressure head of naphtha entering the storage tank. or,-ll+.oze\ - l,o.orrt,zr.rtr, * ,.rrnlI | t I I I 't APlo For a 3-in. Iine, _ - Suction Line : 23.313 2(32'2\ = 9.5110t' Naphtha Pump Hydraulics L :100.863 \3,600/ 9.939 Ot' For 4-in. Sch 40 portion of line, i 4.84 ftlsec L: 1.0 ,rnr,l-l\[) \7.47e1 \601 (0.0s130) ft - 8.34 ft/sec ft 3',0168),s.:0,,+s.:s, K-Values Entrance and exit: 1-4-in. plug valve: 4-in. x 3-in. reducer: K : 1.75 K : 0.306 K=0.163 srLtK = 2.219 For 3-inch Sch 40 portion of line: K-Values (18)(0.018) : 0.324 3-in. diffuser: K:Kr:0.055 3-in.d plug valve: K 4-in. x : D*-*" | tl".: I}- 1 2.6401 .. = t32.449 I \3.600/ f:0.0344 re,.'' = APi. = t ol'l4t(t or la5.5sl,t.r,'(,;) o 3791l(o lr /r.oos\ r| 2\32 2) \,2/ 9.175 ntt Rotating Equipment The total pressure drop for the suction line AP. = APlo + APr3 : : AP, ,0,,0, ,r, i1,uti,, I 1) | N^".'"-'; -ttl 0.686 Psi i z 60.708 ft, 4-in. rl Sch 40 aP,, : l(o : 170 : 0.136 4-4-in. plug valves: K : (4X18X0.017) = 1.224 5-4-in. std 90' elbows: K = (5)(30)(0.017) : 2.550 1-4-in. swing check: K: (100)(0.017) 1-4-in. gate valve: K : (8X0.0i7) Entrance:K=1.0:i.00 D" : o^oto t*. = E*' AP1, : APp = AP1, I too.8b3 l(o : ol2'(6oi7o8) |t 14.0261 I r? select + o.oro 2(32.2) r : | 42'7 + 0 460 : - APo 1 887 psi +x+ friction static head (psi) oressure \ = i/ tiquio uupot x : \preisure 'i rpsiarJ minimum pad pressure required, pslg 20.85 + 21.361 psi x = Tpsig Referring to Figure 6-55 and 6-56, we re-evaluate the pump performance. Since the light naphtha cut has a low viscosity 1.427 Ot' For the 3-in. portion of the discharge line, For 3-in. Sch 40 pipe, d1 3.068 rn. : K-Values 4-in. x 34r(*) I 14.7+x+3.557:0.511 + | APlo o.e43l line tAP.rf \arop on suction I where ar,, = + APi. / = 0.032 (from Equation 1-6a) t * 5r(8 The total pressure drop for the discharge line \3,600/ : (45 0.460 Psi ATM. pressure (psia) s+x+s.ssr 2.6401 f 934'(i o) From Figure 6-54, the pump hydraulic design calculation data sheet, it is obvious that the available NPSH is much higher than the required NPSH. This means that the 10.5 psi pressure for the nitrogen pad is excessrve. The minimum pad pressure required is (0.0884) 026'1,+. roo/ It lr.068l I 17 I K-Values 14 132'449 fi = 0.0344 Discharge Line L= e+o[3 = Entrance: 3-in. reducer: K : 0.780 K:0.163 DK = o,sa3 L : 3 ft. bhp : bhe - QHr (6-2) 3,96Ou (19?)(6172)(9 73) (3,960x0.61) = 3.i or a4 hp motor The Maximum Capacity Condition The small chemical company nearby that manufactures paint thinner needs the naphtha only about once a year. However, when the naphtha is needed, it must be delivere.d quickly. Consequently, delivery time is crucial to the client. Mechanical Design of Process Systems Equivolents of Degrees APl, Degrees Boum6, Specific Grovity, Weight Densily, ond Pounds Per Gollon ot 6OF/5OF Degrees Values for API Scale API oil Baum€ Scale !peci6c Values for Baum6 Scale Liquids Lighter Than water W€ight Pounds LblFt3 Gallon D€nsity, per 6 8 ,,. '.: ,.oooo l8 0.9861 0.9725 0.9593 0.9465 61.50 60.65 59.83 59.03 0.9340 0.9218 0.9100 57 0.E984 56.03 20 22 '),4 '].6 28 0.8871 30 0.8762 32 0.8654 0.8550 0.8448 34 36 38 40 42 Lb 8.337 a.xll 8.108 .998 .891 7 7 .043 6.960 0.8235 0.8140 0.8046 0.7955 0.7865 0.7883 49. 50 0.7796 48.62 48.09 47.57 47 .07 46.57 6.499 6.429 0.7778 0.769X 6.359 6.292 0 .7 0.7389 0.7313 0.7238 46.08 45.61 6.160 6.097 6.034 0.7165 5.973 70 0.7022 0.6953 43.79 43.36 42.94 0.6E86 78 80 a2 84 1.1789 0.8537 0.8434 0.8333 6.646 0.7093 l.1600 .679 7.579 7.48X 7.124 0.8642 49.7?. 68 .781 0.8750 o .797 44.64 44.23 7 7 .305 6.799 45.14 1.1069 1.1240 7 6.879 5E .994 .886 0.8861 5l .46 0.7547 0.7467 8.105 7 7 .396 0.81 55 o.7624 60.63 59.80 58.99 7 0.8251 54 l.o74l 56.70 0.E348 o.77tl 8.337 6t.49 0.909r 0.4974 7 l6 oa.s 7.587 7 .490 52.69 52.06 t ''. 1.0140 1.0284 1.0432 1.0584 58.20 .787 0.8063 7X Gallon Specific Gravity Weight Density, Lb/Ftx 0.7609 527 0.7447 E.Zt9 7 54.57 53.90 53.L4 5L.60 .387 .295 .205 7.117 7 7 7 .03r 5t.97 6.947 50.76 50.18 49.61 49.05 6.786 6.708 48.51 47 .97 47.45 46.94 46.44 45.95 45.4E 45.00 5.913 0.7368 0.7292 o.7216 0.7143 o.7071 5.854 5.797 0.7000 0.6931 43,66 43.22 42.40 42.34 41.98 0.6E63 7E.64 80.03 8t .47 42.96 .29 10.512 10.698 10.891 1r.091 11.297 1.3810 | .4078 86.13 67.80 89.53 91.34 |.4356 11.513 11.737 11.969 12.2rO 12,462 I1.64 14.924 r 14.46 t5.302 1.EE31 t17.44 15.699 1.9333 120.57 16.118 5.836 5.774 5.722 5.666 39.84 39.4E 39.69 39.33 38.98 5.306 5.274 5.096 1.2609 1.2832 1.3063 1.3303 77 I 5.454 5.404 95. 1.5591 97 5.506 s.ttl 3E.63 34.29 37 .96 75.99 1.7901 0.6482 5.r41 1.2185 1.2393 9.828 9.990 10.159 10.332 I . E354 5.424 5.186 1. 1983 6.016 5.955 40.80 40,42 40.05 38.79 38.45 38.12 L67r 73.52 14.22? o.6542 39- 13 9.518 106.39 108.95 5.474 0.6275 o.6120 0.6166 0.6112 9.371 7r.20 1.7059 1.7470 41.58 0.6364 0.6306 0.6250 0.6195 0.6140 0.6087 l.t4t7 9.XX8 6.079 6.143 0.6667 0.6604 0.fl3r. 70.10 13.895 6.209 4t .72 41.33 40.95 40.57 40.20 0.6388 8.955 9.0E9 13.244 r3.583 0.66S0 90 92 94 96 98 100 66.99 67 .99 69.03 4.8L4 12.998 0.6731 0.6422 4.697 99.37 101.60 103.94 0.6796 0.6446 65.06 66.01 1.5934 1.619L 1.6667 42.12 88 8.337 8.454 8.574 l9 .2] 47..53 E6 1 0902 6.484 6.413 6.344 44.10 4t.19 62.36 63.24 64.t4 1.4646 1.4948 0.68r9 0.6754 0.6628 0.6566 0.6506 Pounds per Gatlon .s 0.9333 0.9211 7 ,87 54.64 1.0000 0.9859 4.9722 0.9589 0.9459 46 48 64 66 /Ft3 Pounds pef ',' 50.86 50.28 60 Weight Density, r.0000 l0 t7 I4 Gravity s s 0 2 Specific Liquids Heavier Than Water 5. 1r9 ..' ,'. Figure 6-53. Relationship between 'API and temperature. (Courtesy of Crane Company.) '.. Rotating Equipment Pump Hydraulic Design Calculation Sheet Light Naphtha Liquid Viscosity at PT. (Pumping Temp.) Vapor pressure at PT. Sp. gr (-y) at PT. Flow at ambient temp. Operating flow at PT. Design flow at PT. Cut-68' API _cp '1.1 psia 20.85 0.73 gpm 't92 't92 gpm gpm Discharge Suction Source pressure Static head - APr, line loss Suction pressure - Vapor pressure NPSH avail NPSH avail 25.20 Terminal pressure Static head (litt) APi discharge Piping system Other Discharge press. Suction press. psra psi - = = 0.51 'l 28.248 20.85 7.398 - 1.3 NPSH req'd - psi psia psra psia - ft ft psra = = = = 6.313 psi 1.887 20.o 44.90 psl psl psra 28.244 psia psia feet bhp at Duty onpo = Condition bhp at Maximum Capacity Condition Q{l(IPr)1! (3,960Xn) onp"" = QSTrylI1 (3.960Xr) Figure 6-54. Pump hydraulic design calculation sheet for Example 6-5. Referring to the pump manufacturer's pump performance curve, Figure 6-55, we see that approximately 400 gpm is the maximum limit. Using this flow rate we re-evaluate the pump for the maximum capacity case. Suction Line : APr,, 2.200 ps For the 3-in. portion of the suction line, u.- : lq) r8.34r \t92l **. : = r7.37sa sec :275,e35 (,rr4) 032,44s) Referring to previous calculations on the suction side we have the following: u. From Equation 1-6a, : {gl r4.84r = io.o8jl sec \tvtl 1n ORI N^. : l',"i,'l r100.863) \ +.d4 / f: 0.03395 It I 210.062 From Equation 1-6a we obtain f :0.0315 or,. : APr o1le1'"'r * r,nl (4s.ss)(ro.osf(1-L; [ro 2(32.2) rffi I o:'n''lt o' * o rrnl rffi on,. = ['o : 9.759 Ot' AP,:APso*APi. AP,:2.29*a.trt AP, = 2.959 Ot' l 2(32.2) I ..1 E .z =if, = (oEn E \J ii tal 2 ab L,' 9 -r6 G+i \r l, ,i .2 H ...i ^ :>, (J I +: EE O.;\ =! c.r Ei (\t l!,, \J 9?ts E ,6 tr!J o.E : R .b lrt.:i 9X ttc o ooooo o @(o\fc\l Rotating Equipment Pump Hydraulic Design Calculation Sheet Light Naphtha Cut-68o API Liquid Viscosity al PT. (Pumping Temp-) Vapor pressure at PT Sp- gr. (1) at PI Flow at ambient temp. Operating flow at PTDosign flow at P.T. 1.1 cp psra 20.85 0.73 't92 gpm gpm gpm 192 '192 Suction Source pressure Discharge = 21.70 3.559 Static head = APr, line loss Suction pressure = Vapor pressure = NPSH avail NPSH avail NPSH req'd - psia - 0.51 24.744 psl psi psra - 20.85 psia 12.3 1.3 ft 1 Terminal pressure = Static head aPr discharge Piping system - Other Discharge press. = Suction press. = psra - tt bho" = psra psi 1.847 psi psi psra 24.744 psia psia leet 20.'152 63.77 TDH = bhp at Duty Condition '16.7 6,313 bhp at Back-Pressure Condilion (SPmXTDH)(?) bho"" = (3,960X4) (gPm)[rDH)(?) (3,s60)(a) Figure 6-56, Re-evaluation of pump hydraulic design calculation sheet of Example 6-5. Discharge Line Referring to previous calculations on the discharge side we have the followins: v. sec (lryrt (100,863) I' l4ql \ / : zto,o6z 12 AP6n : I --"-'--'\r44l l,or.rrxro.oo,{*} -^^+ 6.610l [+.ozo\ IrrI | ) 6.143 O.' : APo : lgl(8.34): \t>Ll 2(322\ AP6o * AP1, = 6.143 psi + 1.989 psi 3.132 ntt Referring to Figure 6-57, we reevaluate the pump for the maximum capacity condition. Normally, we would use a 9.5-in. impeller, as indiIn this case, being that the application is infrequent, we keep the 8.Gin. impeller. As the flow rate increases with the same size impeller, the TDH decreases and the required NPSH increases. As we see on Figure 6-55, the available NPSH of 4.589 ft is slightly exceeded at 400 cated on the pump manufacturer's curve, Figure 6-55. For 3-in. portion, u, = 2(32.2) I J APlr:1.939 ap,. _ l(0.031sx60.708) -l f:0.03395 APp ^".- ..^ (,1q; 032,44e) :275,e35 Al-h = l------l--------- + U,y4Jl f:0.0315 t.^ : II ,or.rr,,rr.rrrr(r{) l(0.03395X3.0) ^ ^.^l : {g} (4.84) = ro.o8l \t921 N* : *"" r7.37sa sec Mechanical Design of Process Systems 96 Pump Hydraulic Design Calculation Sheet Maximum Capacity Condilion Reevaluaiion Light Naphtha Liquid Viscosity at PT. (Pumping Temp.) Vapor pressure at Pl Sp. gr- (r) at PT. Flow at ambient temp. Operating flow at PT. Desion flow at cp 0.73 pT. Suction Source pressure = 4no 4uu gpm Terminal pressure Psia psl psi Static (lifi) APr discharge Piping system Other Discharge press. Suction press. - 20.85 1.45 4.589 psia psia - ft ft NPSH req'd 16.70 = TDH TDH 8.132 = = = = = bhp at Duty Condition bhp at Maximum Capacity Condition ono"=9## . . Psia psl 6.313 - psia NPSH avail NPSH avail gpm gpm Discharge 21.70 3.559 - 2.959 Static head - APi, line loss Suction pressure = - Vapor pressure = psia 20.85 20.00 51.145 psi psl psra 22.300 24.845 91.282 psia psia feet (oom)fiDHXr) bnp"" = =.(3GbX4. Figure 6-57. Maximum capacity re-evaluation of pump hydraulic design calculation sheet of Example 6-5. gpm. It is suggested that a flow rate of375 gpm be used to avoid cavitation. From Figure 6-55 the actual TDH is TDH : 34 ft The required brake horsepower rs .. ' necting the reservoir to the storage tank, considering the pipe to be 4-in. schedule 40, is as follows: (375 x34.0X0.73) (3,960X0.65) - J'v' ,, _ (3?r " -' (ciL)(=*-] tl+tl \min/ \7.a79 eau \60 sec/ 0.0884 ft? = 9.45j a sec ttv : A 4-hp motor is sufficient for normal and maximum ca- 2.640 pacity operations. lb' lnr fchr From Equation l-6a, Re.evaluation of Reservoit Line f-05 Since the nitrogen pad on the naphtha storage tank was : -lr"c. [+ . decreased from 10.5 psi to 7.0 psi, we must reconsider the line size. With 38 feet of head in the reservoir, we incurred a pressure drop of 3.9 psi, yielding an entry pressure of 8.5 psi. In the back-pressure condition, we need a flow rate of 375 gpm. The new presure drop in the line con- f:0.031s *]-tt) 196,992 Rotating k From Equation 1-4 we have aP.:lLL*rrl \d - or, = m Pv' l2e" 1+s.ss1 : mw : n: N: N, : NPSH : P: Q: R: R: scfm : fiIo olualgrl,o p * r.rnrl I 1r.+s:;,# (*q-J fr-lh SeC'-lDf APr : 5.41f Or' 38ft:12.008psi : : ratio of specific heats CplC,, dimensionless mass, lb. and re-expansion polytropic expo- flow rate, lb-/hr moles of gas m/mw molecular weight mass : polytropic exponent speed, rpm specific speed, dimensionless net positive suction head, feet or psia pressure, psi flow rate, gpm or ft3/sec R/mw : gas constant of a particular gas universal gas constant : 1545 ft-lbr/lb. molestandard cubic feet per minute, ft3lmin-see discussion under standard volumetric With 38 feet of head in the reservoir we have an entry pressure to the storage tank of Entry pressure 97 nent dl = I (r!flr [,o : : Equipment 12.008 psi - 5.411 psi : 6.597 psi Because 6.597 psi < 7.00 psi pad, we keep the 6-in. schedule 40 pipe. The 6-in. line was evaluated for 513 gpm, so it is adequate for the 375 gpm in the 4-in. line. The system is now completely designed for hydraulics, using a 4-in. x 3-in. horizontal centrifugal pump. t: temperature, "F At : temperature differential, oF V : volume of gas or cylinder, ft3 v = specific volume of gas, ft3/1b* w* : weight of fluid whp = *ur". horsepower, hp y : constant : (k_ lyk z : compressibility factor, dimensionless flow Greek Symbols : : €: p: ? 4 NOTATIOl{ acfm bhp = : e: Co : C. : C" : D: D" ghp = = : icfm : J: H actual cubic feet per minute, ft3lmin 6.u1" horsepower, hp clearance volume, in.3 specific heat at constant pressure, Btu/lb-mole-"F compression ratio specific heat at constant volume, Btu/lb.mole-'F diametef of impeller or rotor, in. specific diameter, dimensionless gas horsepower : horsepower delivered to gas, hp head : energy per pound of mass, ft-lb/Ib., or better known as feet of head, ft actual cubic feet per minute at compressor inlet, ft?/min mechanical equivalent of heat: 778 ft-lbrl Btu specific gravity, dimensionless efficiency, expressed as percent ratio of clearance volume to the volume sweot by the piston stroke density, 1b./ft3 REFEREilCES 1. Buchter, H. Hugo, Industrial Sealing Technology, John Wiley & Sons, New York, N.Y., 1979. 2. Dimoplon, William, "What Process Engineers Need to Know About Compressors," Compressor Handbook for the Hyd,rocarbon Processing Industries, Gulf Publishing Co., Houston, Tx., 1979. 3. Balje, O.8., 'A Study on Design Criteria and Matching of Tirrbo-machines-Part B," Trans. ASME, J. Eng. Power, Jan. 1962. The Mechanical Design of Shell and Tube Heat Exchangers A heat exchanger in process systems allows the transfer of energy as heat from one source to another. Witlout this essential piece of equipment most industrial processes would be impossible. There are various types of heat exchangers, each of which is designed to accommodate the requirements of the specific needs at hand. Shell and tube heat exchangers are by far the most common because of their relative simplicity and ability to handle the largest variety of fluids. Plate fin heat exchangers have become quite popular in cryogenic gas services and have largely replaced shell and tube exchangers in gas processing plants. Finned-tube exchangers are used for gas-gas heat transfer, such as in waste heat recovery units, and have gained popularity in the past few years because of emphasis on cogeneration to satisfu energy needs. bottom shell-side nozzle cooled to the desired temDerature. The tube bundle is supported between two iubesheets with baffle plates spaced at intervals to support and brace the tubes. In this figure the tube-side flow enters the tube bundle on the bottom left side and exits on the top left side with a horizontal baffle plate separating the two tube-side flows. This type of arrangement is called a l-2 exchanger, one shell-side pass and two tubeside passes. The various configurations of exchangers will be discussed shortly. Figure 7 -2 shows a reboiler in which isobutane vapor is formed by heating liquid isobutane. This type of reboiler is called a "kettle" type reboiler because ofthe excess area above the tube bundle that is provided for vapor separation. Figure 7-3 shows another type of reboiler where the shell and tube exchanger is mounted vertically alongside a process tower. Here the heat energy of steam is used to separate the propane and propylene liquid into a gasJiquid two-phase mixture. This type of arrangement is common in the gas processing industry and, as will be discussed later, one must be very careful in designing the support(s) for such an exchanger, because of the tubes' thermal expansion. All shell and tube heat exchangers are exposed to internal pressures, tube-side and shell-side. Thus, in the United States the ASME Section VIII Division I Pressure Vessel Code governs the vessel design of such exchangers. The detailed design of shell and tube exchangers is governed by TEMA (Tubular Exchanger Manufacturing ASsociation), whose published standard classifies exchangers by the severity of process requirements. The three classes are Class "R," Class "C," and Class "B" exchangers. Before discussing these classes, we must clariry heat exchanger design types and terminology (see Figure 74). FUNDAMEHTALS OF SHELL AND TUBE HEAT EXCHANGERS A shell and tube heat exchanger is a cylindrical vessel housing a set oftubes (called the tube bundle) containing a fluid at some temperature and immersed in another fluid at a different temperature. The transfer of heat occurs between the fluid flowing over the tubes and the fluid flowing inside the tubes. The fluid flow inside the tubes is said to be "tube side" and the fluid flow external to the tube bundle is said to be "shell side." The simplest type of shell and tube heat exchanger is the type shown in Figure 7-1, where warm kerosene enters on the top shell side. The kerosene's flow path is guided between the tubes by baffle plates and exits at the 99 100 Mechanical Design of Process Systems WARM WATER OUT KEBOSENE IN KEROSENE OUT (cooLED) COOL WATER IN Figure 7-1. An example of a fixed tubesheet heat exchanger. (Courtesy of Howell Training Company.) ISOBUTANE VAPOF LEAVING AT 2OOOF orL ENTEBTNG AT 6650F LIOUID ISOBUTANE LEAVING AT 2OOOF LIOUID ISOBUTANE ENTERING AT I95OF Figure 7-2. This U-tube exchanger represents a kettle type reboiler. (Courtesy of Howell Training Company.) The Mechanical Desien of Shell-and-Tube Heat Exchangers 101 PAOPANE & PAOPYLENE 50% VAPOR - 50% L|OUTD FRACTIONING TOWER (DE ETHENIZERI PROPAN€ AND PROPYL€NE 50% vaPoR 50% LroulD CONDENSATlON Figure 7-3. Iilustration of a thermos]phon reboiler. (Courtesy of Howell Training Company.) PROPANE ANO PFOPYLENE 100% Ltouto Design Classifications of Heat Exchangers Typical shell and tube heat exchangers and their functions are as follows: Reboiler-transfers heat to a liquid to produce a twophase, gasJiquid mixture used in a distillation column. Thermosiphon Reboiler-provides natural circulation of the boiling fluid by a static liquid head shown in Fig- ure 7-3. Forced Circulation Reboiler-a reboiler in which a pump is used to force the liquid through the heat exchanger (reboiler) into the distillation column. Condenser-a heat exchanger to condense vapors by removing heat from a gas. Partial Condenser-only partially condenses a gas to provide heat to another medium to satisfy a process condition. The residual gas is recirculated through a heater and recycled. A common application is using excess steam to heat up a process fluid. A typical application of a partial condenser on a distillation column is to condense only enough liquid for the reflux when the overhead product is vapor. Final Condenser-an exchanger where all the gas is condensed and all the heat is transferred to the other medium. Steam Generator-a device that generates steam, such as a boiler. to provide energy for process requirements. The most classic example is the old stearn locomotive, which is a shell and tube exchanger "mounted on wheels" with the steam used to Dower the locomotion. (This unit is a fired vessel and is not covered by ASME Section VIII Division.) Vaporizer-an exchanger that fully or partially vaporizes a liquid. Chiller-an exchanger in which a process medium is cooled by evaporating a refrigerant, or by cooling and heating with little or no phase change. 102 Mechanical Design of Process Systems HEAD IYPIS 'AIIONARY I A Uff ' " ANO iEA{OVA8TI COVEP tn F WTh B G LONGIIUOINAT Ul(E "4" STATIONARY HEAO 3AFFIE N LIKE BONNST (INIEGRAI COVER) H SIAIIONARY HEAO '1T STAIIONARY HEAD P OUI5IOE PACKED FTOA'ING c 'IFAO CHANNET INTECFAL WITH IU8E. SHETT AND RE/nOVASIE COVTR s J T N PUIT TIiROUGH FIOATIIIG HE^O ''UBT- CHANNEI INIEGRAL WIIH 5HEET ANO REITOVABLE COVER K U D x SPEC|AL hICH PREsSURE CTOSUI€ Figure 7-4. Nomenclature of shell and tube heat exchangers. (@1978 by Tlrbular Exchanger Manufacturers Associauon.) These classifications are the major types of services that shell and tube exchangers provide in the process industries. Process requirements dictate the type of design to be used. Figure 7-4 shows some of the major types of con- struction. The standard TEMA classification of ex, is to use the shell identification and number with the exchanger designation type. For example, an 18- 150 BEM is an exchanger having an 18-in. shell with 150 tubes, a bonnet (integral) cover with a fixed tube-. sheet at one end (B in Figure 7-4), a fixed tubesheet and a stationary head at the other end (M), and a one-pass changers shell between both ends (E). Fixed Tubesheet Shell and Tube Heat Exchangers Fixed tubesheet shell and tube heat exchansers are the simplest of the shell and tube designs. They ionsisr of a tube bundle attached to a tubesheet on each side of the tube bundle. The tubesheets are welded to the shell pro, viding an absolute seal to prevent the shell-side fluid from leakage. Often the tubesheets extend beyond the shell diameter and have flange bolt holes that allow the tube heads to be bolted to the tubesheets. In fixed tubesheet exchangers, tubes can fill the entire shell to achieve maximum heat exchange (of course, this The Mechanical Desisn of Shell-and-Tube Heat Exchansers also increases shell-side fluid pressure drop) such that tolerances between tubes are minimum. However, this factor limits the shell-side fluid to a relatively clean service, because the exterior of the closely-packed tubes cannot be mechanically cleaned or inspected. Another limitation to the design is that there is no allowance for thermal growth of the tubes , except if an external expansion joint is used, which is quite common for this type of exchanger. Normally, single convoluted bellows are used since the maximum temperature differential is 200"F and the cyclic loading is insignificant. Tube-side headers, channel covers, and internals of tubes can be cleaned quite easily and the shell side can be cleaned only by circulating a cleaning fluid or backwash- ing. U.Tube Shell and Tube Heat Exchangers U+ube shell and tube heat exchansers consist of one tubesheet with tubes bent in a U-shipe atrached to rhe single tubesheet. This type of exchanger is used for large temperature differentials where there is a lot of tube growth. This type of design allows for easy access to the shell side of the tubes and removal of the tube bundle. The inside of tubes must be cleaned with soecial tools and then only when the bending radius is fairly large. This tne of design is also very suitable for chemical cleaning. The maximum number of tubes per tubesheet is less than the fixed tubesheet design beciuse of the minimum bending radius required to form the U-shape. The Utube design is also very applicable to high-pressure servlces. Floating Head Shell and Tube Heat Exchangers This type of shell and tube heat exchanger has a floating head that is designed to accommodate thermal expansion of the tubes and to provide access to the tube-side and shell-side exchangei components. This type of design is expensive and its use should be considered against other possible designs. Packed Lantern Ring Exchanger (Figure 7-5a). This construction is normally limited to design tempera- gland tollower floating-head cover (B) Outside-packed floating head exchanger (A) Packed lanternring exchanger flange floating-head cover backing ring shell f tlange gasket shell cover floating tubesheet floating tubesheei floating-head cover gasket (C) Internal floating head exchanger 103 (D) Pull-through lloating head exchanger Figure 7-5. Several configurations of floating head exchangers. 'lO4 Mechanical Design of Process Systems < 370"F and design pressures < 300 psig. This type of design is used only for mild services, such as steam, air, low viscous oils. In this design the shell-side and tube-side fluids are sealed by separate packings which, in turn, are separated by a lantern ring. The lantern ring fits between the packings that separate the shell and tube-side fluids and normally contains weep holes that accommodate any leakage through the packing. Such leakage, which is passed to the outside and drops to the foundation below, will not cause shell and tube-side fluids to mix. The tubesheet must be designed such that it is large enough in diameter to encompass the packingJanternring ensemble and differential thermal expansion of the tubes. Occasionally, a skirt is attached to a thin tubesheet to act as a bearing surface for the packingJantern-ring tures ensemble. Outside-Packed Floating Head Exchanger (Figure 7-56). Rings of packing contain the shell-side fluid, which is compressed by a gland follower that is guided by a tube sheet skirt. The skirt is integral to the floating tubesheet. This removable-bundle construction allows for differential expansion between the shell and tubes. This design is normally limited to 600"F and 600 psig, which is one reason why it is the most commonly used removable-bundle type exchanger in the petroleumchemical industry, even though usage has decreased over recent years. Internal Floating-Head Exchanger (Figure 7-5c). This design consists of an internal floating tubesheet held by an internal backing ring, which is bolted to an internal floating head cover. The internal backing ring and internal shell cover are beyond the end of the shell containing the tubes. To remove the tube bundle, the shell cover, split backing ring, and internal floating head cover must be removed. The internal floating head cover acts as a return cover for the tube fluid with an even number of tube-side passes. with an odd number of tube-side passes, a nozzle must be extended from the in- ternal floating-head cover through the outside shell cover. Clearances between the shell and the outermost tubes are 1rla in. for pipe shells and 17re in. for mediumsized rolled plate shells. This design is more suitable for higher shell-side temperatures and pressures than for pull-through bundle types of construction. This design has been used extensively in the petroleum-chemical industry, but there has been a decline of use over the past few years. Pull-Through Bundle Floaiing-Head Exchanger (Figure 7-5d). This design consists of a floating head directly bolted to an internal floating head cover. The tube bundle can be removed without removing either internal floating head cover or shell cover when bundle is pulled out an opposite end of shell cover facing internal floating head. This feature reduces down and maintenance time during inspection and repair. The clearance between the outside of the tubes and shell inside must be sufficient to allow space for both the gasket and bolting at the internal floating head cover. This clearance is usually twice that required for the split ring design used in the internal floating head in the previous section. This type of design is normally limited to services where leakage of the internal gasket is tolerable. With an odd number of tube-side passes, a nozzle must extend from the internal floating-head cover through the shell cover. The number of tube-side passes is simply limited by the number of tubes. This design is generally suited for lower temperatures and pressures than that of the internal floatine head exchanger described earlier. General TEIIA Exchanger Glasses-Rr Ct and B There are three basic categories of shell and tube heat exchangers in TEMA-Class R, Class C, and Class B. The difference in class is the degree of severity of service the exchanger will encounter. Descriptions of the three classes are as follows: Class R C/css C includes heat exchangers specified for the most severe service in the petroleum-chemical processing industry. Safety and durability are required for exchangers designed for such rigorous conditions. includes heat exchangers designed for the gen- erally moderate services and requirements. Economy and overall compactness are the two essential features of this class. Class B are exchangers specified for general process service. Maximum economy and optimum compactness are the main criteria of design. Rubin [3] described the TEMA classes of exchangers in terms of the various components and how they vary from one class to another. This data is given in Table 7-1. Ludwig [4] described various types of heat exchangers, their applications and limitations, which include shell and tube exchangers as well as other types. This data is -oresented in Thble 7-2.provide a comprehensive view of tbles 7-1 and 7-2 and their applicaof heat exchangers various types the of the on the components can now focus tions, so we shell and tube design. Table 7-1 Comparison of TEMA Classes R, C and B Exchangers [31 Para- graph Toplc 1.12 Definition 1.51 2.2 2.5 Corrosion allowance on carbon steel 3.3 4.42 4.7 | 5.11 5.31 TUbe diameters Tirbe pitch and minimum cleaning lane for the generally severe requirements of petoleum and related processing applications. r/s inch for the generally for g€neral process moderate requirements of comrnercial and general process applications. sefvrce. 3h, 1,1\+, 1tlz, and 2 R+%, inch od 1.25 x tube od. r/+ inch R+5/E tubes may be lane. located 1.2 8 inch tabulated 6 inch tabulated tho inch 3/s, rlz, and 5/e xtube od r/ro inch R*5/e R*lane may be 3/re inch in 12 inch and smaller shells for s/s and 3/+ tubes. Minimum shell diameter Longtudinal baffle V+ inch minimum t/8 inch 3/s inch % inch in 6-15 inch r/+ alloy, hch CS thickness Minimum tie rod diameter Floating head cover cross-over area Lantern ring construction 6 inch tabulated. Va inch alloy, r/+ inch carbon steel r/+ inch 6-15 inch shells. shells flow 1.3 times tube flow area Same as tube 375"F maximum. 300 psi up to 24 inch diam shell 600 psi maximum. (same as TEMA R) Metal jacketed or solid metal (a) internal floating head. O) 300 psi and up. Asbestos permitted for 300 psi and lower (same as TEMA C) 150 psi for 25-42 shells a.rea Same as tube flow area irch 75 psi for 43-60 inch 6 .2 shells Gasket materials Metal jacketed or solid metal for (a) internal floating head coYer. (b) 300 psi and up. (c) all hydrocarbons. 6.32 7 .131 pressures. Peripheral gasket contact Flatness tolerance No tolerance specified. No tolerance specified. surface specified. Outside diameter of the tube. 0.75 xtube od and smaller. (same as TEMA C) Minimum tubesheet thickness with expanded tube joints .44 Ti.rbe Hole Grooving .51 7.7 Length of expansion 7 7 Ttrbesheet pass partition grooves 9.3 9.32 9.33 9.1 Pipe Tbp Connections 10.1 Pressure Gauge Connections Thermometer for 1 inch z/s TWo grooves inch for 1% od inch for 1tlz od 1.25 inch for 2 od Above 300 psi design (same as TEMA R) Smaller of 2 inch or pressure: above 350'F design temp.-z grooves Smaller of 2 x tube od or (same as TEMA R) tubesheet thickness 3/re inch deep grooves Over 300 psi rAo inch (same as TEMA C) I required 6000 psi coupling with bar stock plug required in nozdes 2 inch & uP. lequired in nozdes 4 inch deep grooves required or other suitable means for retaining gaskets in place 3000 psi coupling (shall be specified by (shal1 be specified by purchaser) Nozzleconstruction no reference to flanges same as Minimum bolt size 3/a t/z inch recommended, inch (same as TEMA R) purchaser) 6a up. Connections 3000 psi coupling with bar stock plug TEMA R smaller bolting may be used (same as TEMA R) All nozzles larger than one inch must be flanged. 5/s inch 106 Mechanical Design of Process Systems Table 7-2 Selection Guide Heat Exchanger Types l4l Relatlre Cost Type Deslgaatlon Fixed Tube Sheet SlEnlficant Feature Both tube sheets fixed to shell Applications Best Sulted Llmltatlons Condensers; liquidJiquid; Temperature difrerence at extremes of about 200" F. due to differential expansion 1.0 Jnternal qasketsofter danqer t.2a Bends must be carefully 1.08 gas-gas; gasliquid; cooling and heating, horizontal or vertical, reboiling Floating Head or Tube Sheet (Removable and nonremovable bundles) One tube shea "floats" in shell or with shell, tube bundle mav or mav not be removable from shell. but back cover can be rej moved to expose tub€ ends. U-Tubei U-Bundle Only one tube sheet required. Tubes bent in Ushape. Bundle is removable. Kettle Tube bundle removable High temperature differedtials, above about 200' F. extremes; dirty fluids .equiring cleaning of inside as well as outside of shell, hori- zontal or vertical. High t€mperature differentials. which migbt require provtslon tor exDanslon ln 6xed tube units.elean service or easily cleaned coodi tions on both tube side and shell side. Horizontal or vertical. Boiling, fluid on shell side, as U-type or as relrrgerant, or (r!9engagrng. flu-id in floating head. Shell €nlarqed to allow boiling and vapot proc€ss fluid beioe vaporized. Chilline or co6lini of tube side Co[structlon of leakine. Corrosivenesjoi fluids on-shell side floatins parts. Usually confined t-o horizontal units- made or mechanical damase and danqer of ruDture ctn result. fube side'velocities can cause erosion of inside of bends. Fluid should be free of susp€nded particles. For horizontal installation. Phy.sically large for other applcatrons. retrig;rant evapora- tiofl on shell sideDouble Pipe Each tube has own shell forminq annular for aliy she-il side use soace fluid. ijsu- externally finned ba[ks for larger applications. Especially suited for high prcs- sures in tube above 400 psig. tuDe. Pipe Coil Relatively small transfer area service. or in Pipe coil for submersion rn coll-trox ol water or with water is simplest type of exsprayed Services suitable for 6nned tube, Piping-up a 0.8-1.4 large numDer olten r€qurres cost and space, Condensins, or relativelv low heat l;ads on sensiblir transfe!. Transfer coefiicient is low, Condensing, relatively low heat loads on s€nsible trans. fer. Transler coefiicient is low, takes up less space than plpe co{. 0.8-1.1 Condensing, high level heat transter. Transfer coefiicient is low, if natuaal convectiol cir- 0.8-1.8 requir€.s, space lt relatively 0.5.{}.7 l.arge heat loaq rs hrgh, changet. Open Tube Sections (Water cooled) Tubes require no shell, only end headers, usually long, water sprays over surface, sheds scales on outside tubes bv exoansion and contraciion.tan also be used in water box. Open '(AirTube Sections Cooled) Plain or finned tubes No shell required, only end headers similar to 'w'ater untts. culation, but is improved with forced air flow across tubes. Plate and Frame Composed of metal-form- ed thin plates separated by gaskets. Compact, easy to Viscous fluids, corrosive fluids slurries, High heat transfer, clean. Not well suited for boilins or condensing; limit 350500'F by gaskets. Used for Liquid-Liquid only; not 0.8-1.5 gas-gas. Spiral Compact, concentric Cross-flow, condensing, Process corrosion, suspended materials. 0.8-1.5 Chemical resistance of Clean fluids, tubes; no tube fouling. condensing, Low heat transfer coefrci- 2.0-4.0 plates; no bypassing, high turbulence. Small-tube Teflon heating. ln C.arbon Steel The Mechanical Design of Shell-and-Tube Heat Baslc Gomponents of Shell and Tube Heat Exchangels There are various components to a shell and tube heat exchanger, but the following are the essential ones: 1. Tubes 2. Baffles 3. Tie rods 4. Tubesheets Tubes There are basically two types-finned tubes and bare tubes. Finned tubes have external fins mounted by various mechanical means. The necessity of having external fins mounted on tubes is to provide more heat transfer area and thus more heat influx to the tube fluid. Finned tubes are most common where there is a gasJiquid or gas-gas transfer of heat with the gas always being external to the tubes. Typical applications of finned tubes are waste heat recovery exchangers, waste heat boilers, gas turbine regenerators, and air-cooled exchangers. Examples of some finned tube designs are shown later. Plain or bare tubes are the most common in shell and tube design. These tubes come in two basic types-solid wall construction and duplex construction. The duplex design consists ofa tube within a tube in which the outer tube is mechanically drawn over the inner tube. The solid wall tube is what the name implies, a simple tube of solid wall construction. Tubing is available in almost as many materials as piping and is available in standard gauge sizes listed in Table 7-3, along with diamerers and section properties. In applying the U-tube exchanger design, tubes must be bent 180'. Thble 7-4 lists the recommended minimum bend radii. Baffles Baffles serve several functions and consequently the design of each is dependent on its purpose. Baffles can act as: l 2. 3. Structural supports for the tubes. Dampers against vibration. Devices 1o control and direct flow Datterns of the shell-side liquid. Baffles as Tube Structural Supports. Like piping, tubes behave as structural beams and consequently will develop excessive deflection, or sag, if left unsupported. Baffles act as the structural supports in the shell and tube exchanger. Another structural function of baffles is to add stiffness to the tubes so that each tube. in effect. is Exchangers 1o7 constrained at each baffle. Thus, the hole in the baffle, being larger by varying amounts than the outside tube diameter, acts as a limit stop for the tube. In piping mechanics (see Chapter 2) a limit stop is a restraint that limits the amount of pipe (in this case, tube) movement to the distance between the hole diameter and the outside diameter of the tube. In other words, the tube can translate in the lateral direction perpendicular to the tube axis only by the amount of clearance between the tube OD and the hole diameter. Translation is mentioned instead of rotation because even though the tube rotates, it is insignificant. Thus, the baffle hole acts as a limit stop and prevents lateral buckling of the tubes when they are induced to thermal expansion by temperature differentials. In this sense the tubes are much stiffer and stronger than they would be without the baffle supports. The consequences of strengthened tubes affect the integrity of tube joint connections in the tubesheets and this will be discussed shortly. We see from this discussion that the baffle plates act as both structural supports and as buckiing stabilizers. Baftles as Tube Vibralion Dampers. Figure 7-6 shows baffles of circular rings with rods that run vertically in the first two rings and horizontally in the second two rings, thus damping vibration much in the same way as helical vortex strakes on stacks (Chapter 5). The rods break up forming vortices that induce vibrations, a phenomenon discussed in Chapters 4 and 5 called vortex shedding. The rods also reduce turbulence to below res- onant levels of the natural frequency of the tubes and they reduce fluid elastic vibration. Baffles Conlrol and Direct the Flow Pattern of the Shell-Side Fluid. There are various types of baffles that direct and/or control the flow ofthe shell side fluid. Fieures 7-l and 7-2 are examples of baffles guiding or d'irecting the flow in the vertical direction. Fig]ure 7-7 shows baffles diverting flow in the horizontal direction. The flow direction is a function of the orientation of the baffles and their respective geometries and is dependent upon process requirements. The arrangement in Figure 7-7 is said to be vertically cut and the arrangements in Figures 7-l and 7-2 arc said to be horizontally cut. Often, process conditions require the shell-side fluid to flow horizontally, parallel to the longitudinal axis of the exchanger. This arrangement, called a longitudinal baffle, is shown in Figure 7-8. Figure 7-8a shows a twopass shell-side arrangement and Figure 7-8b shows a four-pass shell-side arrangement. The baffles control the flow in the sense that both the direction and flow rate are dependent on orientation and number of passes, respectively. With the same inlet flow rate, the fluid velocity 108 Mechanical Design of Process Systems Table 7-3 Characteristics of Tubing Sq. tt. Sq. Ft. o.D. Y. tt B.W.C. Gage 22 24 2? yt t8 % % Yl 20 22 ?4 h l8 20 v, 22 % % t2 % vs % % l3 l4 l5 Sq.Inch .028 .018 .016 .0360 .0313 .049 .035 .028 .0603 .0731 .0799 .0962 .09E2 .0982 .0725 .0798 .0835 .022 .0850 _0982 .0E57 .065 .1075 .1269 .1309 .035 .028 .t452 .1309 .1309 .1546 .1309 .109 .095 .1301 .14E6 .1655 .1817 .1924 .2035 -049 .0E3 17 .05E x 20 t/. l0 .134 .1E25 .t20 .2043 .109 .063 .2223 .2463 .2679 .0t2 .2884 .055 .056 .049 .035 .3019 .3157 .165 .134 \2 % % 1A l3 l4 l5 t7 l8 20 I .0508 _0539 .0560 .022 l6 II lengrtl .0655 .0655 .0655 .0555 .072 .065 l8 l9 LenAtlr .0295 .0333 .049 .042 .035 ',| WGisht len8th Tube .095 .218t -2298 .2419 .1636 .1636 .1636 .1636 .0570 [21 Steel Tubo t.D. Ssctlon .194 .054 .045 .26 .00012 .00011 .2t4 .040 .218 .00009 .00008 ,lil .277 .00083 .00071 .0810 .0E?4 52 t.2t4 l.16E LI46 .0195 .0159 .0t31 1.354 .0502 1.233 .0374 .0305 .00064 .0829 56 56 _l164 94 .1556 .1606 _305 .319 .00045 .083 .331 .00036 .0969 .302 .0022 .00E5 .1052 .236 .0018 .l t26 .l162 .@72 .171 .370 .402 .430 .00t4 _0056 .0012 .0046 .1066 .1139 .602 .537 .019i .t202 .479 .425 .388 .0061 .0057 .0053 .0049 .0045 .l4I .350 .303 .407 .435 .459 .461 .495 .509 .0042 .0037 .0033 .t636 _1453 .262 .221 _555 .0028 .1963 .1963 .1953 .1262 .1335 .884 .809 .482 .0129 .510 .0122 .1393 .1466 .1529 .748 .532 .560 .t587 .520 .1623 _1660 .4t6 .0116 .0107 .0098 .0089 .0083 .367 .t963 46 .104 .1380 .1963 .1963 .1963 .9792 .t27 .1636 .1636 .1963 .00098 ,0036 .0029 .0025 .0020 .14t6 .3339 .1953 .3632 .1963 .\107 .1780 .3525 .4?AE .4536 .4803 .2618 .1754 _2618 .2618 ,2618 .51t3 .5463 .666 .592 .428 .269 .521 .541 .5E4 .606 .620 .634 .652 .680 .0076 .0163 .0170 .0155 .0145 .0131 .0118 .0105 .0091 .12t3 lt4 .\227 125 .\248 134 .1649 .167r .1864 .1903 .1938 .1971 .I993 198 227 241 232 258 283 300 .2016 3V .2043 340 .2068 .2089 358 377 .0344 .0326 .0309 .0285 .2229 285 319 347 .0262 -23/6 .24t0 .0238 .0221 .2267 .2299 .2340 .2433 -2455 384 416 450 471 .649 .6390 .26t8 .2361 20 .035 .6793 .2618 .2435 .496 .360 tt/t 1 t% t% .6221 .3272 .2330 .32t2 _2409 .890 .920 _\425 .6648 2.057 1.921 .0E90 l0 .180 .165 .134 _0847 .1355 .t20 .7574 _25t I.59E .982 1.010 .0741 .u86 .8012 .8365 .0666 1.a32 .4612 1.094 .3272 .3272 .3212 _3?t2 .3272 .3272 .3212 .327? .3089 .456 Ll80 .0579 .0521 .0426 ,0334 .0247 .1100 .1027 .0926 .0833 .06E2 .0534 .0395 Ll92 _3927 1.232 .3927 .3927 .3921 .3225 .3356 1.955 1.291 1.398 l.6lE t.2E? .3492 1258 .996 1.334 l_370 .0755 _1008 .5079 2,410 1_760 .3144 .6660 2.201 t.934 t.182 .2904 _6697 3890 .4739 .2586 .3141 .2904 .2586 .6144 4014 _4801 1.6s9 .2300 .2300 ,6784 1t/t II lYa t2 tYl ty. l3 l4 t% t6 t)A t\ IE 20 .083 .065 ,049 .035 t\t tw t\t l0 .134 \2 .i09 tk l4 l6 z lt z 2 2 t2 l4 .109 .095 .0E3 _8825 _9229 .9852 '\.042 .065 t.471 .120 2.433 2.494 2-513 2.642 .t09 .095 .0E3 .5236 .5236 .5236 .2644 .?t02 1,448 1.329 .2715 Ln3 .2E36 1,033 _823 1.060 1.0E4 1.120 .629 1.t52 .2932 .3587 _4606 .1665 1.810 1.834 .103 l_186 1.155 .089 L125 .065 1.556 1.410 1.339 .260 .238 .220 .196 t.284 _174 l.?3E .153 .140 .0t7 t.411 t.2t0 .t26 0t24 _z?t8 _049 I 1.228 1.235 1.199 .5755 .5945 E 1.263 .079 .813 I .125 .430 .364 .332 .305 .?10 .239 .2183 _2241 l8 .l4l .ll4 1299 1.493 1.366 1.316 .2618 .2618 .2618 .714 .158 1.352 550 .9lE l5 .t7l 1.43i .3009 .3098 .2t21 I I .0415 .0784 .0700 .0654 .0615 .0559 .0507 .0455 .0419 .0332 .0241 _2518 l3 l4 1.126 1.536 1.103 .760 .782 .610 .634 .856 .870 .902 .930 I 1.241 L163 Ll50 1.037 -132 -0244 .(]EE6 _0694 .0511 521 567 .0051) Lt29 .109 .095 .083 .072 .065 l133 .2484 .2532 .0067 .1990 2041 .t20 t2 1.176 1.183 .19t6 l0 .0!t7 {92 .0203 .0178 .0134 .670 I I 1.289 1.351 L46? 1.2t1 E 5q. Inch t.D. _066 .00068 .00055 .1259 .1296 .1333 o.D. .0392 .0350 .0321 .0307 .0280 .0253 .0227 .0210 .0166 .1354 .1159 .0931 .3140 .3V4 .3211 .3255 .3291 555 708 749 E04 852 898 .l0E 1.279 t.167 _210 .3314 921 1.149 .191 .3366 997 1.t09 .146 .341{ 1060 1.075 _106 .3836 .3880 .3974 .4018 970 1.404 1.359 .565 .4052 1037 ll82 .605 '\.273 1250 1305 1.238 I440 I537 I.153 t.2t _470 _426 .391 I .4097 .1136 .4196 _4250 .4291 I31l 1.0E5 .185 t707 L059 _134 .1806 ,1546 _4853 .4933 1860 .t241 .50tE .575 .476 .370 2299 1.218 1-170 1.121 1.095 3795 1.136 .709 .647 l5?6 2014 2l6l 4t2l Ll79 .315 .304 .212 t.ll6 .293 l.\22 Ll05 .559 .500 t.090 l.0i 1.09 l t3 l.I4 The Mechanical Design of Shell-and-Tube Heat Exchangers 109 Table 7-4 Minimum Tube Bend Radii l4l Tube Outside Dia. (in.) Duplex, all sizes *Plain:5/s I Bend Radius (in.) 3 times Tube O.D. Center-to-Center Oistance (in.) 6 times Tube OD t3/te 15/s 1 2 131t6 2z/s *For bends this sharp, the tube wall on the outer circumference of the tube ma\ thin down lt/z to 2 gauge rhicknesses. dependin| on condition and specific tube materiaL Morc genercus ndii \9ill reduce this thinning. TEMA presents a formula for calculating the minimum wall thickness. VAPOR IN LET FLUID IN LET FLUIO OUTLET CONDENSATE OUTLET Figure 7-7. Baffles can divert flow horizontally. (Courtesy of Howell Training Company.) Figure 7-6. Although complex, this design eliminates tube vi- bration. To use this configuration, one must be cognizant of pressure data [5]. (Courtesy of Heat Transfer Engineering, Hemisphere Publishing Corporation, New York, Washington, D.C.) Figure 7-8. Longitudinal baffles direct flow in the axial direction. (Courtesy of Howell Training Company.) 1 10 Mechanical Design of Process Systems flow area decreases, that is, the velocity increases with an increase in the number of oasses. The control of flow in exchangers is accomplished as increases as the well with orifice baffles. Figure 7-9 shows an annular orifice baffle. To utilize this type of design a very clean shell-side fluid is required, since the fluid must flow in the annular space between the tube outside diameter and the hole in the baffle forming the orifice. The flow at the orifice is very turbulent and the pressure drop through an orifice-baffle arrangement is very high. Consequently, these baffles are not used often in industry. Also, since the orifice baffle requires a very clean fluid, non-Newtonian fluids are completely ruled out. We will see later in the chapter that the plate fin type of exchanger is superior to the shell and tube design for many clean services. The reason for the shell and tube desisn to be dominant is because of the wider variery of fliids it can handle versus any other design. Other baffle arrangements are possible with varying baffle shapes and orientations. Figure 7-10 shows baffles in disc and doughnut shapes, which disperse the flow in a radial direction. Baffles can be cut to allow for horizontal or vertical flow in varying amounts as shown in Figure 7-11. Figure 7-9. Annular orifices between tube outside surface and hole in baffle plate [6]. Tie Rods These are structural rods that run oarallel to the exchanger tubes through the outer perimeter of the baffles. fastened to the tubesheets such that they space and support the baffles. Tie rods, being attached to the baffle plates, also prevent them from vibrating and damaging the tubes. Table 7-5 lists what TEMA recommends as a minimum number of tie rods and rod diameters for a set of shell diameters. Figure 7-10. Doughnut and disc type baffles [6]. Tubesheets These are the structured plates in which the tubes are connected at each end ofthe exchanger. Tubesheets come in two basic types-single and double. Double tube- sheets consist of two tubesheets mounted together at each end of the tubes with a clearance between the two sheets. The reason for using two tubesheets at each end is to reduce the possibility of a leak of the tube-side fluid. Dou- ble tubesheets are quite common with highly toxic services, where a leak cannot be tolerated. Single tubesheets are much more common than double tubesheets because ofprocess applications and economy. Typical tube-tubesheet connections are shown in Figure 1 1a Of great immediate concern in tubesheet design is the loading induced by the tubes thermal movement, which Table 7-5 TEMA Tie Rod Standards (in.) Nominal "R" Exchanger ShellDiameter 8-15 r6-27 28-33 34-48 49-60 "c" "R" Exchanger Tie Rod Dlameter & "8" Exchanger Tie Rod irinlmum Dlameter of Tie Rods 3/z 3/t 4 3/a tlz tlz tlz Number rlz tlz o o 8 10 The Mechanical Design of Shell-and-Tube Heat Exchangers is a definite problem in fixed % Cul Bd!.d on Diomehr tubesheet exchangers. TEMA gives two equations for determining the compressive stress induced on tubesheets for all three types of exchangers-Classes R, C, and B: Ihis Areo Cll Ool to Arlor Vopor Passog.. Siz€ of Cul Set by Combiiolions ol Heol Troisf€r Co€llici€nt oid Pressure Drop. : :: when Cc < ktlr z\Ku r _ | ,,-,,-,1 o. = : ll - llllJ I when C" > k#r t I lLc I o, This Areo Reooead lron Soiil€ lo Allo* lor Liquid D,oinoqa,Sire Sel to Slil Erp€cl.d Fkr Soltb {iidor, Voror Possoq. Areo where rl Bollh Cll or lor 0.oininq olrer lfoshout.sir. ro Suil Flor.Ihis b l'lol Becohriended tor Should be Rrhoved coidensed liquid = oy : t Tubes) rh.n rhr C" : : tr : ki = : Mun be Horironlor, Ihe. S€dionlind0ding (7 is High. tloriron16l Condenseri. I8) tlorkonlol C!l 8!ftle Figure 7-11. Baffle details [4]. (7-2) [rf,:i" minimum yield stress oftube material ofdesign remperalure radius of gyration of tube 0.25[d3 + (d" - 2t,)2]0 50, in. tube wall thickness, in. equivalent effective unsupported length of the tube. in. unsupported tube span, in. Applied Process Design for Chemicol ond Petrochemicol Plonts Flush lo Tube Shee Clod Tobe Sheet I Ferrule,some l/l6"to l/4' nne 0s tnner Tube Woll 8= l5'Avirose Beoded or Belled Flored We ld ed Dupler Tube Beoded or Eelled This Tube Moy olso be Inslolled Ploin End (No Ferrule)or Flqred With or Withoul Ferrule, l/8" 5/16' Minimu m I Minimum p-tre'' Uinirr.,Usuolly l/4" ssq+ $\ -r) f lA) VeflicolCul Eoltle Ploin 111 usn" Typicol Grooved Detoil Figure 7-12. Typical tubesheet-tube connections [4]. 112 Mechanical Design of Process Systems r {o' ['o : 4 : oc : Et for unsupported tube lengths between two tubesheets for unsupported tube lengths between where f" : C: mode constant from Thble 7-6 span length, in. I: E= I = W: Wt : Wq : W6o : a tubesheet and a baffle for unsupported tube lengths between two baffles modulus of elasticity of tube material at mean tube metal temperature, psi outside diameter of tubes, in. allowable tube compressive stress, psi, for the tubes at the outer periphery of the tube bundle Equation 7-1 is based on Euler's columl equation and Equation 7-2 is based on the short column formula developed by Professor J. B. Johnson during the nineteenth century. Other TEMA formulations are summarized in the following sections. The reader is urged to be familiar with the TEMA standard and follow its guidelines in designing a shell and tube heat exchanger. tube natural frequency, Hz modulus of elasricity. psi moment of inertia, in.a (Table 7-3) Wr + Wn + MWr", lbs/ft weight of empty tube (Table 7-3) weight of fluid inside tube 0.00545 p"d"'? M : added mass coefficient from p : fluid density, lbs/ft3 d : diameter of tube, in Table 7-6 subscripts: i : o: inside outside Allowable Tube Compressive Stress-Periphery of Bundle. The allowable tube compressive stress, psi, for the tubes at the periphery of the bundle is given by: TEMA Formulations a,:ffi-28 Baffles and Support Plates Natural Frequencies ot Straight Tubes on Multiple Equal Spans -r s"=\l - 21r - when C. -. I (kur)l 2C"l s kf/ror whenc >kur /:* 3.36C where C"'Vsr = l/ ^ Table 7-o Mode Constant-C Extreme Ends Supported No. of Spans lst I 2 3 4 Mode 31.73 31.73 3r.73 5 6 7 31.73 9 31,73 31.73 a to 2nd Mode 126.94 [21 Extreme Ends ClamDed ,l-r+r Fr-l-'-l*,.1 |--___l /T-7\--lzf-R lst Mode 2nd Mode 49.59 49.59 37.O2 37.O2 198.34 72.36 59.56 49.59 34.99 34.32 33.67 34.99 34.32 33.67 40.52 38.40 &.52 33.O2 33.02 72.36 40,52 33.02 33.02 33.02 p1d1, weight of fluid displaced by tube 0.00545 Extreme Ends Clamped-Supported r-fr-fr lst Mode 49.59 37.O2 34.32 44.r9 37.O2 34.99 znd Mode 160.66 63.99 49.59 42.70 39.10 37.O2 32.37 31.73 31.73 35.66 34.99 34.32 33.67 The Mechanical Desien of Shell-and-T[be Heat Exchansers yield stress, psi, oftube material at design metal temperature used. radius of gyration of tube 0.25 KT: .vu +la" - 2tJ1, only, may be calculated as follows: 2.74C" R2 where fnu R = : : U-tube natural frequency, Hz mode constant for U-bend bend radius, in. spans between two tube- Note: For other than simple support conditions the calculated frequency may be estimated by multiplying the above spans between a tubesheet value for f,, by the appropriate ratio of mode constants from Thble 7-6 using single span values. sheets. 0,8 for unsupported quency, assuming simple supports and for the first mode in. (Table 7-3) equivalent unsupported buckling length of the tube, inches. Use the largest value considering unsupported tube spans. unsupported tube span, in. 0.6 for unsupported 113 and a baffle. 1.0 for unsupported spans between two baf- fles. Note: The value of S" shall not exceed the Code allowable tensile stress of the tube material at desisn metal temperature used. Effect ot Longitudinal Tube Stress ASME Tube Joint Load Grlteria I The ASME Secrion VItr Division Dressure vessel code lists formularions in evaluating tube forces exerted on tubesheets. Referring to Figure 7-13 and Table 7-7 the formulas for the maximum tube force are as follows: Dt2 'Er.,j where fnp : tube natural frequency in stressed condition, Hz tensile, negative for compressive) P = axial force, lbs (positive for Natural Frequencies of Straight Tubes on Unequal Multiple Spans f" : For F, : joint types a, b, c, d, (7-3) A,o,11f, For joint types F, : e: f, g, h, i, j, k: (7-4) A,o"11f,f"f, where : maximum tube joint force, lb1 cross-sectional metal area of tube, in.2 oall : ASME maximum allowable stress. psi f= joint reliability factor Ft 10.83 t'z f. (no tesg = maximum value without test given For a tube on multiple unequal spans with the extreme ends fixed and simply supported at the intermediate supports, ki can be obtained by solving the following characteristic determinant for an n span system. Natural Frequencies of U-Tubes. It must be recognized that each tube is a continuous beam that has a single fundamental frequency. This frequency may be largely governed by the lowest "stand alone" frequency of either the longest straight span or the U-bend. It is suggested that both be calculated and that the lower value be used, keeping in mind the approximate and somewhat conservative nature of the result. The straight span frequency may be determined from Thble 7-6 using the appropriate mode constant. The U-bend out-of-plane fre- f, (teso : in Table 7-'7 maximum value with test as specified in the ASME Section VIII Division 1 code, per section UA-002 Figre 7-14 shows how the tube joint load varies for various tube gauges of various process conditions. Naturally, as the tube wall increases, the tube stiffens and, consequently, the force exerted by the tube on the tubesheet joint increases. The engineer should evaluate the tube loads with the various process conditions possible and use the worst for determining the maximum tube joint force, as shown in Figure 7-14. The TEMA standard gives the formulations to determine the tube ioint lorces and the user is referred to this standard for these expressrons. The buckling of exchanger tubes can be a problem if thermal expansion is not properly accounted for in de- Mechanical Design of Process Systems 114 Table 7-7 Reliability Factors, f, Joint Type Notes Descriptions Welded only, a> 1.4r Welded only, tsa<L.4t a b (1)(7X8) (1X2) (1X3) (1X6) (1X7X8) Brazed, examined Brazed, not fully examinable Rolled, welded, a> l.4t Rolled, two or more grooves, and welded, a< l.4r Rolled, single-groove, and welded, a < 1.4r Rolled, no grooves, and and welded, a < 1.4r Rolled, two or more grooves Rolled, single groove Rolled, no grooves c d f c h I j k [71 l. (tesr) f, (no test) 1.00 0.50 1.00 0.80 0.55 0.80 0.40 0.80 0.95 o.75 0.85 0.65 0.70 0.90 0.80 0.60 0.50 0.70 0.65 0.50 0.70 1.00 (1X4)(s) (7) (l )(4)(s) (7) (l)(4)(5) (7) (l)(4xs) (l)(4x5) (l)(4)(5) Notes: (l) The use of f. Ceso factor requires qualification in accordance with UA-003 and UA-004. (2) For welds where a is less than t, fi (no test) 0. Tubes with Type (b) joints where a<t may be considered as acting as stays and contributing to the strength of the tubesheet only when the joint is tested in accordance with UA 003 and UA-o(X. (3) A value of 1 00 for f, (test) or .80 for f, (no test) can be applied only to joints in which visual examination assures that the brazing filler metal has penetrated the entire joint [see UB-14(a)] and the depth of penetration is not less than three times the nominal thickness of the tube wall. (4) When the ralio of OD. to LD., using nominal tube dimensioos, is less than 1.05 or geater than l-410, qualification in accordance with UA403 and UA-oO1 is required. (5) The nominal pitch used in the desigo of tubesheets for roller expanded joints shall not be less than the following: - P= d" + 0.165 (d" + 2r) = nominal pitch (center-to-center distance of adjacent tube holes), = tube o.D_, in. I = nominal thickness of average wall tube, in. in. except that: (a) nominal pitch shalt not be less than 4 + 2t unless the joint is qualified in accordance with UA-003 and UA-004; and (b) 96% of the ligaments between tube holes throughout the thickrcss of the rnachined tubesheet shall not be less than 0.85 (P-4). Ligaments which do not meet this requirement shall be evaluated and €orrections made as may be necessary. (6) A value of .50 for f, (test) or .40 for f, (no t€so shall be used for joinls in which visual examination will not provide proof that the brazing filler metal has penetrated the entire joint Isee US-14(b)1. (7) The value of f. (no test) applies only to material combinations as provided for under Section IX. For material combinations not provided for under Section IX, f. must be determined by test in accordance with UA-003 and LIA-0O4. (8) For joint types involving more than one fastening method, the sequence used in the joint descriptions does not necessarily indicate the order in which the oDerations are Derformed. sign. One such formulation to predict the critical buckling load is as follows: P., q'' t0.5216r - , " ,, I L** l' \Ns + t/ where L,u6" : NB : t7-51 total length of tubei between tubesheets number of baffles Equation 7-5 is based on the Euler column formula. In situations where there are several baffles, such that the effective length, L", divided by the radius of gyration, k, is between 30 and 120, exclusive, then the Johnson short column equation is more accurate. For a tube to be considered as a series of short columns constrained by fixed ends, one must be certain that the baffles constraining the tubes allow practically no translational or rotational movement. The stiffness of the baffle plate should be analyzed, as small translational and rotational tube movement allowed by the baffle plate could considerably alter the buckling characteristics of the tube. The evaluation of a baffle plate containing several tubes can be a somewhat detailed analysis, and it may be faster to consider the tube as a continuous beam in determining buckling characteristics. For further details on the mechanical design of exchangers, the reader is referred to TEMA. We will discuss tube vibrations shortly. The Mechanical Desien of Shell-and-Tube Heat PBOCESS EVALUATION OF SHELL AND TUBE EXCHAI{GERS mechanical engineering coincide. Thus, the mechanical engineer must be cognizant of process evaluation of heat exchangers in order to design these units. A thermal evaluation of shell and tube heat exchansers concerns primarily two modes of heat transfer-conJuction and convection. In Chapter 3 we considered heat transfer through piping and vessel components as well as jacketed systems. As described in Chapter 3, the basic expressions used in conveetion are as follows: We are concerned here only with any particular heat exchanger and determining whether it can transfer heat energy as required. How the unit affects process conditions of the entire system is not our concern here, because we are interested only in the proper performance of the unit. Evaluating the exchanger in relation to the process system is the primary concern of the chemical engineer. The thermal evaluation of the exchanger is one area where chemical and mechanical engineering overlap; just as in Chapters 2 and 4 we saw how civil and : q: q rhcpat (3-24) UA(LMTD) (3-26) t2l {1t Some ecceptable weld geometriea where t is not less (61 lhan Exchansers t15 l.4t l7l (81 Figure 7-13. Joint types [7]. (Courtesy of ASME.) 116 Mechanical Design of Process Systems J ; sooo l! F = - 7t)00 U ul .o * 6000 .o5 .o5 st .oa .o9 Jo 11 12 13 .1+ .15 16 t7 TUBE WALL THICKNESS Iin| Figure 7-14. Tube joint loads. Equation 3-9 is a variant of Fourier's heat law of conduction in which, q: KAAI (7-6) The treatment of shell and tube exchangers requires the same basic theory for use in Chapter 3, but a different application. In these types of exchangers we are pri- marily concerned with the heat duty or heat load required in the same general sense as the jacketed vessels in Chapter 3. Process requirements are the criteria used to determine the heat duty. The two basic components of heat transfer in the shell and tube exchanger are sensible heat and latent heat. These concepts are described mathematically with the use of Equation 3-24. Using this relation we have: q = r;cp(ao q : rimrg (7-7) (7-8) The Mechanical Design of Shell-and-Ti.rbe Heat Exchangers Equation 7-7 determines sensible heat change and Equation 7-8 determines latent heat change and is a form of Equation 3-13. You will recall that sensible heat is the amount of heat energy required to either heat or cool a given mass (solid, liquid, or gas-without a phase change) to a measurable degree. Thus, if we have a kettle full of water and we heat the water mass at atmospheric pressure to 212'F, adding additional heat to the kettle will not raise the temperature. Thus, the sensible heat is the amount of heat required to raise the water temperature to 212'F. The additional amount of heat required to convert the water to steam is called latent heat. Sensible heat can be detected by the human senses and thus physically measured, as with a thermometer. Latent heat is heat energy that cannot be detected by the human senses and is more intrinsic to the basic nrocess-the hot steam plus the additional heat provided- to rhe kertle to convert the water to steam. While these terms are rudimentary, their importance is fundamental to heat exchangers. Combining Equations 7 -'7 and 7-8 we arrive at the total heat duty of the exchanger as: q:rirco1a9:rirtrr, \'7 117 pass to another in a muhipass exchanger. Figure 7-15 illustrates how a different LMTD occurs for each oass. showing that using the inlet and outlet ofrhe rubesid; and shellside would not produce an accurate LMTD value. Thus, the value obtained from Figure 3-10 must be multiplied by a correction factor, F, as provided in Figure 716. These correction factors were tabulated by TEMA and are determined by the "P" and "R" parameters shown in Figure 7-16. For a true counterflow or parallel exchanger a correction factor is not necessary. Use of these tables is demonstrated in the examples which follow. It should be pointed out that the straightline exchanger curve in Figure 7-15 is for a single-component fluid. Most industrial applications are multicomponent mixtures. Chemical engineers do vapor-liquid equilibrium calculations that show vapor and liquid compositions in multicomponent mixtures to be different and changing within the exchanger. Thus, real curves are not straight, but often can be approximated as such in multicomponent flow. Assuming a straight line is a source of many oesrsn errors. -9) The first term on the right side of Equation 7-9 represents the sensible (cooling or heating) heat and the sec- ond right-hand term represents the latent (condensing or boiling) heat. In Chapter 3 we discussed the LMTD and the reader can use Figure 3-10 to quickly determine this parameter. The difference between that value used in Chaoter 3 and the application here is that the LMTD will vary from one Tube Wall Temperature and Caloric Temperature Chapter 3 dealt with the LMTD in the computation of heat transfer problems. One of the assumptions used in defining the LMTD is that the overall heat transfer coefficient, U, remains constant. With multipass exchangers this is certainly not always the case, as indicated by Figure 7-15. Even with counterflow exchangers, as the cold fluid gets hotter, the viscosity decreases, changing the overall U-value. In many instances, the U value will vary more than the inside tube coefficient. Colburn [8] addressed this problem by assuming that the U value will change linearly with temperature and deriving an expression for the temperature differential. Colburn thus elected to obtain a single overall coefficient, U,, at which all heat transfer surfaces can be assumed to transfer heat at the computed LMTD. In this way the overall U-value, U*, can be expressed as r. E P \|TTD/ Toral Heat Transler, Btu Figure 7-15. The amount ofheat transferred varies from to another [4]. pass a_ ,, IGTTD - LITD ;- uxt,l I\ r" lcrrDl I (7-10) I / Such a value of U* exists at a temperature, t", known as the caloric temperature. It is this value of t" at which the inside and outside tube film coefficients, h1 and h., respectively, are evaluated. The caloric temperature is found by multiplying the respective hot and cold temper(tert continued on page 122) 118 Mechanical Design of Process Systems r.0 5 F o.s 2 (l o -.' : P .TEMPERATURE EFFICIENCY I /tL--.....-.-, lr-t' l.-+<_ LMTD CORRECTION FACTOR SHEIL PASS ' D ! EVEN NUMBER OF TUBE PASSES -.:l-J Gl= T,-t, r '2 -l/ oa o F O.9 z 9^" o 0.7 = o.6 P . 03 0.5 0.6 T€MPERATURE EFFICIENCY LMTO CORRE 2 SHETL PASSES 4 OR MUTTIPLE OF 4 TUBE PASSES P'++ I:I Q-tr Figure 7'16. LMTD correction factor. (@1978 Ttrbular Exchanger Manufacturers Association.) The Mechanical Design of Shell-and-Tlrbe Heat Exchangers 5 o.g F z I o.e o o.7 F o.6 P ' TEMPERATURE EFFICIENGY 3 SHELL LMTD CORRECTION FACTOR PASSES 6 OR MORE EVEN NUMBER OF TUBE PASSES P'++ I:l R' tr-1r P o.s 2 o tr o.8 o O.7 F t o.6 T- 4 SHELL LMTD CORRECTION FACTOR OR MULTIPLE OF 8 TUBE PASSES 8 gHELIS I I -r_ "'++ Figure 7-16. Continued. ]-J tr- tr PASSES 119 '120 Mechanical Design of Process Systems t.o E P o.g z tr o.8 tr o.7 : 5 SHELL PASSES 10 OR MORE EVEN NUMBER OF TUBE PASSES r'#-+ .t o.3 0.4 Tr-Tr "= 0.5 0.6 P = TEMPERATURE EFFIoIENcY LMTD CORRECTION FACTOR 6 SHELL PASSES T2 OR MORE EVEN NUMBER 9:-]3-J ' T,-t' Figure 7-16. Continued. R = -l--3 OF IUBE PASSES The Mechanical Desien of Shell-and-Tube Heat Exchangers P =TEMPERATURE EFFICIENCY I DIVIDED FLOW SHELL PASS o. -13--:! ' I T,-t, EVEN NUMEER OF TUBE PASSES I-I, o.g z P o.t o F o.7 = o.6 P.IEMPERA LMTD CORRECTION FACTOR SPLIT FLOW SHELL e'f{ Figure 7.16. Continued. 2 ''r-rE TUBE PASSES 121 122 Mechanical Design of Process Systems ature differentials by a caloric fraction, F". That is, the fraction, F., is multiplied by the temperature rise of the controlling stream and adding the resulting rise to the lower terminal temperature of the stream. Figure 7-17 helps in determining the controlling streiim. Colburn [8] correlated the data for the insert in the top left-hand corner of Figure 7- 17. The fluid stream, either shell-side or tube-side, that has the largest U-value corresponds to the controlling heat transfer film coefficients, h1 and h., which are used to determine U*. Basically, rhis implies that we must find the values of U6 and U" for both separate streams, and the stream that has the largest c value, based on Figure 7-17 is the one used to compute h. and hi in computing U,, where Uh is the overall heat transfer coefficient at the hot end of each respective stream and Uc is the overall heat transfer coefficient at the cold end of each respective stream. In equation form we express the caloric temperatures as derived by Kern [9] as follows: t* = The hot fluid caloric temperature ls h1" : ho : tqh:th.*F.(th,-th") (7-1 1) The cold fluid caloric temperature is r.c: tc + F"(t." - r") where tch : caloric temperature ofhot fluid, .F th" : outlet hot fluid temperature, oF 1,, : inler hot fluid temperature. .F t.. = caloric t" : tc" F" : : (7 -r2) temperature ofcold fluid, .F inlet cold fluid temperature, .F outlet cold fluid temperature, "F correction factor determined from Figure 7-16 Outside tube wall temperature for the hot inside of the tube is fluid on the hi^ , nio f- no (t.h - t".) (7- l5) or t.h h +. ]:. n,. + (r.r, no - l.) (7 -16) Thus, the pipe wall temperature can be computed when the caloric temperature values are determined. The temperature difference across the tube wall is customarily assumed to be negligible because the entire tube is at the outside surface temperature. The terms in Equations 7-13 through 7-16 are as follows: t* : tube (outside surface) wall temperature, 'F inside film coefficient of tube using outside surface temperature, Btu/hr-ft2-' F outside film coefficient of tube, using outside tube surface temperature, Btu/hr-ft2-'F The tube wall temperatures are to be used in computing thermal movements of the tubes and all other mechanical computations. As explained previously, these tube wall temperatures are based on the caloric temperature values that truly reflect the mean value of the varying values of h1, ho, and U,. It is a common oversight in exchanger design to use the arithmetic mean rather than the caloric values. Equation 3-26 should not be used because Equation 7-10 more accurately describes the true mean values in the exchanger. Overall Heat Transter Coefficient Once the hot and cold caloric temperatures are determined we can now compute the tube wall temperature, because the caloric temperatures represent the true mean values for the varying values of U^, hi, and h". Kern [9] has expressed the tube wall temperatures in the follow- ing forms: Outside tube wall temperature with hot fluid external to tube is The thermal duty of an exchanger cannot be discussed without first defining the overall heat transfer coefficient, or "U-value." This parameter is referred to in the previous discussion and it is noted that this value can vary with various types of configurations. Now, after discussing how a variable U-value is handled on multipass units using the caloric temperature, we are ready to treat the overall coefficient in detail. The overall heat transfer coefficient, denoted as U, is defined as follows: hi.. t" = t.r, .n,o + - (t"n nu - r...t (.7 -13) or t" = t.r, u= l,TuT,tT" -r- hi Kr, k" h" n,o - + (Lr, no - t".J (7 -14) where hj Tn (1- 11) -h. -l- -k. = inside tube film coefficient, Btu/hr-ft2-'F = thickress of inside tube deposits. ft The Mechanical Desien of Shell-and-Tirbe Heat Exchansers 123 E ut e 3 t4 ul g 4 = F u,l e 3 |'|- ul () e ul tlll .f J .9 s' F o\ o o t\ to tt ;l; lJ 110 J0 rr|ivr9 'l 'd'v : 124 Mechanical Design of Process Systems kn : T" = k* : ho Tro k,o : : = thermal conductivity of foreign deposits on inside of tube, Btu/hr_ftr_.F tube wall thickness, ft thermal conductivity of tube wall, it contacts tube surface, resultinq in a coating effect. Thus, the depositing of foreign miterial adds to the resistance of heat flow from the tube and she side flows. Fouling can occur inside and outside of tube surfaces. The complexity of fouling and how it occurs does not easily allow this phenomenon to be treated analytically. There are far too many variables involved for one to accurately compute fouling factors. Thus, this phenomenon is treated in a more subjective light, using experience as a guideline. Years of experience with various services have resulted in the use of accurate foulins facphases when Btu/hr-ft2-"F outside tube film coefficient, Btu/hr-ftr-.F thickness of outside tube deDosits. ft rhermal conductivity of deposits on outside of tube, Btu/hr-ft2_oF The terms in Equation 7-17 , llh, T/kf, and T*/k*, are known as film resistance, fouling resistance (we will refer to this as fouling factors), and tube wall resistance, respectively. These parameters represent the resistance to heat flow through the fluid film, foreign deposits, and the tube wall. This is shown in Fisure 7-18 where the temperature is shown varying throGh the various resistance zones. This figure is a conceptualization of the temperature profile, as the degree of gradient change in temperature is a function of the flow conditions daminar versus turbulent) and on the type and amount of foreign deposits. To understand Equation 7-17 we will discuis each resistance separately. Fouling of Inside and Outside Tube Surfaces Fouling occurs when deposits are made on the walls by particles contained in the fluid medium or bv the fluid itself forming a layer on the tube walls. This can occur two ways, either by adhesive characteristics of the deposited matter or by the foreign material being bonded to the tube surface by thermal gradients between the tube wall and the foreign material, so that the latter chanses tors. Fouling factors are very important in the design of shell and tube heat exchangers. Bare or plain tubes, which are almost always used, generate low U-values when compared to those generated by tubes with fin attachments. Finned tubes, especially those with fairly high fins, experience very little fouling unless the deposIts cover an appreciable portion of the fin height. With the normally accepted long periods between tube cleaning in plants, fouling certainly must be considered in the calculation of the U-value. One must be aware of the shell- and tube-side fluids and select those foulins factors thar best reflecr the op{imum fouling thar williffect thermal duty. The fouling factor in Equation 7-17 is T/fu. This term is the inverse of the thermal conductance of heat throush the foreign matter. denoted by k,/T,. Thus, the reciproial of the thermal conductiviry of the foreign material is known as the fouling factor. Fouling can exist on both or one side of the tube. Typical values for fouling factors for common services are siven in Table 7-8. Direction + Att At1 = Temperature drop through inside Att Atz = Te6p"tu,ur" Orop through laminar boundary tayer inside Atr At. At" -----T At, turbulent boundary rayer tube Ats = Tsrnpsr.lrra drop through fouling layer inside tube At4 = Temperaiure drop through tube wall Ats = Tsrnpg,.1r,a drop through outside touling layer At6 = Temperature drop through outside laminar boundary rayer Atz = T66p"r"rrr" drop through outside turbulent boundary taver Figure 7-18. Temperature profile through tube wall. n fl The Mechanical Design of Shell-and-Tube Heat Table 7-8 Recommended Minimum Fouling Resistances Fouling Factor Gases and vapors Cenrrifugal compressor exiaust Reciprocating compressor exhaust Reciprocating compressor refrigerant vapor Centrifugal compressor refrigerant vapor Oil-free and clean high-quality steam Oil-free and clean low-qualitv steam Oil-bearing steam Compressed air - l-,iatural gasl Liquiafs Bay water - 0.002s 0.0015 0.0003 0.0005 0.001 - Acid gas ;olr€rt rapors 0.001 0.01 0.002 0.001 0.001 0.001 Fuel oils 0.0025 0.0005 0.0033 0.0033 0.0015 0.0012 0.0015 0.006 Clean organic solvents 0.001 Vegetable oils 0.004 Refrigerant liquids Industrial heat -transfer oils 0.001 0.001 0.001 Distilled water Hard well water Untreated cooling tower water Treated cooling tower water Engine jacket water Treated boiler feed water Hydraulic fluid Natural gasoline and liquefied petroleum Rich oil Lean oil gases and Tate as fbllo$ N-," : coetTicienr \\:, : \r. : : \p. L = greater heat transfer between the shell-side and tube-side fluids, resulting in higher film coefficients. For a more detailed discussion of boundary layer theory one is referred to a basic text on heat transfer, such as the l/andbook of Heat and Mass Transfer, Volumes I and 2, N. P Cheremisinoff, ed., Gulf Publishing Co., Houston, Texas, 1986. oi thernal conductivity of fluid rn,lde rub('. lJlu hr-ft- "ts \usselt number (see Chapter 3) Re) nolds number Prandd nunber (see Chapter 3) total tube lensth. ft lluid viscosity at bulk tenperature. Ib,,,/ft-hr or cp fluid viscosity at wall, lb./ft hr or cp The viscosity at the wall, p,", should be evaluated using either Equation 7-15 or Equation 7-16. The bulk temperature of the fluid is in practice the average of the inlet and outlet tube fluid temperatures. For turbulent flow inside tubes wall effects can play a role in the film coefficient value. The correlation that is widely used is the one developed by Sieder and Thte, which is as follows: In the region close to the tube wall the fluid becomes stagnant and forms a film around the tube surface-on inside and outside surfaces. This stagnant region is called the "boundary layer" because it forms at the boundary of the tube wall. The size and properties of the particular boundary layer are a function of the fluid properties itself and whether the fluid flow is either turbulent or laminar. Turbulent fluid motion always leads to (7-18) inside pipe or tube diameter. ft where i Tube Film Coefficients s: = r 86{Nn.)r' (\,.)'' (q)'" (4)''' T 0.002 - 125 Inside Tube Coefticients. In Example 3-5 we used correlations to determine film coefficients inside tubes. Here, we will give a more comprehensive treatment of film coefficients inside tubes. In laminar flow there is more fluid stagnation around the tubes because in the boundary layer itself the flow is laminar, whereas in a turbulent boundary layer the sublaminar boundary layer is only a small percentage of the total layer. Thus, fluid properties at the walls in laminar flow must be evaluated. The laminar film coefficient is largely dependent upon the viscosity and, thus, the temperature (which controls the viscosity) of the wall controls the value of h. The most commonly used correlation for laminar flow inside pipes is that given by Sieder 0.001 0.00 Exchangers NN,^ " : for 0.7 / \o 14 0.027(NR"ro < Np, < \N.,t' ' l4l \4"/ (7- le) 17,000 As for Equation 7- 18, the value of p*, should be determined using temperature values calculated using Equations 7- 15 or 7- 16. McAdams [10] suggests that for temperature differences between the bulk fluid temperature and the pipe wall surface temperature the following expression can be used: Nu, = 0.023(NnJo 8(NrJ" (7 20) 126 where Mechanical Design of process Systems n = 0.4 for heating n : 0.3 for cooling Nr, And the temperature differences are as follows: At At At : pipe surface temp-bulk < lO'F for liquids < 100"F for gases fluid temp Outside Tube Film Coefticients, Forced convection around immersed bodies is a complex subject, especially when a bundle oftubes is involved. We will only give L rather brief discussion of how one can obtain a s;neral magnitude of film coefficients. The -reader should be aware that process design is not addressed. Thus, for solving problems dealing with condensation, order of nucleate boiling, and film boiling-to name a few_the reader should consult other sources that treat Drocess de- sign in detai[ [4.81. For gases flowing normal to circular cylinders a simple relationship is contrived by M. Jakob [1] using an dyercge Nusselt number for the gas. An empirical version of this expression is given by hd, where h : = C(NIJ" ('7 -2r) hd' - : Kf Forced convection normal to tube bundles is mucl: more complex than that of a single tube. The size of the bundle and how the tubes are oriented (tube pitch ar_ rangements) in the bundle are of prime importance. First. we will discuss an approach io determining the film coefficients for bundles and then discuss the mr-erits of arranging tubes in various geometries. There are four basic types oT tube arrangements-tri- angular pitch, inJine triangular pitch, inJine square pitch-, and diamond-square pitch. These four geomelries are shown in Figure 7-19. Tubes arranged in bundles are more complex than a single tube becaule the flow vortices formed by the flow around the first tubes affect the flow around the tubes farther inside the bundle. Mose researchers agree that this transient effect is substantially dampened after the flow passes over the first ten tubei. Numerous research studies have been made that analyzed flow effects on tube bundles. E. D. Grimson [12] concluded from several studies that for tube bundlei ai least l0 tubes in depth the following expression can be used to predict the film coefficient: hd, : B(pvd"irr.r)" -23) average where pf : _: h p: ki : A variant of Equation 7-21 is widely used for forced ofair normal to a cylinder is given by the fol- B and n do Range ol Reynolds Numbers 0.989 40 < NR" < 4000 0.683 0.193 0.027 4000<NRe<40,000 : = Reynolds number at maximum fluid velocity, 0.91 I V.", film coefficient, Btu/hr-ftr-.F air density, lb./ft3 thermal conductivity of fluid, Btu/br-ft-'F average constants given in Table ?-10 tube outside diameter (4, Triangular pitch, NR" <4.0 NR" <40 lb-/ft-hr Figure 7-19): Circular Cylinders 40,000 <NR" <400,000 absolute viscosity, The Reynolds number in Equation 7-23 is evaluated at the maximum fluid velocity. This velocity is obtained at the minimum flow passage between the tubes. This minimum distance is shown in Figure 7-19. Tbe minimum distance is expressed in terms of the tube bundle geometry for each of the four configurations. as follois isee Table 7-9 Parameters for Fluid Flow Normal to 0.40< : V : velocity of air, ft/hr Nx" convection rowrng: < (7 k1 film coefficient for gas, Btu/hr-ft2-.F dt = tube diameter, ft ks : gas coefficient of thermal conductivity, Btu/hr-ft-.F C and n : parameters from Thble 7-9 4 C(PJ'/r(NRJn d-," : * 2'' 0.330 0.385 (b) InJine triangular pitch, dni" 0.466 (c.l 0.618 0.805 . =W - d, InJine square pitch, dmi. = W (d) Diamond square pitch, d.;" : P cos 45' 0.707p - D - D : The Mechanical Design of Shell-and-T[be Heat Exchangers 127 (B) Inline triangular pitch-apex facing nor- (A) Triangular pitch-apex facing tlow mal to flow l Flow + + +++ 9- (D) Oiamond squars pitch (C) Inline square pitch P= Pitch Figure 7-19. Tirbe bundle anangements. Table 7-10 Grimson Constants for TUbe Bundles Containing 10 or More Tube6 w/do Ratlo Tube wdo Bank Geometry Flgure 7-19) Inline t.25 .348 1.50 .JO 2.00 3.00 0.600 0.900 1.000 Staggered 1.25 (see / .418 .290 2.0 1.5 .5E2 .586 .570 .601 Bn B .275 .608 .100 .7U .250 .620 .101 .299 .357 .@2 .584 .229 .702 .632 .cgl .))a .581 .063 .068 .752 .74 .198 .&8 .286 .608 .213 .636 .446 .571 .401 .581 .565 .Jl6 .560 .srs .so .478 1.250 .505 .ssc .519 .451 .4U .460 .416 .562 2.000 3.000 .568 .572 .452 .482 .522 .488 .562 1.500 .556 .s68 .556 .310 .592 .356 .562 .421 t.125 .568 .580 .40 .449 .568 .570 .574 128 Mechanical Design of Process Systems The cross-flow are for various types oftube bundles is shown in Figure 7-20. From the concept of continuity, where for two points . along a flow path, or streamline, : V2A2 where V1 : velocity of fluid at point I, ftlsec Al : cross-sectional area, ftz VrAl 'A )</ e-24) \@ we can deduce For staggered and iniine tube arrays, : With all tubes being placed at a constant pitch and Vr Vr : fluid velocity, we have v.,, = v'l+l (7-2s) \o.,"i o, = o'10 - p,"" * 9!: *]44 [o" Pn - [ o,yl "l ,rc For triangular layouts, .= B n. r++ [^ - -D," + o,^-dr. ..1 .^ (P - dJl [D" +---i ,rt'? where, DL = OD of tube bundle D" = lD ol shell dr = OD of tube Equation 7-25 represents the fluid velocity that would be used in Equation 7-23. For tube bundles containing less than l0 tubes, values of the film coefficient in Equation 7-23 must be multiplied by the correction factors in Table 7-1 1. Each tube pitch arrangement has its own advantages and disadvantages. A listing of these facts is given in lable 7-12. Whatever the tube arrangement selected, the tube arrangement in the tubesheet should be made verv carefully. Clearances, which could be such items as impingement baffles, channel and head baffle lanes, must be considered. Table 7 -13 is a compilation of various industrial standards for tube sheet layouts. Fipure 7-21 shows a typical tube sheet layout. One of the easiest and most common methods used to calculate shell-side film coefficients is that proposed by Kern [9]. The Kern correlation, which is used for all fluids. is as follows: 'lu l' ' o ro lq"o)"'l,9url' k \p/ \t/ \pJ h"& B = baffte spacing Ar = flow area-cross-llow area for one s€ction tween two baffles Figwe 7-20. Tube bundle cross-flow area. (7-26) or h"rD": o.:orN""f t,*rr"t (")o'' Equation 7-26 is divided into two components, jH and Np" in which Figure 7-21. Typical tubesheet layouts. T :iw The Mechanical Design of Shell-and-Tube Heat Exchangers j":+H'(,+) Table 7-1 where h. -27) film coefficient, Btu/hr-ft "F G, flow rate of fluid, Iby/hr mass thermal conductivity of shell-side fluid, Btu/hr- ft-"F D. = shell-side equivalent tube diameter, in. C, : sPecific heat of fluid, Btunb-"F 123456789 0.64 0.80 0.87 0.90 0.92 0.94 0.96 0.98 0.99 Staggered 0.68 0.75 0.83 0.89 O.92 0.95 0.97 0.98 0.99 ('7 outside tube bundle : k: Kays and London Constants for Tube Bundles Containing 9 Tubes or Fewer Number of Tubes In-line : 1 129 For a square pitch tube arrangement, l(p: - nd; ) l i- (7-28) ?iorn Table 7-'12 Pros and Cons of Various Tube Arangements Tube Pitch Arrangement Advantage Disadvantage Yields higher film Medium to h igh Pitch coefficients than pressure drop. in-line square Cannot be used in pitch. More tubes foulrng serrice.. can be contained in Can only have shell becau.e of chemical cleantng. For a 60'equilateral triangular arrangement, D. : .1(0.-13o: - -_: 0.5rdi ilt (.7 in 29) a (a) Triangular (b) In-line Triangular Pitch compact arrange- g rcB' ment. p(144) Film coefficients Medium to h igh are not as high pressure drop. Can only have chemical cleaning. as triangular pitch, but greater than inline square pitch. Suitable for fouling conditions. (c) InJine Good for condi- Relative low film Square tions requiring low coefficients. Pitch pressure drop. Ar- for easy access of Square Pitch pitch. Easy access for mechanical cleaning. Good for fouling service. ft: 17-30 r D, = ID of shell, in c: clearance bgtween tubes nleasured along tube pitch, in. B : baffle spacing, in. G, : mass flow rate of fluid, lb,/hr G.:th p : viscosity of the shell-side fluid at the caas at the tube wall temperature, lb/ft-hr tubes for mechanical cleaning. Good for fouling service. Better film coefficients than inline square pitch, but not as good as triangular or in-line ft: loric temperature, lb/ft hr p* = viscosity of the shell-side fluid rangement allows (d) Diamond uhere p : tube pitch. ir. d,. = ID of shell. in a, : flow area of tube bundle, Relative low film coefficients. Does not have as lowpressure drop as the inline square prtcn arrangement. The parameter js is plotted against Nx" in Figure l-22a. The value ofjH is determined from the figure after the Reynolds number is calculated. Then from Equation 7 -27 the film coefficient is determined. The use of baffles is extremely important in directing the shell-side flow, tube support, and controlling the shell-side flow rate. As the number of baffles is increased, the flow rate increases. Likewise with an increased flow rate, the pressure drop increases substantially with an increasing number ofbaffles, with the film coefficient increasing as well. Ludwig [4] reports that for a constant flow rate, the velocity across the bundle is doubled with an increase in the film coefficient of approxirnately 44% . (text conttuued on page 139) 130 Mechanical Design of Process Systems Tube Count for TEMA Fixed Tubesheet Outside Packed No. ol Passes No. of Passes Head 668 588 18 t2 26 24 52 48 98 84 142 t28 168 156 232 220 798 292 388 3s2 484 456 570 s48 922 902 812 808 22 10.02 0 12.N 170 212 21.25 23.25 25.00 27 .00 29.00 31.00 33.00 35.00 P 70 t6 30 28 66 60 106 96 164 148 196 r88 270 252 348 332 440 420 554 524 646 612 5.047 6.065 7 .981 13.25 15.25 17 .25 19.25 Table 7-13 in. OD Tr.rbes on 13^6-in. A pitch TEMA LorM Shell lD in. g/a 68 283 3& 454 562 1230 868 l2t2 lt72 1590 1560 1516 TEMA Type s Head No, ot Passes l106 1092 1040 1438 1430 1496 1468 6l 104 151 178 24r 316 396 490 764 1336 Tube Count for s/s in. OD Tubes on Z8 in, TEMA TEMA LorM Fixed Tubesheet No. of Passes Shell lD in. 5.047 6.065 7 .981 l0.02 12.N 13.25 15.25 t7 .25 19.25 21.25 23.25 25.W 27.W 29.W 31.00 33.00 3s.00 P 18 t6 30 24 61 s2 48 96 94 80 151 138 132 187 176 168 241 232 224 302 292 396 384 352 482 472 456 568 554 536 792 780 752 Outside Packed Head No. of Passes 418 506 14 t2 26 16 48 44 82 76 124 t12 148 t32 196 184 266 252 334 312 4t6 396 492 472 704 700 22 19 31 26 1062 1030 1008 13s6 t346 13c4 55 88 130 151 206 270 JJO 946 930 660 896 1234 1220 n80 U Inside t9 14 t2 31 26 16 56 52 44 96 90 76 lsl 138 t28 187 184 160 258 242 224 336 326 304 421 412 392 s26 502 480 608 s98 556 868 836 804 t152 lt24 t088 t9 JI TEMA U-Tube No. of Passes 1424 A pitch TEMA Tvoe S Inside Head No, ot Passes 14 t4 t2 22 20 16 51 48 40 85 76 72 130 120 112 163 152 144 216 2r4 196 288 282 264 358 350 340 450 436 416 526 506 484 724 720 696 994 978 948 1288 1252 1220 TEMA U U-Tube No. of Passes The Mechanical Design of Shell-and-Tube Heat Exchangers Table 7-13 Continued Tube Count for s/s-in, OD Tubes on ZB-in. TEMA M Type L or Shell lD in. 5.047 6.065 7 .981 r 0.02 12.00 13.25 t5.25 .25 19.25 t'7 21.25 23.25 25.00 27 .00 29.00 31.00 33.00 35.00 Fixed Tubesheel No. ol Passes 21 16 26 26 52 52 89 82 128 124 158 158 2r3 208 277 266 344 332 420 404 502 4't6 694 668 922 910 1181 1166 TEMA Type P Outside Packed Floating Head 908 I 160 1070 l0g 52 80 r20 148 208 264 336 400 488 664 l2 16 44 68 92 r20 164 220 284 TEMA TEMA TYPe S Type l2 2l '74 109 138 188 246 TEMA M 316 394 432 456 .1.18 14 608 6.10 636 62.1 812 86? 8.18 8,10 Fixed Tubesheet Shell lD in. 5.O4'7 6.065 7.981 10.02 12.00 13.25 15.25 t7 .25 19.25 2r.25 23.25 25.00 2'7 .00 29.00 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00 No. ol Passes 19 14 t2 27 26 20 55 48 40 85 76 72 126 118 104 151 148 140 206 196 180 268 266 240 340 330 320 416 408 392 499 480 460 576 558 530 675 661 632 790 ',7',13 736 896 875 858 1018 1011 976 1166 I137 1098 1307 1277 1242 1464 1425 1386 1688 1669 1618 1943 l9t2 1878 2229 2189 2134 2513 2489 2432 2823 2792 2752 352'7 3477 3414 TEMA Type P Outside Packed Floating Head No. of Passes U-Tube No. of Passes 12 12 16 16 38 32 10 68 92 88 136 128 18,1 t'76 241 210 308 30,+ 388 38,1 360 1048 U Inside I122 1112 Tube Count for 3/4-in. OD Tubes on 1sA6-in. Type L or Pitch Floaling Head No. of Passes No. of Passes 13 t2 22 22 45 44 76 76 109 104 137 t28 \'77 t76 241 236 293 284 366 364 436 432 612 608 828 812 t6 ! 1100 A Pitch TEMA Type S lnside Floating Head No, of Passes TEMA Type U-Tube No, ot Passes l0 104 64 t4t48 t9 18 12 t4 8 l8 22 18 16 38 42 40 36 32 42 40 32 30 32 24 68 14 72 60 54 73 66 60 54 56 52 98 109 106 96 86 109 106 92 86 92 80 134 130 124 112 108 140 138 124 108 114 104 r'76 114 168 156 152 187 184 168 152 83 74 230 24t 222 2t6 2r0 253 242 224 2tO 220 204 302 288 282 2@ 260 320 294 280 2@ 290 268 384 384 368 344 338 400 380 352 338 360 340 456 469 449 430 418 454 436 416 410 220 21.O 516 544 529 500 490 514 498 471 465 506 488 s96 @3 616 600 s1s 607 s87 560 558 614 580 720 744 132 '704 695 707 690 '769 663 657 720 684 760 830 804 859 83s 812 800 816 79'7 9'13 959 926 900 931 910 876 870 944 916 1118 1093 1054 l0l0 1062 1039 998 993 1076 940 1253 t224 ll84 1150 1200 lt77 tt35 |24 1218 1184 1392 1359 l3l8 1286 1341 1318 1282 t2g 1366 1324 1616 1602 1552 1482 1558 1554 1870 1833 1800 1770 1875 1834 2145 2107 2060 2025 2132 2100 2411 2395 2344 2305 2431 2392 273'7 2683 2@2 2612 2730 2684 3400 3359 3294 3220 3395 3346 U 1502 1482 1600 1552 1'736 1708 1854 1800 1998 196/. 2122 2064 2286 2250 2410 2356 2574 2536 2732 2668 3228 3196 3398 3336 131 132 Mechanical Design of Process Systems Table 7-13 Continued Tube Count for 3/a-in. OD Tubes on 1-in. TEMA TEMA LorM 5.047 6.065 7 .981 10.02 12.00 13.25 15.25 17 .25 t9.25 21.25 23.25 25.00 27 .00 29.N 31.00 33.00 35.00 37 .00 39.00 42.00 45.00 48.00 51.00 54.00 60.00 14 14 t2 22 20 16 42 40 36 7372& 109 86 80 139 134 124 187 180 168 241 232 220 296 290 280 372 354 344 434 420 404 507 489 476 604 s94 s68 689 679 660 808 804 772 906 891 860 1030 1152 1273 1485 r72r 1026 1000 1134 1090 1259 1222 1461 \434 1693 1650 1968 l94l 2221 2187 2502 2465 3099 3069 1902 2134 2414 3010 TEMA Outside Packed Head Head No. ol Passes 10 108 10 104 64 19 18 16 19 14 l2 108 40 38 36 32 28 37 32 28 26 28 24 64 &62 6058 61 60 48 46 56 44 98 95 94 84 78 96 94 80 78 86 72 122 12L ll0 100 98 r21 ll8 104 98 106 96 t& 151 146 140 138 163 1& 144 140 148 136 212 208 196 188 160 216 214 196 158 200 184 270 258 242 232 230 276 270 260 235 254 240 330 320 316 296 298 338 338 324 3m 3r4 300 404 380 372 364 33s 396 396 376 339 388 368 482 475 466 452 430 460 440 420 4r4 452 432 582 530 526 508 49s 558 554 536 494 538 524 672 653 &2 620 610 624 605 s89 581 632 612 724 696 688 669 7s6 744 '116 669 732 708 859 848 818 805 818 797 783 771 838 808 946 922 9M 880 980 978 944 880 950 916 1106 1081 1054 996 tU1 1039 1001 996 1074 rO40 1218 1208 tr74 1r2s rt72 1164 1130 1125 1200 1164 1426 1399 1376 1306 1367 1350 1322 13M 1406 1364 1652 1620 1586 1635 1608 1536 1s04 1632 1s84 1894 1861 1820 1887 tUz 1768 1740 1870 1832 2142 2101. 2060 2143 2lA4 2019 1992 2122 2076 2417 2379 2326 2399 2366 2270 2244 2396 2340 29W 29s7 2906 2981 2940 2932 2800 2992 2936 TEMA LorM 6.065 2l .98r 38 61 7 10.02 12.00 13.25 ).5.25 t7 .25 19.25 2r.25 23.25 25.00 27.N 29.N 31.00 97 117 158 zlo 262 J10 370 442 524 602 698 f-in. ! Pitch TEMA TEMA s P U Fixed Outside Packed Tubesheet No. ol Passes lnside Head No. ol Passes No. ol Passes l2 t2 16 16 38 32 60 52 90 88 I 16 112 158 148 208 188 256 244 316 308 372 368 432 428 524 500 596 580 692 688 U-Tube No. of Passes 22 TEMA 5.U7 U Inside No. ot Passes Tube Count for g/q-in. OD Tubes on Shell lD in. TEMA s P Fixed Tubesheet No. ol Passes Shell lD in. A pitch 12 16 37 t2 16 32 )/ )t) 89 82 9'7 94 t37 128 177 176 224 216 274 270 333 332 414 406 464 456 570 562 628 620 Head 98 16 16 32 12 52 24 56 52 76 56 89 82 88 80 104 104 120 lt4 r45 140 164 160 188 184 208 198 238 236 268 260 304 292 316 308 344 332 392 344 398 386 448 424 484 472 548 496 554 532 612 576 650 @8 4 12 U-Tube No. of Passes 64 88 32 t2 24 20 'tA <t 44 40 80 56 68 68 96 80 90 88 140 tl4 128 120 180 160 176 168 232 198 112 108 284 260 138 134 332 308 340 332 366 344 400 388 468 424 472 460 510 496 554 544 640 576 640 624 4 t2 Exchangers The Mechanical Design of Shell-and-Tube Heat Table 7-13 Continued Tube Count lor s/+-in. OD Tubes on 1-in' LorM Fixed Tubesheei No. of Passes Shell lD in. 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 s4.00 60.00 782 768 894 892 1004 978 I102 1096 768 880 964 1076 1283 1285 1270 1.484 1472 1456 l70l 1691 1610 1928 1904 1888 2154 2138 2106 2683 2650 2636 s P Outside Packed Head No. of Passes TEMA M Fixed Tubesheet No. of Passes Shell lD in. 5.047 6.065 7 .981 10.02 12.00 t3.25 t5.25 .25 19.25 17 21.25 23.25 25.00 27 .00 29.00 31.00 33.00 35.00 37.00 39.00 42.OO 45.00 48.00 5l .00 54.00 60.00 \2 2r 37 l0 8 18 16 28 32 61 54 97 90 113 108 156 146 208 196 256 244 314 299 379 363 448 432 522 504 603 583 688 667 788 7'70 897 873 1009 983 48 84 104 136 184 236 294 352 416 486 568 654 756 850 958 1118 1092 1066 1298 1269 1250 1500 1470 1440 1714 1681 1650 1939 1903 i868 2173 2135 2098 2692 2651 261.2 682 824 882 1062 1045 1026 972 1048 1028 996 1232 1222 1218 1140 1224 1200 1170 1424 1415 1386 1336 1421 1394 1350 1636 t634 1602 1536 1628 1598 1548 1845 1832 1818 1764 1862 1823 l7'/9 2080 2066 2044 1992 2096 20.+8 2010 2582 2566 2556 2476 2585 2552 2512 TEMA No. ol f in. ' 668 724 160 836 8'72 940 't20 8L2 924 9'72 1048 10/10 1140 1222 1204 1336 1420 1400 rs36 1624 1604 t'164 1852 1820 1992 2084 2064 2416 2596 2564 TEMA TYPe S TYPe U Inside Head Passes No. of Passes 1864 1837 1804 2098 2062 2026 26W 2560 2520 No. of Passes Pitch Head t2 10 8 16 t2 8 32 28 24 52 46 40 81 74 68 9't 92 84 140 134 128 188 178 168 241 228 216 300 286 272 359 343 328 42t 404 392 489 472 456 575 556 540 660 639 624 749 728 708 849 826 804 952 928 908 1068 1041 1016 1238 t2t6 tt96 1432 1407 1378 1644 t6Il 1580 U-Tube Head No. ol Passes 742 732 732 668 '130 112 816 8r2 804 760 848 828 952 931 928 8'72 931 918 Type P Outside Packed U lnside Tube Count tor 3/4-in. Oo Tubes on Type L or TEMA TEMA TEMA TEMA n Pitch U-Tube No. ol Passes 108 24 20 42 36 66 64 86 80 124 116 174 164 2t8 202 272 260 334 320 390 380 468 452 550 532 626 '720 608 700 818 796 928 904 1036 1016 1220 rr92 t4t2 1384 804 788 1834 1804 2584 2544 20'72 2036 133 134 Mechanical Design of Process Systems Table 7-13 Continued Tube Count for TEMA M Fixed Tubesheet Shell lD in. 5.M7 6.065 7 .98r 10.02 12.00 t3.25 15.25 .25 19.25 17 21.25 23.25 25.00 27 .U) 29.OO 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00 864 14 148 26 26 16 42 40 36 64 61 56 85 '76 72 ll0 106 100 147 138 128 184 175 168 227 220 212 280 265 252 316 313 294 371 370 358 434 424 408 503 489 468 576 558 534 643 634 604 738 709 6U 8M 787 772 946 928 898 1087 1069 1042 1240 1230 rl98 t397 1389 1354 1592 1561 1530 1969 1945 t90/. OD Tubes on 11/a-in. TEMA Type L or No. ol Passes l-in. Type TEMA P outside Packed Floating Head No. of Passes TEMA M Shell lD in. 5.O47 6.065 7 .981 10.02 12.00 13.25 15.25 17 .25 19.25 21.25 23.25 25.00 27.W 29.00 31.00 Fixed Tubesheet No. ot Passes 86 12 24 37 57 70 97 r29 t62 205 238 275 330 379 436 l0 4 8 20 l6 32 53 28 48 70 90 & 84 r20 r52 1t2 193 184 228 264 220 256 315 363 300 360 422 410 142 TEMA Type S Inside Floating Head No. ot Passes Type U U-Tube No. of Passes 74400 l0 104 44 22 18 16 14 l8 t4 812 14 8 38 36 28 24 33 28 16 18 26 24 56 52 48 46 51 48 42 44 44 36 13 72 60 44 73 68 52 44 56 52 100 98 88 80 93 90 78 76 86 76 130 126 116 104 126 122 112 192 114 104 170 162 148 140 159 152 132 136 152 136 2r2 20r 188 176 202 r92 182 172 19? 176 258 2s0 232 220 249 238 21.6 2t2 232 220 296 294 276 250 29r 278 250 240 270 256 3ss 346 328 300 345 330 298 288 322 3U 416 408 392 360 400 388 356 348 378 3U 475 466 446 420 459 450 414 400 444 424 544 529 510 498 s26 514 484 4& 508 492 619 604 582 s66 596 584 548 536 s78 560 696 679 660 646 672 68 626 608 660 632 768 753 730 723 756 736 '7M 692 740 '1r2 908 891 860 840 890 878 834 808 872 836 1041 1017 990 968 1035 lm8 966 948 1010 980 1189 1182 1152 1132 1181 l162 lll8 tO92 1156 tt24 1348 133'1 1300 1280 1350 1327 1277 1254 1322 1284 l53i 1503 1462 r4r'iO 1520 r49Z 1436 1416 1496 1452 1906 1879 1842 1802 1884 1858 1800 1764 1866 Tube Count tor 1-in. OD Tubes on 11/4-in. Type L or A Pitch TEMA Type P Outside Packed Floating Head No. ot Passes 54 12 2t l) 4 l0 8 18 16 lt 52 46 61 58 89 82 113 1r2 148 138 180 r74 22r 210 261 248 308 296 359 345 418 40r 28 40 56 76 104 128 168 2N 236 286 336 388 1828 v Pitch TEMA TEMA Type S Inside Floating Head No. of Passes Type U U-Tube No. of Passes 00 44 108 24 i0 36 32 50 44 70 64 96 88 124 t20 156 152 200 188 232 220 282 268 330 320 382 368 {l The Mechanical Design of Shell-and-Tube Heat Exchangers Table 7-13 Continued Tube Count for 1-in. OD Tubes on 11/4-in. 0 Pitch TEMA Type L or Shell lD in. 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51 .00 54.00 60.00 M Fixed Tubesheet No, of Passes 495 556 632 705 822 946 478 472 552 538 613 598 685 672 '799 786 922 912 1079 1061 1052 1220 t159 1176 1389 1359 1330 1714 l69t t6& TEMA Type P Outside Packed Floating Head No. ol Passes 477 540 608 674 788 910 1037 1181 1337 1658 Tube Count TEMA M Type L or Shell lD in. 5.O4'7 6.065 7 .981 10.02 12.00 13.25 15.25 17 .25 19.25 21.25 23.25 25.00 27.N 29.N 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51 .00 54.00 60.00 Fixed Tubesheet No. of Passes 964 L2 l2 12 22 20 16 38 38 32 )o )b Jz 69 66 66 97 90 88 t29 \24 120 t64 158 148 202 l9l 184 234 234 222 272 267 264 328 317 310 378 370 370 434 428 428 496 484 484 554 553 s32 628 621 608 708 682 682 811 811 804 940 931 918 1076 1218 1370 1701 106l l0,l0 1202 tt92 1354 1350 1699 1684 460 526 588 654 765 885 TEMA Type S lnside Floating Head No. ol Passes &O 7s6 866 1138 1292 r@4 OD Tubes on 1tA-in. TEMA Type P Outside Packed Floating Head No. ol Passes U-Tube 1002 1018 1000 1160 1142 1307 1292 1626 1594 ! U No. ol Passes 440 498 562 630 144 872 448 508 568 lor 1-in. Type 424 484 548 620 728 852 980 1116 12@. 1576 Pitch TEMA Type S lnside Floating Head No. ot Passes TEMA Type U U-Tube No. ot Passes 544-544-00 1264-126444 21 16 16 12 t7 12 812 12 8 32 32 32 18 30 30 16 18 24 20 52 52 44 24 52 48 42 24 38 36 61 60 52 50 61 56 52 50 52 48 8984806485786264.7268 l 13 112 rt2 96 108 108 104 96 98 96 148 144 140 114 144 136 130 tt4 t28 124 t'18 178 t'72 156 1',73 166 154 156 166 156 216 216 208 192 217 208 194 192 200 196 258 256 256 212 252 240 230 212 240 232 302 300 296 260 296 280 2'70 260 284 276 356 353 338 314 345 336 310 314 332 332 4r4 406 392 368 402 390 366 368 290 384 476 460 460 420 461 452 432 420 442 436 542 530 518 484 520 sr4 494 484 254 248 602 596 580 550 588 572 562 548 574 560 676 649 648 625 66r &0 624 620 W 628 782 780 768 730 776 7s6 738 724 758 748 9M 894 874 850 900 882 862 844 872 868 1034 rO27 101,2 980 1029 i0l6 984 9'72 1002 988 1178 1155 1150 1125 1170 1156 tt26 1114 1146 ll40 1322 1307 1284 1262 1310 1296 t268 1256 1300 1288 1654 1640 1632 1585 t64t 1624 1598 15'76 1620 1604 135 136 Mechanical Design of Process Systems Table 7-13 Continued Tube Count tor 11/4-in, OD Tubes on 1sfi6-in. TEMA Type L or shell lD in. 5.047 6.065 7 .981 10.02 12.00 13.25 15.25 1',7 .25 19.25 21.25 23.25 25.00 27.W 29.W 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00 M Fixed Tubesheel No. of Passes 744 864 t9 14 12 29 26 20 423834 52 48 44 69 68 60 92 84 78 121 1l0 104 147 138 128 r74 165 156 196 196 184 237 226 224 280 269 256 3t3 313 294 357 346 332 4t6 401 386 461 453 432 511 493 478 596 579 s70 687 673 662 790 782 758 896 871 860 1008 994 968 1243 1243 l2l0 Type P Outside Packed Floatlng Head No. of Passes TyPe LorM Shell lD in. 5.04',1 6.065 7 .981 10.02 12.00 t3.25 15.25 17 .25 19.25 21.25 23.25 25.00 S TYPe U Inside Floating Head U-Tube No. ol Passes No. ol Passes 00 00 64 14 22 32 48 64 86 tt4 138 t62 196 232 268 310 356 4M 452 534 626 720 822 930 00076414 14822 20 16 37 36 28 22 44 44 36 28 64 62 48 45 85 78 72 69 109 w2 96 86 130 130 116 1r2 163 152 r44 130 184 184 1"12 164 22r 216 208 196 262 252 242 228 302 302 280 270 345 332 318 305 392 383 3& 3s7 442 429 4r2 407 493 479 460 449 576 557 544 5r2 657 640 628 596 756 745 728 696 859 839 832 820 964 959 940 892 1199 1195 1170 1160 1116 Tube Count for 11/4-in, OD Tubes on 11fi6-in' TEMA A Pitch ! t20 144 164 296 3M 388 440 522 6t2 700 800 908 1140 fvoe rtinq Head 88 184 220 256 TEMA No. ol Passes 52 76 132 152 Tvpe S lnside I Head 42 104 l'vDe P No. ol Passes 32 60 80 TEMA No. of Passes 16 44 Pitch Fixed Tubesheet 12 28 TEMA Outside Packed 444 664 12 12 24 22 37 34 45 42 61 60 80 76 97 95 t24 124 t45 145 172 168 12 20 0000000 6640664 t2 12 lZ 21 16 16 32 32 32 38 38 32 52 52 52 70 7o 68 89 88 88 rr2 112 ll2 138 138 130 164 l@ 156 0r2 12 21 18 29 24 38 48 52 s0 70 80 85 96 108 114 136 136 154 12 12 28 34 48 66 84 108 128 rs4 4 8 16 34 44 56 70 100 128 142 U No. of Passes 000 000 064 12 128 18 20 20 24 28 28 48 42 36 50 56 56 80 74 68 96 98 96 114 124 120 136 140 136 n The Mechanical Design of Shell-and-Tube Heat Exchangers Table 7-13 Continued Tube Count lor 'l'tlq-in. OD Tubes on l/rs-in. TEMA Type L or M Shell lD in. 27 .OO 29.00 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00 TEMA Fixed Tubesheet No. of Passes 210 202 24r 234 272 268 310 306 356 353 396 387 442 438 518 518 602 602 682 681 7'.70 760 862 860 1084 1070 202 230 268 302 338 384 434 502 588 676 756 8s6 1054 ! lnside Floating Head U-Tube No. of Passes No, of Passes No. of Passes 1042 t034 1026 1008 5.047 6.065 7 .981 10.02 12.00 13.25 t5.25 t7 .25 r9.25 2t .25 23.25 25.O0 27 .O0 29.00 31.00 33.00 35.00 37.00 39.00 42.O0 45.00 48.00 51.00 54.00 60.00 544 664 13 108 24 20 16 37 32 28 45 40 40 60 56 '79 56 76 '16 97 94 94 t24 tt6 ll2 148 t42 t36 174 166 160 209 202 t92 238 232 232 275 264 264 314 307 300 359 345 334 401 387 380 442 427 424 522 506 500 603 583 572 682 669 660 1"t"t '762 756 875 857 850 1088 1080 1058 < , TEMA Type P Outside Packed Floating Head Type S lnside Floating Head No. of Passes ,l ,tl 12 108 2t 18 16 32 28 28 3',7 34 32 52 52 48 70 70 64 90 90 84 tt2 108 104 140 138 128 162 162 156 191 188 184 442 ,130 416 26t 249 244 300 286 280 34t 330 320 384 372 360 428 412 404 497 484 4'72 5',75 562 552 660 648 640 743 '728 716 843 822 812 1049 1029 t0t6 U Pitch TEMA No. ot Passes Type 184 180 158 r12 176 176 2t7 212 204 198 200 196 252 248 234 236 232 232 289 2',76 270 264 272 268 329 316 310 304 312 296 312 368 354 340 348 348 420 .102 402 392 396 392 485 116 468 464 472 456 565 55J 5+6 544 552 536 653 616 628 ',705 620 '7t2 628 620 738 126 ?20 708 837 820 811 80.+ 808 804 1036 l0lE i0r2 1008 l0t2 992 Tube Count tor 1tlc-in. OD Tubes on 1el16-in. Shell lD in. TEMA Type P Outside Packed Floating Head 193 184 184 172 224 224 216 198 258 256 256 236 296 296 282 264 336 332 332 304 378 3'70 370 358 428 426 414 408 492 492 4U 464 570 566 556 544 658 648 648 620 742 '729 722 7t2 838 823 810 804 TEMA Type L or M Fixed Tubesheet No, of Passes Pitch TEMA Type S TEMA Type U U-Tube No. ol Passes 00 00 44 12 20 26 40 56 74 96 t2 20 24 36 52 68 88 120 ttz 142 136 170 164 200 192 228 220 268 256 306 296 346 336 390 380 456 448 542 528 618 604 708 692 802 '784 l0l0 984 '137 -o9. 9. " . ? 9o o o a P 6 N | ld o"l-: -l | F F 6 0 d €; ci <; ;.rsso , , Rsg$ lo !9 INrl N < trli-: ! 3 i li t.tc o "1.;o { o"l;;;; i:aic;e';<; tr-' F!::"i j d<;d .r (9l <j i <; <j .9 : ,'€ t2 i ; i"'c:!i::gl:: onoofs{{{{ ,''i€e-i3t<i< Al rD^ iiH xl:.:.*;ia++l+a{ ii .El* ?l * i |.e "" t. -_.i =' a" i.i; c; ': Ea :< ol" / l14 ii:a | <tEt +{ -l6 _ aa a; <F NY ri,i*;;ital:i; rs 6|-= .9n lI-: Eo i6 t4> oo|. \ .oor -_,,' len-\dt I /11 y-s-\ i /or o,t E The Mechanical Design of Shell-and-Tube Heat iGlD.(NB + 1) (5.22X10)roD"7 r where (p/p,,). G,, D., D. NB Polh ot Fluid A. Shell side fluid baffling showing segmental cut baffles. ^l t. Fluid Flo13 Poroll.lhTubrs os,t Po3r.3 /From one Bolll.d A..o io N.rr. eorrrr "wintoi' or "co'l 03 %cu!,{hkh O O J Eac$ed sotlrs Ooid O B. Segmental baffles showing window are for fluid flow. oootoo ooolooo ooooo ooooo ooooo ooooo )OOOooO oo Iilol.:Ar0o Avo,l0bla tor Cror! Flor i:l:1if.' 4,i! *, C. Cross orhe' L3ed Cort,r,!rr r .' peler*ce I . oth.t a,,olq!-e.rt ro ooh . E3se"',- ||e so-. flow area for iube layouts. Figurc 7-228. Various baffle *indou schemes [,1]. Baffles neveq except for unusual designs such as orifice baffles, extend a full 360" around the shell. The baffle plate is cut such that the shell-side fluid can flow around its edge. The open area between the baffle edge and the shell wall is known as a baffle "window." Baffle windows are commonly referred to in terms of percentages of the entire circular shell area. Figure 7-22b illustrates various baffle window schemes. Shell-Side Pressure Drop. There are several methods to calculate the frictional pressure drop across tube bundles, and the reader is referred to Ludwig [4] or Kern [9] who give comprehensive discussions of the various techniques. The method we will (7 31) : : are previously defined number of bafiles = specific gravity of : shell-sidc fluid combined friction factor deter mined from Figure 7 23 is {%XSherl 10.). Ner Fror Ateo ol Wiido* is Full Windor A/.0 Diius Ar.o Boftr.s @0,'d@ 139 Kern [9], where the expression for the shell-side pressure drop is given as follows: Sallle Pilch or Stoci.q ;9 ] Exchangers use is the one developed bv TUBE VIBRATIONS Chapters I and -1 described how fluids moving around objects can produce r ibrations. The same thing happens in shell and tube heat exchangers, but it creates a different problenr. Chapters I and ,1 were primarily concerned with Yorte\ sheddrng. This chapter covers vortex shedding and sereral olher t\pes of vibration phenomena. Also. the problen is difterent from rhat in Chapter 4 because the boundarr conditions of the system have chansed. Chapter I used a cantile\er beam to show how a til\\ er or srack is restrained several different ways at the ends." There have been nrany research studies made in the field of tube vibrations. Probably the most numerous stem lrom the nuclear industry. The problem is complex and no one method proposed is a full and complete anal- ysis of tube vibrations. Consequently, research is still being done to better understand the causes and prevention of tube vibrations. Here we will outline the causes of the phenomena and present some quanlitative approaches to the problems. Presented first is a simple and quick approach to pre, dict tube vibrations caused by shell-side flow. This approach was originally developed by John T. Thorngren [14] in 1970 and is called the "maximum velocity method." We will present a modified version of the method proposed by Thorngren to encompass a wider range of applications and to specifically define all the variables in the equations. This method addresses the tube vibration caused by vortex shedding when the shellside fluid alters direction at the baffle plate and strikes the tubes. The arrows in Figure 7-l show how flow di, rection of a fluid turns at the baffle plate and strikes the tubes midwal between rhe bafile plates. Thi5 causes rhe tubes to deflect and the hole in the baffle plale acts as a fulcrum for the tubes to deflect against. Two types of problems can result a fatiguing of the tubes at the baf: fle hole and eventual tube rupture, or the tubes colliding For low-Finned Tubes f" (sq. ft)/(sq. in.) ' oooF iol) 6 a <tQ ||' F ^z.E ^z,E .!. l-€-e;; - -- g rtx 3: :- =l -'; ; .3 -i 3 q "- :E -al -- ? F 3l; tree lli:E fr xla E I -.j i; xlo :i X -. --:'i 3; 5 'rli :lu,r, 5c; -= ;= 6e= < --- --=: =F= "el "'59 -tr -c6; 'r =-Ft* {SS s5- E} ^i' i;t--E E\.E tl+ P; tld ES.= E c* E E :lr=-E zl x Sooo -o9= eElDF; o. -8 . = g:: -E+xld.FsE:;.E-E€ ;l: @ ;9-e A;o.9 g ol - -:;- :1:;5#!=sji5Fi; ^6+ - oo !: c(r(-)oE I go -oo ; 6r9 0'--jzz, o,< @-1. ! E5 j: r: ri=\= gi 99 ;E e: :5 P = - =t d > o :: "l ,: E=.E EEP ;€ rj6tr :d*+ o._ !2.f --;;; !{E- --es ;==* !ii; 3= i; iE s r !'EE Ess_ii3;S ; t -: a*:L:L+: oooF <t lo |.l rt n) -ooFtoI' t ro N x: ..!A .9: fri {.) N ": tl.E oti ii, The Mechanical Desien of Shell and-Tube Heat with each other resulting in abrasion and rupture. This phenomenon can be offset somewhat by anticipating shell-side velocities. The velocity of the shell-side fluid can be kept reasonable if the entry and exit nozzles are properly sized. To determine the force exerted on the tubes by the fluid vortices we refer to Equation 4-80, the von Karman eauation as follows: E_ Co pY212 (4-80) 2g" In the case of tubes the characteristic area, f2, can be replaced by the outside tube diameter, d. (ft), and the value for the force becomes: CFpV2do : force per unit length of tubes (4-80a) Chapler 2 introduced the concept of the Strouhal number as the numeric constant between the resonant frequency of vortex shedding, f,, and the cylinder diameter, d., divided by the free stream velocity, V This is written AS: f.d" ()-31) Exchanqers 141 7 -24, we notice how the drag coefficient varies over a wide range of Reynolds numbers. For viscous liquids moving at low velocities, it is very possible for the Reynolds number to be low, making the drag coefficient high. Thus, we keep Cp as a variable in Equation 4-80. In Figure 2-32 we see that at NR" > 3.5 x 106 the vortex street is again developed. At this Reynolds number the fluid flow velocity would be too high to consider wind design as discussed in Chapters 2 and 4. Also, those two chapters were only concerned with a single cylinder, whereas here we are studying the effects of vortices on an array oftubes. At values of Nn" ) 3.5 x 106 for tube arrays we would be more concerned with flow-induced vibration. which is discussed in the next section. Also. Reynolds numbers in this range rarely, if ever, occur in heat erchangers. In an arral oftubes the maximum velocity ofthe shellside fluid occurs at the minimum cross section between the tubes. Thus. V increases such that as the tubes get closer together the ralue of Nq. approache\ 3.0 x 105 and the rorter street is broken up as previously described. Thus. the effect of vottex shedding in tube arrays is onl1 si-enificant for tubes spaced such that the Relnolds number falls within the appropriate range. The effects of tubes being spaced closer are discussed later in this chapter. viscous liquids. Now, observing Figtre For considering vorteK shedding, Equation 4-80 represents the maximum force exerted on the tubes. To ana- As observed in Figure 2-32 the vortices break up when Nq" approaches 3.0 x 105. Referring to Figures 4-21 and 4-29 we see that the force or drag coefficient is constant in this range. However, in Chapter 4 rve are dealing with air as the flow medium. In our application here we are dealing with a wide range of fluids-gases to heavy, lyze the tubes, one must consider them as continuous beams supported by baffle plates. The baffle plates act like beam supports as the fluid exerts a force in the tubes forcing them against the baffles. The general equations for the shear force and deflections of a continuous beam take the following general forms: FiE)re 7-24. Drag coefficients versus Reynolds number for long circular cylinders in crossflow. 'to '142 Mechanical Design of Process Systems F. : aFrL ^ bFI L4 EI (7 -32) (7 -33) The values for a and b are dependent upon the boundary conditions of the continuous beam. Typical values are presented in Figure 7-25 and are fairly comprehensive for most shell and tube exchangers. For cases not covered in Figure 7-25, the specific values must be solved for using the analysis for a continuous beam. As the shell fluid exerts pressure on the tube, the tube deflects at mid-span forcing the tube at the baffle against the baffle hole. The stresses induced in the tube are a resuit of localized forces at the tube-baffle contact points. At these points the tube behaves similarly to a horizontal vessel such that only a portion of the tube wall offers effective resistance against collapse. Thus, Equation 4-2 predicts the amount of tube wall that effectively resists the baffle wall reaction, and is written as a:11{\12+ :olI (4-2) 180 Continuous Beams dmar br"r I l .200 2 3 0.550 0.0059 0.0099 0.0069 0.0094 0.0097 0.0065 1.100 1.223 4 0.572 1.143 5 6 4 [.r. (0,130 r fton A] = t.005r ,rrlsl A € comtruous ! il.r. (0.tt , tioE ^ .' a r.& o.raa I rroi A o. D) - 0,0rl !r. (0,415 r koh E, 5 o.m!a !r./al BEAM-FoUR Eeual spaNs-LoAD FtRsr aND THrRo spANs o) a 0,00n &,4/El a 6. rr.r. tl.r. (t az rlr.n A) E 0.6tt {,r/al coNTlNuous BEAM-FoUR EeuAL spANs--{LL spaNs LoAoEo r ^ .L (Gaa I lr.h A .na a) Figure 7-25. Boundary conditions of continuous beams u5l. - O.Ol5 d./s The Mechanical Design of Shell-and-Ttbe Heat where d = A= angle of contact where sisting tube wall area : that neither the tube nor baffle hole will deform to reduce stfesses, which is the worst condition. For determining contact stresses between the two bodies, Timoshenko [16] has shown that for the case in Figure 7-26 the diameter of the circle of contact is : 149 constant that represents the amount of effective re- radians Thorngren [14] proposed that about 40% of the tube metal is effective in resisting wall membrane stresses. In Equation 4-2 this would make the value of 0 144' , greatef than most saddle-shell connections for horizontal vessels . To take the problem furtter we consider the tube wall as a ring shown in Figwe 716. The assumption is d : q Exchangers 1.76E(qi_e")g4" l"' [ 2EEB(d, + dJl Now combining Equations 7 -32 and 7-35 we have the followins: : " I--Lil--qe-)||--t')' \aF,L/ \4 + dB / \0.798/ r-v! l-u$ where c = z, = hisson ratio for the tube material, dimension- less /B = hisson ratio for the baffle plate material, di- mensionless E= Ea From Equation 7-34 one can deduce that the tub€-bafalLalyzed as point loadings. For such loadings as shown in Figure 7-26 the contact force representing the shear of the tube against the baffle plate : modulus of elasticity for tube material, psi nodrlus of elasticity for baffle plate material, pst fle interface should be *. (#,.J"L,,*',J' c = constant, in./lbr cr : constatrt, dimensionless To arrive at the modified damage numtrr damage we solve for F1 in Equation 7-32: Q-3s) (7-37) EB Q-34) ts (7-36) F,: - for baffle F" o'al- Evaluating the relationship for shear in Equation 7-32 we have F. = aaFrl- Now dividing this relation into Equation 4-80 we obtain Cpd,p\Palc _ 1.0 2g"F. Letting the baffle damage number be represented by Nss, a dimensionless parameter, we have: *, ^"" - Cpd.pV2alcv --fdE- where Nss ( Q-38) 1.0 If NBE > 1.0, then tube damage at the baffle is very probable and a tlicker tube should be selected and the analysis repeated. The analysis of determining the dimensionless parameter, NsD, which governs tube damage induced by excessive displacements in tube movements, is similar to that for the baffle damage parameter. Solving for F1 in Equation 7-33 we determine F1 as follows: Figule 7-26. Fluid foroe causing tube to impinge on plate. baffle F"" : E bL4 144 Mechanical Design of Process Systems Dividing this expression into Equation 4-80 we have Ded,pV'?bLa _ 2g.6E,I 1.0 We define N6p as rrcD - CDd,pv2bL4 2g.6E where NcD < (7 I -39) 1.0 > 1.0, then thicker tubes should Once again, if NcD be selected and the analysis repeated. Equation 7-39 is similar to that obtained by Thorngren [14] and Coit [17]. The dimensionless parameters, Nss and N6o, in Equations 7-38 and 7-39 should be regarded as mere rules of thumb. Even though they are dimensionless, they do not have the same firm basis as do dimensionless parameters used in fluid mechanics and transport phenomena. One can approximate the tube behavior by using the principles in Chapter 2, Example 2-6. Using the baffles as supports and spacing them (either equally or unequally), one can simulate the tube displacements. However, since we are not dealing with a single tube, vortex shedding around tube bundles can presently only be accounted for in design by being conservative. Flow-induced vibration of exchanger tubes is another mode different and distinct from vortex shedding. In vortex shedding a component of the flow, the vortex, is the contributing cause to the tube vibration. In flow-induced vibration, forces are exerted on the tubes that are caused by flow field interactions around the tubes. Fluid that flows normal to the tubes is forced into a smaller area between the tubes resulting in a Venturi effect known as "jetting" or "jet switching." This phenomenon is shown in Figure 7-27 where a control volume of fluid is shown being compressed between two tubes. The result of this 'letting" effect is the fluid exiting the narrow area between the tubes diverges into a diffused mass that whips or whirls around remaining tubes. This "whirling" effect is another mode of vibration. Vibration induced by turbulence is the most common mode. This phenomenon is commonly confused with the other modes because the term turbulence is viewed synonymously with fluid flow and vibration resulting from such flow. However, vortex shedding, jetting, and whirling are different from turbulence because even though they exist in turbulent flow, they can all be final causes of failure and each must be controlled. Turbulence can be best viewed as a pressure field around a tube shown in Figure 7-28. Herc we see a pressure dis- FigUJe 7-27. Jet switching in tube arrays. F-+ 6= futr) p = p_(t) where t= iime (r\ Figure 7-28. The magnitude of the direction of the fluid striking the cylinder can be thought of mathematically as a forcing function, F-, mapping a pressure distribution around the cylinder over region R. 'wi The Mechanical Design of Shell-and-Tube Heat Exchangers tribution around a cylinder in much the same way as an aircraft airfoil. This pressure field, or distribution, varies all through the flow regime and is also a function of time. As this pressure distribution fluctuates and changes, the tube is subject to vibration as the fluctuation frequency approaches that of the natural frequency of the tube. It is this fluctuation frequency that is referred to as the turbulence response spectra. As the pressure distribution changes over random time intervals, vibration is generated. We will describe briefly the methods to analyze these modes of vibration. The subject is exhaustive and is far from being a perfected science. One could spend many volumes the size of this one and not adequately cover the subject. For this reason the reader is referred to Blevins [18] for more details. As previously stated, turbulent flow induces continuously varying pressure distributions all around the tube surface(s). The efficiency as to how the pressure forces excite the tubes in each mode (first, second, third, etc.) of vibration is termed 'Joint efficiency," denoted by J;(<,r). This parameter represents the model efficiency of the pressure forces at a given frequency c,.r, where col is the natural frequency ofthejth mode. Figure 7-29 shows the joint acceptance of a single tube plotted against cull V. (U in Figure 7-29), where L is the tube length between spans and V is the fluid velocity. The ratio of the t 5 : 3 0.01 fluid velocity to the turbulence frequency, as the correlation length ard is given by 145 r,r, is known (7-4o) > I, then the varying pressure forces that act If L. > along the tube oscillate in phase. Also, ifthe value of L" is much smaller than the length of the tube, such that coL _ >> I then the joint acceptance is independent of the mode shape and is proportional to the value of LclL. The mean response of the tube is the average tube displacement induced by the mean flow over the specified time interval. The greatest percentage of the response exists in the fundamental mode. For a tube that spans several baffle supports the following expression is used for the mean response: 6-, = 0 036cv'd, (*)(*) where C =9.7x10 p= '(*.)""'" ('.J (7 -4r) 1(sec)05/(ft)r5 density of fiuid external to tubes, slugs/ft3 slue 32.2 lb.) : (1 /''i V""-;''\ ,,, ,,, Figure 7-29. -Th€ joint acceptance of a simply suppofted tube subjected to turbulent flow. (From FlowJnduced Vibration by R. Blevins @ 1977 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.) 146 Mechanical Design of Process Systems V : fluid velocity of fluid external : dr : L: Lr : fN : m mass density of to tubes, ft/sec fluid external to tubes, slug/ft tube OD, ft tube length between baffles, ft total length of tube between tubesheets, ft fundamental natural frequency of tube portion between baffles, Hz sum of structural damping and the fluid dynamic damping distance along tube, ft I : x: d" : 4Rs : 4(hydraulic radius) : 4 (flow area between tubes) wetted perimetel - ;] ". tubes on an equilateral triangular pitch of P _ -; +0, [/r\ t\-dJ - f] - ro.,"0", on a square pitch ot P t2 o*": E-Cp1*-y 6.* : : 2.586.-, (for x : L/2) F i,l2 -L ,lZ r0 (7 4= = (7 -46) /\ ."^ _ pv'0, 6"" 16,l 2e, where K, : \d,/ 2T- tn D T /nVfor :r ) l 5 \T/ D' Kr: l:l (7-43) 5 - ;;; 6L- dti -4s) (P\'", \T/ r< D 1.5 drag coefficient of tube surfaces The value for the natural frequency at the tube in : mr : (7 \o,/ K, = C'(D/T) Equation 7-41 takes on several forms. The easiest to use is the formulation developed by Blevins [18]: where E, zE" (7-42) Equation 7-42 represents the maximum tube deflection to be incurred. The factor 2.58 represents the ampl! tude of the highest one percent of cycles. "7( rN pv':d, -. 16,l ru' : -N" l=l - Using Figure 7-29 the value of thejoint acceptance for the appropriate mode and the first mode are obtained. The ratio of the joint acceptance of the mode being considered to that of the first mode is multiplied by the value of 6.*, obtained from Equation 7 41. The relationship in Equation 7-41 is based on the theory of tube turbulence developed by Wambsganss and Chen [9], which yields the followins maximum stress value: where Ce port end conditions, and tubes that have equal spans and unequal spans. These expressions were presented earlier in this chapter and in Thble 7-6. Equation 7-44 is simplest to use because it requires less input. However, when the information is available and time permits, the expressions recommended by TEMA should be used. The phenomena of "jetting" and "whirling" are not as well founded as vortex shedding and turbulence. This does not say that vortex shedding and turbulence are solidly based, but relatively speaking, they are compared to the other vibration modes, such as jetting and whirling. From Figure 7-28 one can predict that when the tubes are inclined to the fluid flow, the results are force components about the x and y axes. Equation 4-80 illustrates how one can determine the force induced per unit length of a circular cylinder. In the case of whirling and jetting the term CD is a variable. This term is called the force coefficient and is used in Equation 4-80 to evolve the following expressions: -44) modulus of elasticity of tube metal, psi mass density of tube metal. slugs/ftl tube OD, in tube ID, in. TEMA gives a listing of expressions for the natural frequencies of the tubes based on several types of sup- -(,n)'.,(,n)' where D and T are parameters defined in Figure 7-30 and Fig- ure 7-31. Values for K, have been plotted against the parameter T/D. These values are shown in Figures 7-30 and 7-31 to represent the whirling parameter 2(2?r)0 5/(C"Kr)0 '?5. Experiments indicate that the lower the whirling parameter the greater the probability that whirling (and jetting) will occur. To determine if the tube deflections are within a safe range one must estimate the components F, and F* at their maximum values using Equation 4-80. From the tube spacing determine the force coefficients K, and C* from Equation 7-46. Then solve for 6, and 6" and determine if those deflections are acceptable. After determin- The Mechanical Design of Shell-and-Tube Heat Exchangers ing that the deflections are in a safe range, use Figures 7 -30 and7 -31 to determine the whirling parameter. If the parameter is on the low side, then the tube spacing should be increased to raise the whirling parameter. Unfortunately, at the current state of technology, there are no critical values to decide whether the whirling parameter is critical. One manner in which to avoid nroblems with whirling is to use Table 7-14 in derermining the maximum shell-side fluid velocity flow. This table and the previous discussion will eliminate any problems with jetting or whirling. If the velocities cannot be controlled, because of someone else's design or a client's requests, then this procedure can give one an idea of whether whirling can be anticipated. The main focus is to keep the tubes spaced such that the maximum velocity will be reasonable. It has been confirmed bv exneriment that the critical velocity for whirling increises'rapidly wirh the minimum spacing between the tubes and that inline tube arrangements have lower critical velocities than staggered tube arrangements (refer to Figure 7-19 for the various illustrations of arrangements). PLATE.FIN HEAT EXCHANGERS These units use have been on the increase the past sev- eral years because of an increasing number of liquified gas and cryogenic plants. The plate fin heat exchanger is 1 147 more efficient than the shell and tube exchanser because the comparable shell and tube exchanger req-uired to re- fin would be eight times the volume and twenty-four times the weight of the plate fin if constructed of aluminum. The reason for this is that if the plate-fin is made of brazed aluminum, the aluminum place a plate conducts heat better than most materials and can be used down to absolute zero (-460'F). Since the ductility of carbon steel is lost at -20"F, one must revert to expensive nickel alloys or stainless steels in the shell and tube design. Thus, for cold services, the plate-fin offers some advantages. It is here that the advantages of the brazed plate-fin exchanger end. For the plare-fin to be applied, a very clean service is required. Even in clean services, these units can accommodate certain thermal shock and fatisue. It is quite possible after continued and repeated therrial loading in excess of differential temperatures of 50'F that internal components can fail. In addition, because these units are aluminum. external nozzle loadings induced by the piping can cause pipe stress problems. One must be extremel! careful ho\\' much loading is induced to the nozzles. because even if failures do not occur, leaks are common if overloading exisrs. Thus, if the service is not clean. a shell and tube design must be used. In gas processing and cryogenic services, the plate-fin exchanger suffices because in these applications the ser- --loF \JT rl-L o Oo ./ ./ ,-7 -rlA ---_ - i, . -2 . 5,onr-3ro'2 ' xY -lDt'3 (0,1,3 Figure 7-30. Whirling parameter of a tube row expressed as a function of transverse spacing. (From Flow-lnduced Vibration by R. Blevins @1977 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.) 148 Mechanical Design of Process Systems !M!! "F A o o o .-1'h >; -/l ,r1 o --r. h -- u+ I o Figure 7-31. Whirling parameter for tube ar- rays. (From Flow-lnduced Vibration by R. Blevins Oi977 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.) With newly developed techniques in vacuum brazing, stronger bonds have been achieved that reduce failures of internal components subjected to thermal shock and Table 7-14 Maximum Recommended Shell-Side Velocities All liquids in 10 fusec Gases and Vapors-in fl/sec Pressure (psi) 18 30 50 100 150 200 2'7 -tn.(vac) 250 185 160 110 100 90 15-in.(vac) 130 100 85 65 60 52 0 100 80 70 50 45 40 50 65 55 45 35 30 25 100 200 500 1000 fatigue. Molecular Weight 55 45 35 25 20 18 50 40 30 23 19 t7 40 30 20 20 15 400 77 45 35 20 16 vices are relatively clean. However, it must be noted that shell and tube exchangers are more popular because of their flexibility ofuse. Certainly with moderate to heavy viscous fluids, the shell and tube exchanger is the only design to use. Figtre 7 -32 shows a plate-fin exchanger with rectangular boxes containing an assortment of plates and fins resembling honeycomb structures. Fluids flow in tubu- lar channels formed by fin attachments between plates (Figure 7-33). The plates that separate the two services vary from approximately 0.006 in. to 0.023 in. in thickness, depending on the pressure of the service. This design is commercially available at a temperature and pressure of approximately - 452"F at 1,400 psig. The aluminum flanges used on these units are designed per ASME Section VIII Division I and, quite commonly, are identical to ANSI 816.5 flanges. For further discussion on the thermal analysis and design of plate-fin units, the reader is referred to Kays and London [20]. EXAMPLE 7.1: REGENERATED GAS EXCHANGER DESIGN A gas-gas shell and tube heat exchanger is to be designed. The exchanger is to be used to exchange heat between a hydrocarbon process gas and a gas used for regeneration. The unit is to be designed per specification sheet in Figure 7 -34. The exchanger is shown in Figure 7-35. The process gas is to be cooled from 965'F to 705'F. The regeneration gas is to be heated from 200"F to 661'F in a parallel configuration. Thus, 975'F 200'F GTTD:775"F 750'F tiITD : 625"F 125'F .M The Mechanical Design of Shell-and-Tube Heat Exchangers LMTD: '7'75 - 125 149 :356"F h (E,l u25/ now, q : riCo(LMTD) The shell-side mass flow rate : 22,050 lb,/hr for the shellside gas, Co : 1. 10 Btu/lb.-'F. The required heat duty of the unit is q = 122.050r ' q : l!hr rr. ror j'l= 1:so.r"r lb",-'F -- Rfr 8.634.780 I nt The available tube area in the exchanger is determined follows: From Table 7-3, we determine that for a l1/+in. tube the square feet of external surface per foot of tube is 0.3272 ft:. Thus. as Figure 7-32. The plate-fin exchanger. (Courtesy of Albraze International, Inc.) Available area = (0.3171) 'ft T (ZS:),u0., (tr) ,, = 1.38E.95 it: ng Sh€el Bar Turning Distributor Fin Figure 7-33. Tubular channels in plate surfaces result in excellent heat transfer in plate-fin heat exchangers. (Courtesy ofAlbraze International. Inc.) 150 Mechadcal Design of Process Systems I HEAT EXCHANGER SPECIFICATION SHEET 2 5 5 7 a 9 lo ll t2 l3 l5 l6 t7 t8 t9 20 2l 22 23 ?1 27 2E ?9 30 3l 33 34 35 36 38 39 40 41 42 43 1t6 47 4E 19 T"b"-T,rb".h".t J.i.t 50 Bundle Entranc€ Bundtc Erir 52 53 57 5a 59 6l Figure 7'34. Heat exchanger specification sheet. (O1978 Tubular Exchanger Manufacturers Association.) The Mechanical Design of Shell-and-T[be Heat Exchangers 151 For the tube-side gas, 1%-in.-11 gauge tubes sa-tua-600 : k: osME) 0.7, obtained ftom Process data Np" P 0.03 Btu/hr-ftL'F 0.01 Cp : 0.024 lb/ft-hr = Tirbe-side mass r.gu;riil{ flow rate = 41,884 lb./hr For each tube, . ---- 41:qq4 9./hr 283 tubes : 148 rb-ihr : O.1524lbJft3 ' 4 =: l'25 in" 1'010 in'; di Ar : 0.8012 in''? P : 48.48 ff/sec From Table 7-14 this velocity is reasonable sa-ra8-6lrt (^snE) Flgure 7-35. Vertical gas-gas exchanger. Shell-side nozzles C and makes the flow area l. = a'(16)'z= D are 16 in. in diametel which _: Nr" : Nr" 2ol.o6 in.2 : t.396 ftz (48.4D a 93,278 > (1.oro) in. ffi ,o tou * 10,000 and Equation 7-19 applies 0.027(93,278)0.8(0.7)t/3(1.0) : 226.78 h..1. Shell-side mass density v: 22,050 : p. rr. / rr,. \ + nr l=.:;r-l Ijbtt, secl j::--l:i:- : 0.09 lb./ft3 Nr" ::+:1 From which, : 48.75 ff:/sec ------o.os !!r n.396) ft, ftr From Table 7-14 we observe that this is a reasonable velocity. ftrbe.Slde Film Coellicient Btu : ro -- hr-ft2-"F -- lt For turbulent flow inside tubes we use Equation 7-19, the Sieder-Thte correlation, Shell-Side Fllm Goefficlent Nu" N.," = 0.027(NrJ03(Np.)18 (rJrJ''4 : ? = o.:o (Ps, )"'rN*,',, (;)" Q-26) 152 Mechanical Design of Process Systems For 60"-4 arrangement, p : 1.75 rn. 1.r. ^"" _ - - 8[0.43P'z 0.52'd"'z/4] -- - c= B : 0.119 : L75 - 1.25 : _I 0.50 in. 80.83 -. - -^. I - ln. n 8 baffles : = (1.75xt44) in j\ hr-ftr-"F 1.lso;"n 1,384.91 ft': From previous calculation, - l. t9 rt' -ft' Available area : 1,388.95 ft'z In most applications the available area should not be n : p 0.09 lb-/fC average for tem0.05 lbm/ft-hr : Shell.Side Pressu:e Drop Ap- lh <n '"m 12.348.00-15 hr-ft2 D.G, {0.119) fr (12.J48.00) lb./hr-ttz ^, _ 4 __. 0.05 lb./ft-hr NR":29,388.24 Ns D. G, = : : ure 7-22, 8 baffles t) (7_Jt) : : 3.333 40 in. shell ID 12,348.00 lb./hr-ft2 = For Np" 29,388.24, f = 0.0022 ft from Figure 7-23. f f,=::=0.00t8 t.1. : 'y : D" 100 / rr.re,r"t f C.rD,(l_.,t8__t (5.22X10)!oD"1d For plain and bare tubes, The exchanger has baffles with 25 % cut, thus from Fig- = : . +nr 10% greater than the required area, such material is not wasted. c"" - .=^.+ = 1.79 11' Np. 8,634,780 1tz.st,) as ff "l/'\l--- hr-ft2-'F a,, 2 For the shell-side gas, p peratures specified, and : I + 23.40 Btu : (7-301 (40) in. (0.50) in. (22.50) rt + 0.001 Area required : D.(cXB) . , a\=-ll" p(t44) ^rn 0.001 22.50 rn. Computing the flow area of tube bundle n" + distance between baffles B: : Btu hr-ft2-o F IT _ ft tube clearance ._ jn tnnll l^',',"=l t0.8tr/\tt \u. r lvl For gases used in this application the fouling factors are 0.001 shell-side and 0.001 tube-side. Solving for the overall heat transfer coefficient, or : 1100) (7-2e) "dr, 8[0.43(1.75)7 - 0.5rr1.25r']l41 _,/1rr^' _ r(l .25) D" = \o t+ [aJ 0.119 specific gravity of shell-side gas r 0.8 from process data d : r.0: / \o t+ tl] = 0.9 Exchangers The Mechanical Design of Shell-and-Tube Heat (0.0018)(12,348.00f (3.333X8 aP" = AP. + From Equation 7-35 we compute the shear force induced on the tube at the baffle hole, 1) (5.22X10)ro(0. l 19)(0.9X1.0) = 0.0015 psi 7-34 < < 10 psi allowed on data sheet, Figure I ^" \ /R:l#kltto-.tnr] V t='' qEB + --l --f",&: "= EXAIIPLE 7.2: VIBRATION CIIECK FOF c_ 2(1.00 span between baffles = Shell-side gas density 4 : : = 22.50 in. 16.015 1.25 in. ds : = = * in. 1/o+ <olito.ri Fr. : 1.200 lbr/ft F. : eaF, 1.156, where t/e+ in. is the baffle hole clearance (s€e Figure 7-34) A,' : + [o," - o,"* + D'= d'te - al nz t44t P I ^, Ar 210.0 in., D,o : 37.125, P =#[oo : - rr.,r, = G": 18,522.0 (5.145) (1. 1ox1.2oo) rtBE ^, - - 117.236 A sec b : 0.0069 o SeC" F + (zig*") - = 6.471 CpdlpV2ale (7-38) ------;----zE"r ' r.2s)] lh .:"' !-: lDf J-(l6.0lt - SeC- +n ft'-sec , (2.0s1) ft, 5 n'-sec 0.0e : :5.14s -;l tt'-hr 1.10 and aFrL 2(32., l|1 : - Nse 2.051 ft2 *,0-', (oryJ 16.015 lbf/ft 1.75 .tf#6.?s 1trpsi 10_E p orr.rrur$ (9 z1tzz1 !": tDf L = q: From Figure 7-20 we compute the shell-side gas velocity bgtween tubes. : x ft= in. D. 27.0 crPP4 Fr: 18,052 psi at shell-side conditions 1.25 = lbr/ft Frorn Figure 7-25, a 0.09 lb-/ft3 * = '. [.' ?]il''"l,o From ASME Section VIII Div. I (see Chapter 4) for the tube rnaterial at design temperature, o"n, = 4.941 x 7-l is to be checked for possible vibration problems. To accomplish this we compute the damage numbers of equations 7-38 and 7-39. B = tube - Es (7-35) 0.?33) 27xlop REGENERATED GAS EXCHANGER The exchanger in Example 153 5 betwe€n tubes NeB : rr.rr (lJoJ ft6.471) 1.00 Cedp\Pbla ,.." ", _ _EJE;_ (7-39) 154 ^ Mechanical Design of Process Systems bF, L4 For the tube-side, E,I/\ (o.oo6ex t.2o) 6 : N.o l]i I (22.50)a \Lz ln.i 106)::] (0.06881 in f( x l0-5 9.520 rt th- \ (27 ry M,:1.448f:o.o+sf fr 0.036 r4.94r 6.., : 7.553 in. \ 12 | : 0,.. : x l0 7 ft 1.000 H (;9" [.J",r [.) o.o36cV2d, (7 -4r) (1-44) d, = 1.25 dt : 1.084 '" - 8(rrjo4: 9.063 x 10-6 in. in. = in. 0. 104 : EXAMPLE 7.3: CHLORINE SUPERHEATER DESIGN A plant wishes to use hot oil to heat chlorine sas. The exchanger unit. a chlorine superheater. is to be i TEMA 18-150 AEL. The chlorine gas is to be heated from 77oF to 158'F and the hot oil is cooled from 250.F ro 176.F. The exchanger is to be rated and analyzed for tubetubesheet loading. The exchanger specification is shown in Figure 7-36. The thermal duty is 600,000 Btu/hr. The exchanger is a parallel flowing unit. ft 0.090 ft ., ,0"" lb. " "*- *l ttt.zsF in.2 + (1.084)2 in.2 / r ,rug \ /rzza in.r\ 1:z-z ruJ \-- ft-/ LMTD = For shell-side fluid, crrD - (with a lbJ| LTTD \tttol _ 173 'n - t8 :68.496.F irz:\ \-tr / parallel exchanger no correction is needed for LMTD) Tube-Side Film Goefficient For chlorine gas, frr \ 32.2 250'F 77"F : . /crro\ '" 1.710 Hz ,'^ /,^,..^\ r:!,llils in. 176'F out in. 158'F out 173'F LTTD: l8"F Shell-side (hot oil) Tube-side (chlorine gas) GTTD (27 x. ro6)-,-]k o.oe : With this magnitude of tube displacement and Nss and Nsp being in the safe zone, we conclude that the exchanger will not have vibration problems. With NBE and NcD not exceeding 1.0, we do not expect vibration trouble. To be certain we compute the maximum tube deflections as follows: p ' = ol x t0-)(t,r.rru,2 lit,ltl F \ 12 / \0.04s/ - fr I 9.520 x l0-5 lb. rt2 /rr <n\n tItT.236f " , (0.00691 l':::l fi. sec' f" = : : ", Nco d-, 4 : rb-/fc o.oo3:15 ft' q : rirCog-Uf O; Co:0. l16 Btu/lb.-'Fi p: |.667 The Mechanical Desisn of Shell-and-Tube Heat H Exchansers EAT EXCHANGER SPECIFICATION SHEET I 2 3 Add.€ss Plaht Locarion Prcposal No. Dale Rev. 5 6 7 a 9 Siz. (Horlvert) TypG Surf/Unii (Gross/Eff.) In Pa.allet Series So rl PERFORMANCE OF ONE UNI'I ShcllSid€ Ffuid Ouantitv. Total Tube Side Ur:T otL to ll Connected Surr/Sh.ll (Gross/Eft.) So Ft: Shells/ Unit Lb/Hr EEDfuflE GA- 72 Liquid 14 t5 l6 t7 T€mper.tur. l8 soecific (lnlo!l) , cravitv lC l9 Viscosity, Liquid 20 2l 22 23 21 25 26 27 2E 29 30 3l 32 33 31 ^IEg I ^fiO Cp Molecular W6isht, Vapor Molecular Weighl Noncondensable o.+zao Specitic Heat Btu/Lb "F Thermal Conducalvity Btu Ftltlt Sq Fr ' F Latent Heat Btu,/Lb @ "F Inlet Pressure O.11to Psia Ftls Pressur€ Drop, Allow. Calc. Foulins Resisranc. (Min.) Psi (D O O.OOO Heat Exchansed Bru/Hr: MTD (Correcr€d\ b ,t,5 Transler Rate. Service CONSTRUCTION OF ONE SHELL sletch (Bundle,Noz:le Orientation) Shell Side D€siRn,/T€st Pressur. Psir 15U DesiEn TemD€rature 35 No. Passes Der Shell 36 Corrosion Allowance t 'F /,79 ln, ln 37 3a 39 7{6 'F Sizo & Out Ralins op I rube No.,5O 4l Tsbe Type 1to 4Z Shell 13 11 45 46 47 4a 49 Channel or Bonnet Tubesh€ct-Stationary FloatinE Head Cover Bafites.cross In.;rhk (Min/^vs) In.r r€nsrh r5Ff': Ft; Pitch Material If{ In. +30 a.50€-so €>a5 Tubesheet.Floating lmpins€menr Protectio! b Supports-Tube Bypass Seal Arransem€nt TvDe 4h % cut (Diam/area) 1 .j/4"spacine: U-Bend cuc tnlet In Type Tube-Tubesheet Joint 50 5l Bundle Exit Gaskers-Shell Side Code Reo0irem€nts Weight/sherl TEMA Class 55 57 59 50 5l Figure 7-36. Chlorine superheater heat exchanger specification sheet. Lb 155 156 Mechanical Design of Process Systems P nr 700,000 ft: Btl, 9.116 _ t* 88.0ee.783'u.( hr \3600 ^ 5nr 88,099.733 (68.496).F -r rDm- : (.42o ) sec/ lh ftr For each of the 150-l-in.-14 BWG tubes, 14,680 : 25.'796 ft/sec Llg{'o) sec\12 / ', (1.667r ' The smallest shell-side nozzle is the 3-in. outlet, where !!r Ar ftr \ lhr"''l/ {:ooo 'frhr (5.0 ' = 0.027(298,860.527)0E(0.835)r/3(1.01 (re)' '', 0.7 < (610.464r(5.0 N",:\!i =h, lqi,t\n l -+nr-n'- -f Shell.Slde Film Goefficient p fiCP(LMTD) : lh Np, : < 17,000 ^ _ 619.a64 D" : 8[0.43 p') 0.5rd!4] 8(0.43)(1.2sf - 0.5 r(l.0)z l 4l r(1.0) 0.711 or De : 0.059 ft c: |.25 - 1.00 : 0.25 in. B : 30 in. for 6 baffles D, : 18.00 in. : shell ID D.cB I-" = _- ( 18.00)(0.25 X30) p(144) \1.2s)(t44) : t-t.11 ll. as .a^ iI (3.600)::: lh sec hr : 31.987.20 ^ : ______=-_:=_______j:: -G. .+ (J. /) rt' hr-tt' (6.664) k= - Tdo ^rn 0.426 Btu/lb,-"F; 62 46 -;T: Btu hr-ft- "F t l0-,) Bt' hr-ft-'F \12 : Btu For 60" A arrangement, NN" cp = lb^ ft-hrro.426rlb.-'F = t4.075 0.077 Btu x l0 3) 'hr-ft-"F ' Very reasonable u = 2.544ltt^tft-hr ,0.116r ' ft-hr lb^-'F _____ =Aal( tN.,l,' ft2 v : _-- !g :2.092:! 0.051 ftr sec Np, 0.027(NrJo : in.'?:0.051 fr3 Btu : q 7.393 12.5+4t N*" h, = 41.866 : r'l'.: &, u".:l.Cp,k=5.0x to-r-gu ^' k hr-fc'F =_ 0.10? ft3/sec Reasonable :298,860.527 lb' : ftr - lb' (0.036) -r' l9r E9 62.46= Nq. = j:l; I = 0.0148 Cp = 0.036 lb./[t-hr ro.036r 6.664 ft3 I Nn. = !r sec th v = -........- 2( J9c = (0.0037941ft 50)tubes r2s.7e6t 6.664 sec :! | .667 : i-frl 14.680 d+ (68.4e6).F 0.077 Btu/hr-ft-'F lh The Mechanical Design of Shell-and-T\rbe Heat Exchangers Nn" : DG _ (o'059)ft(31'987. P z.su ,0# lb^ 'v = 741.842 ft-hr r,.12 I h- - ratio of OD to ID of tube 1.199 h' 73'629 ot.+os Blu : Ar = l.l99 - --"-'br-ftL'F \0.14 U" =Jx!11-trr:l "' Pl D.' : Ar = 1-JJ in= 1.001 d=1.0 Aa The exchanger has baffles with 45 % cut, so from Figure = \p", (l2xo.o77) Btu tt t tt ;$:F o.o5964.025)r/36) Since both gases are relatively clean, the fouling factors for both sides are 0.0001. - h= 196.720 t* = 161.436"F 6r.M + 107.480 Maximum allovable tube joint load 1 - 99.680) = L"*" 1..* = A,ouf, For SB-l6l-2fi) at 162"F, * o.oor + o.ooo8 * 43.866 ,1 .. 37.779 (196.720 61.,109 r -, : o"n: 10,000 psi g = (0.239)in.1lo,m) tn.' (1.0) 2,3e0.00 lbr U=19 700,0m# Area required : = 521.875 ftz (re.582h;h(68.4e6) Available area = (0.2618X150X15) : 589.050 ff3 This implies a 12.87 lo excess, which is acceptable. The tube wall tenperature is used in a method developed by Miller [21], which is a more exact approach than most and consequerdy results in a more economical design. P, : shell-side pressure At = tw - : D" ID = 18 in. = 1.5 ft ft,gSZ.Z0,l\. nr-n' shell = , . .. 18.0 ID = - f i= 0.w225 D" = 0.059 ft 70'F Ds 0.0 - : 91.436'F CA 18.0 in. (looxg'o) PR -= og - qfp- <te"zooltt.ol -o.ettool = 0.0558 in. Use ta'a = 34rc-in. For the shell, f"= : 70oF CA = corrosion allowance = 0 for pure helium (inert)(erosion is negligitle) 'st'ctt C" - : + l) o)'D.rd 6 baffles shell 161.436"F ambient air temperaturo Plessure Drop f"G.,D"(N" \ : D, : = 100 psi : D. : At ^'' = iSzrl ta; ta : aPs = = F.+ = = 0.1875 in. 27.546 x lffpsi (0.w2zs)(3r,987.20f(1.5x6 at 161.436'F + l) (s.22X10)ro(0.059)(1.00lx1.0) 0.008 psi which is acceptable 158 Mechanical Design of process Systems Tube Metal Temperature : : ar : : n: na, : where E1, modulus of elasticity of tubesheet metal tubesheet thickness 1.1875 in. cross-sectional area of tube (see Table 7-3) : T For parallel flow, Atn:259-77:173.F At: tla - 158 : At": 18 =o,no Atn 113 lS.F 600,000 rt I Ol2 /rtr'vr- 4 B= :6.794 (s 10.510x173) 6oo'o00 ' = (s 10.510)(18) ltl ^'-l_ luh A = -u"l _ 6.794 U[ ,-i-5i% From Figure 7-1"1, F" : 65.2e41 176 L": t"i + + (0.28X250 F"(t"" - O.28 (7-11) - 176) : tljOt : Pri : = 99.6t0", C : 254.469 in.2 -t2) I' Ler = !4a, E,B- dt = - 70"F : Ul8.J75P .{l8.r2s),J - Let APn = (13.79q t21.546 86.394 in.2 : 168.075 in.2 : : 100 psi ^y 106X35.850) 106X7.1668) -) sosr equivalent pressure difference. psi D rri in./in.-'F at 161.436"F tube-side (channel-side) pressure At = 161.436'F total cross-sectional Area or tube holes ^ For the shell material, 10-o - (A-C) tl :-- coefficient of thermal expansion, in./in.-.F o, : 6.090 x shell cross-secrional area 86.394 in.z -o3r = I t*=t"i,-,n,o!.+ tt.n-r".t n. : : .1668 in.2 r96.jZO.F (7 711 254.469 in.2 expressed as t"i) t-=77 + (0.28X158 - ct = The ratio of the inside shell bore area to the net tubesheet area minus the tubes is the net area that resists the tube and shell reaction forces and moments. This ratio is referred to as the ligament or deflexion efficiency and is l=u6eo Lr,=tr,o*F.(tr-tm) t"i - 7 - 6s )q^ (Di" { : For cold end, g- : 4 c- : number of tubes 150 (ls0)(0.239) 35,850 in.2 rr lR Or2 A = ':A For hot end, Ul: 0.239 in.2 n ar : 100 - 100 - (100)(35 850) 168.075 -21.3298 psi Computing the differential thermal expansion : Ac Aa=e,A,-o,A. 4*: 91.436.F (7.010 x 10 6X91.436) - (6.090 x t0 9(91.436) :0.000084 0.834 PE : the effective pressure differential induced by the equivalent pressure difference, APs, and thermal expansion, Aq P,:P+(ao) qna' A_C (7 47) fl The Mechanical Desien of Shell-and-Tube Heat Exchansers Pe: : (13 -2r.32e8 + (0.000084) 7e?l 159 lq6)(3s 85) 168.075 226.263 psr Assume ihe normal tube projection beyond the tub€sheet to be r/a in., L : (13X12) - 2(1.1875) - 2(0.125): Defining the dimensionless parameter, tr, \ | : 1.08 as t025 - :rr-l l--[Lr -DTdA - 153.375 in. (748) D. L,J a 1.08 "I (13.799 x i09(3s.8s0) (153.37sX1. 12sf(27.s46 x 109(168.075) 4 6 A '10.25 I (18.125) 1ot2 \ Figure 7-37. Tube stress factor 14 Ir 16 versus \. \:2.696 : 4r-*r : q,(.-r -415.968 psi for | : f+ : -0.046 -415.968 psi is well below the maximum allowable stress, which means that the tubesheet is of sufficient thickness. One could repeat the process if it was desired to use a thinner tubeshe€t. Had o.1-o*1 exceeded the maximum lowable stress for the.tubesheet material, then a greater tubesheet thickness would have to be selected and theprocess repeated. al- From Figures '7 -37 , 7 -38, fI : 1.55; lz:3.12l, l: : 7 -39 , and 7 40: -0.046; f+ = 1.970 The maximum radial stress in the tubesheet is expressed .'-.,,ffi11,9' f-" I00){2s4.469X2.sOs8) : I (rg.rz5\t (168.07s) I \ 1.125 i 4[(2.50s8X1.ss) o.1.""; as (7-4e) 4(Vfr + fr) l,o,o.,, -- -{ 1oo q -1,418.659 compression for the tubesheet material + < 3.12] 16,?00 psi allowable 2 4 6 a lo12 14',r6 X Figure 7-38. Tube stress factor 12 versus tr. |a 160 Mechanical Design of Process Systems The maximum stress in the tubes is the sreater of the follow- ins: ", :u-[^,.na, (n, APt* - A_C (7-50) ({ + lr) I or [ -\- -:t'e (A-crl]l ",{t" _clAP,_ =A nu,[ (* + |.4) o.2 q o.o (7 -sr) I -o2 ;.lr"-l-,,,,n -ot -0.6 (100x254.469X2.50s8) ro^ -,lrr^ 168.075 t-" -' -oa -1.O (2.5058 + 1.970) T Figure 7-39. TUbe stress factor f3 versus \. o,1^ 1: -92.62 psi for Equation 7-51 EXAMPLE 7-4: ASPHALT COATII{G lllx HEATER-A NON.IIEWTONIAN FLUID APPLICATION A roofing manufacturer needs a shell and tube heat exchanger to heat an asphalt coating mix from 425'F to 500'F to improve flow characteristics. The fluid to heat the asphalt coating mix is a leading manufacturet's hot oil heat transfer fluid. The asphalt coating mix is to be tube-side and the hot oil is to be shell-side. Determine the size of unit required with the design to be counterflow. The process is described in Example 3-6. The exchanger heat duty is to be 1,000,000 Btu/hr. See Figure 7-41 for complete exchanger specifications. First we compute the LMTD for a counterflow exchanger, Shell-side (hot oil) 650"F in 550'F out 500'F out 425'F rt 150'F LTTD: 125"F TLrbe-side (asphalt coating mix) GTTD: 2 4 6 8 rO12 I 14 16 Figure 7-40. Tube stress factor f4 versus 18 \. - qrp . lcrrDl '"\rt-/ LMrD: crrP _ l5o_- l?5 : r.7.t2"F , 11501 '\*/ The Mechanical Design of Shell-and-Tube Heat Exchangers 161 HEAT EXCHANGER SPECIFICATION SHEET I Job No. 2 Addr€ss Plant Location Proposal No. Date Rev. 5 6 Siz. 7 Surf/Unit (Gross/E f.) (Horlv€rt) Type 9 HOT otr- to t1 Ffuid OuantitY, Total t2 t3 Liquld t1 2l Lb/Hr Tsmpe.ature (lnlout) t8 sDecific cravirv @ l9 Viscosity, Llquid 20 gtu/Lb "F Btu Ft Hr Sq Ft ' F Btu/Lb @ 'F 26 Ftls Pressure Drop, 2a Foulins Resisranc€ (Min.) Heat Exchanaed r-".r". n"r", 4z€ q3* 7 l-lz, d.<2b a.7b a.7> Ft 0.52b q4? D:47 t I IO Psi b t0 tO atu/Hri MIO (Correcied) "F S"-i." so 32 DeEisn/TestPressurc Psis l<D r 221 rt " r Sketch (Bundle/No:?le Orientation) CONSTRUCTION OF ONE SHELL Shell Side 3l EO / 226 O.sasn Temperature 35 No. Passes D€r Shcll 36 Corrosion 3a 39 40 Si2G & Ratins Allowanc€ ln. Out op 74 tp 274l luge !o. 5gt Tubc Type 42 sh€l 11 Channel or Eonnet Tubesheel-StationarY Flo.lina Head Cover 16 47 4a 49 So Psia Allow.,/Calc. 27 41 a h.4) Cp Specitic Heat Thermal conductivity 24 Latent tleaa 25 Inlet Pressurc 31 Se.i€s ASHJNLTCd'NN6FNIf, Molccula. Weipht. Vaoo. Molccula. Weisht, Noncondensable 23 30 5= //.60 t.60 656cp 22 29 Parall€l PERFORMANCE OF ONE UNIT ShellSide a 77 Connected In Su.r/Shell (G.oss/Efi .) Sq Ft: Shells/Unit Baftles-Lorg Supports-Tube Bypass Seal ArranAem€nt In.:rhk (Min/^ve lIl 8ly6 In.; Len$h 20 Fr; Pitch I.A In. <- 30 fgl+119 9 !! Material op In. lshen cover 0nt€s.) (Rernov.) I Channel Cover Tubesheet-FloatinE lmoineement P.otection o/o Cur (Dia6lA.ezt Seal Typ€ U'Bend Spacina: c/c Inlet In Type Tub€-Tubesh.et Jolnt 50 5l pvt-lnlet Nozzl€ Gaskets"shelr 53 side Bundle Entranc€ Bundle Exit Tube side -FloatinE Head codc Requirements TEMA Class 55 59 50 61 Figure 7-41. Asphalt heater heat exchanger specification sheet. l@1978 Tubular Exchanger Manufacturers Association.) 162 Mechanical Design of Process Systems In a counterflow exchanger we must correct the LMTD. Using Figure 7-16 we have for a one-shell-pass, two-tube-Dass. P= 500 6s0 - 425 - = 425 0.333; R : (0.93X137.12) 650 500 :0.93. From Figure 7-16, F LMTD becomes LMTD : : 127 - 550 425 Thus, the corrected For asphalt coating mix at 450'F we have the following properties: q : : : 0.368 Btu/lb.-'F; 2,251.20 tb^/ft-hr fiCo (LMTD) = 1,ooo,ooo rO 16Rr ---'''lh -i:L r -oF p : 89.2321b.ift3; p : 933 "O 1,000,000 Btu/hr 9!! hr l--t? : 2l,309.196 lb^/hr {t)\oF' '---' /\ thf 21.309.196 "' l ' '" hr \3600 sec/ ^ ^,, _tt3 i u.uob th I Nn" l-4x13*xal3 1-xa I lh co,'tt'"m sec where x We will try 594-3lq-in. tubes-14 BWG. Checking the tube wall thickness for internal pressure, 150 psig PD) - 0.6P o"11E : E: P: ID : where o1 t-," "- = t""r4 : maximum allowable stress for tube material, psi tube weld joint efficiency l.g internal pressure, psig tube ID, in. 150)(0.584) (17.s00x1.0) - :0.005 0.6( 150) 0.083 in. Flow velocity through each tube is v i: - =j!L (0.0019)ft'z(594)tubes -0.066 = fi3 0.059 frlsec ratio of the fluid particle yield stress to the shear Lab tests reveal that fluid particles at the tube wall x : 0.5 (0.5r .I 4 (U.)) .^ - - -. + -:-------" n= 1l (u.)f := - =:; = and 1 : 3.9 for which O.378 Now, : ( : stress in the It, t-,": (1-7 ) When working with non-Newtonian fluids, rheological data are necessary. The reader is encouraged to refer to Govier [22], but will often find that rheological data are not available in literature. In this situation a samole of the fluid must be sent to a testing lab. Do not attempt to approximate a non-Newtonian fluid with Newtonian equations and assumptions-the results can be a catastrophe. At the current state-of-the-art there are no simple answers for such complicated subjects such as non-Newtonian fluids. Samples of our fluid were sent to a testing lab to have the properties evaluated. Some of these properties have already been given. The fluid is determined by the lab to be a Bingham fluid, in which the shear stress and velocity gradient ofthe fluid particles are linearly related. For a Bingham plastic, n in Equation 1-7 is I ^ DiV2 - ip : .522"F Tube.Side Film Coefficient Cp To obtain the tube-side film coefficient we must obtain the Reynolds number. The asphalt base coating mix is a non-Newtonian fluid (see Chapter 1), so Equation 1-6 is not valid. So, to compute the Reynolds numbet we must use Eouation 1-7. (0.584)0 r78(0.059)?-" N.'* = €r -1 (89.232) sec 8.0 th +n" : 0.092 in. The film coefficient is determined from Figure 7-42, which is the Metzner-Reed-Reynolds number (Equation 1-7) versus friction factot f. From this figure we obtain f : 180 Now, we must compute the pressure drop through each tube to determine if a 3/+ in. 14 BWG tube is adequate. - The Mechanical Design of Shell-and-Tube Heat Exchangers 163 with a viscosity of almost 1,000 cp. The Prandtl number for our fluid is (2251.20\ f N".: Np, o = lb' ,0.368' Btu ft-hr lb--"F Btu (o.lo) ' - hr-ft-"F 8284.416 For laminar flow, the Sieder-Tate correlation is lt- c N", = .9 .9 u- N", hrD k Meizner Reed Reynolds Number' Re"* : T: r.86 , eo kl'' ffi]"',t., [,o.or,,rrro.o,u, = 2.r85 Rr,r (- j6) ){{l ll Figurc 7-42. Friction factors for flow of non-Newtonian fluids [22]. [6*.16.,;[n)]'' "L_,| hr-ft-'F 10.5841 \ '-'' 12 / -^ Btu hr-ft2-'F For our velocity heads we use the entrance and exit loses Shell-Side Film Coef ticient and get : !f O.ZS + 1.00 : 1.78 (see Figure l-1 l) q Using Equation 1-4 we compute the pressure drop over 2O-ftJong tube as * r* )qr ' : ILL \d - lze, : p!g(zo{l?I'* * (t -4) : r.zr ] (8e.82)k(o.o5eFg(,-iI--J 2(32.2) = 2.47gpsi : : 0.526 Btu/lb--'F; 62.213 tb^/tt' 0.076 Btu/hr-ft-'F; : Acceptable _/-\ l'tu I p: p : t Looking at this pressure drop one realizes that a flow velocity of 0.059 ft/sec is not so slow for a bulky fluid 0.30 cp I tb.-'F It-lD;T sec'-rDl (O.997)(O.a) : 0.720 nr hr \J.600 sec/ , ... Rf {0.526) "'- 1127.522\'F t.000.000 m aP, rirCp(LMTD) For the hot oil at 600"F the following properties exist: a Ce op, ae, : 4.141 62.213 th :! sec: th +tt' ^.- ^ U.UD/ ftt -Sec lb- lb.ift-hr 164 Mechanical Design of Process Systems The smallest nozzle shell-side is a 3-in. nozzle, making the maximum shell-side velocit) 0.067 Fouling factors are as follows: i:fr3 sec ' - boslF : Btu h-" = 155.959 hr-fta'F Asphalt coating mix 1.305 ftlsec - Hot oil Very reasonable : : 0.01 0.004 1 (0.720) lb' ,,., rrpr _ - Btu ro.526r ft-hr lh -oF ACp k _ rl + 0.004 + 0.01 + 155.959 Btu (o.o76t ' 'hr-ft-'F " -" 4.695 Elr,r hr-ft2-'F Fora60'Aarrangement, n 810.43 p']- 0.5rdl/41 810.4311.00) - - r4 D" = 0.127 or De : 0.5rrl.0r/41 ?t "(0 D.(c)B (27.00X0.25X 15.0) ^ -^^ 144p (1.00)(144) . 4.t41jl t3,600r l ^msechr U<=-: as = 0.703 21.201 .920 *, _ D.G, _ 1\Rc--- fl th p 5 nr-It" lh ' jH: \o ' Available area = 323.918 Tlr,r - i27.s22f nr-rt'- -|:] -'.- : 1,830.308 : (0.1963) F ft'? iIt (zo) rt 694) : 2,332.94^ tt extra margin is needed, so25% to 30% excess area is not unreasonable. For more heat exchange it would be better to consider a surge tank with interior and exterior heating elements, since we are at t}te limits of the shell and tube design and, with a more viscous fluid, a surge tank of the type in Examples 3-3 and 3-4 is more practical. ft-hr 12 for baffles with 15% cut Shell-Side Pressure Drop tGiD,{NB + l) ^. _ (slt(t0t6.1d rq From laboratory tests it was determined thar plp* = 2.0. Ns = 16 baffles D. = shell ID ( nr Twenty-seven percent of the excess area can be eliminated by reducing the number of tubes. This would increase the flow rate in each tube and thus the pressure , :'*L n" = lo4rNr,f ':[aJ (4.284) !! drop, which already is at 2.5 psi. For non-Newtonian fluids, properties can vary from sample to sample and (0.011) fr (2t,201.9201 / " nr-n' From Figure'1-21 : 0.011 ft c: 1.00 - 0.75 = 0.25 in. B : 15.0 in. for 16 equally spaced baffles over 20 ft D. = 27.00 : shell ID " Area required 1,000,000 Btu- ft l2)(0.076) hr-ftr-'F (4.983)'/r(2.0)o (0.011) ft : 27 in. : 2.25 ft G, = 21,201.92 lb./hr-ft2 r4 Nr" = 324 and from Figure 7-24, f = O.0O75 The Mechanical Design of Shell-and-Tube Heat f o nn75 F_'-"'"--nnn<t< ' t.2 : dT(t) d: specific gravity / a, and if the ratio of dT(t)/dt to _l dt : 0.997 -: L{r, = ln l2oo \o t+ - t\ \80/ dl(r) / ao \/-r\ 1.0: (E dr (0.0062s)(2 r,20 l. 9D, Q.2s) (r7 ) (s.22)(10)'0(0.01 1)(0.997)(1.0) : 165 T(t):(200-0-(140-60) 1.2 D" = 0.011 ft "y : L(t) : 0 when t dl(t)/dt exists, then : For plain and bare tubes, Exchangers \200 - ri \80i -1 200-t I'Hospital's rule states that 0.188 psi, which is acceptable EXAMPLE 7.5: ZERO LMTD EXCHANGER A candy manufacturer wishes to cool hot molasses to 140"F for the food processing of various confectionaries. The molasses is coming from a heating-blend kettle at 200'F. Spring water is to be used and it never varies ( + t/+'F) from 60'F. The water is to be heated to 120'F, and held at that temperature to heat honey. Determine the LMTD. The exchanser is a counterflow desien. Tube-side Shell-side at: 200'F in 120'F out 80'F 140"F out 60'F in At = ,. T(t.) .. dT(r)/dt 1.'t L(t) i-= d dl(r)/dr or, witha : 120'R r1 | -1 liml r.al _I l= I | troo lim t-uu - tl Therefore, LMTD : to-Ro .lnt/so\ - t) 80"F 80'F With this value of LMTD, the exchanger can be designed, using the correction factor in the case of a counterflow unit. 80'F Now using Equation 3-23 we have LMTD: (200 o NOTATION A : tube surface area, ft2 At : cross-sectional area of tube, in.2 a = constant for a continuous beam shear, dimen- o I \80/ This problem is somewhat similar to that of Example 3-4 in its formulation. We must define the LMTD as the ratio of two functions T(t) and L(t) for which b: c= c: C : sionless constant for a continuous beam deflection tube clearance, in. constant, in.2/lb1 (Equation 7-37) 10 a(sec)05/(ft)'5 (Equaconstant :9.7 x tion 741) 1141P : T(t) Lt) : (200-0-(140-60) .ln l-l1200 \80/ rl As temperature t approaches a certain value such that T(t) and L(t) become zero being divided by zero. The derivatives of T(t) and L(t) exist when t approaches this value of t, so we can apply I'Hospital's rule that if T(t) g" = 12fE t or)o 5 (Equation 7-2) : drag or force coefficient for a body immersed in a fluid, dimensionless Cp : specific heat at constant pressure, Btu/lbn'-'F D:4 x hydraulic radius. in. D : tube diameter, in. D : parameter (Equation 7-27) ds = diameter of baffle hole, in. di : inside tube diameter. in. Cp 166 Mechanical Design of Process Systems : outside tube diameter, in. : 4 outside tube diameter, ft Ea : modulus of elasticity of baffle material, psi 4 : modulus of elasticity of tube material, psi F" : correction factor, dimensionless (Figure 7-16) F". : critical buckling strength for tubes, lb. Fr : force induced by fluid flowing around immersed body, lbg F, : shear force against tube at baffle, lbr used in determining tubejoint force, ; I constants lbs (Equations 7-3 and 7-4) i' I f" 1 fundamental natural frequency of tube, Hz gc : gravitational constant : 32.2 lb.-ftilbr-sec, : parameter (Figures 7-30 and 7-31) Tn : thickness of inside tube deposits, ft Tro : thickness of outside tube deposits, ft T* : tube wall thickness, ft t"" = caloric temperature of cold fluid, 'F t"1 : caloric temperature of hot fluid, "F Li = inlet cold fluid temperature, oF t"" : caloric temperature of cold fluid, 'F thi : inlet hot fluid temperature, 'F th. : outlet hot fluid temperature, oF t = tube wali thickness, in. t* : outside tube wall temperature, 'F ar = temperature differential (tr - tz), .F U : overall heat transfer coefficient for exchanger, Btu/hr-ft2-'F U, : the value of the overall heat transfer coefficient at the caloric temperature. Btu/hr-ft2-.F V : flow velocity, ft/sec T do GTTD = greatest temperature difference between the shell and tube side fluids, 'F h = film coefficient, Btu/hr-ft -'F hi = film coefficient inside tube, Btu/hr-fl:,-'F h" : film coefficient outside tube, Btu/hr-ft -'F hi, : outside film coefficient of tube, using outside I: : k: k: k* : Ir tube surfaces temperature, Btu/hr-ftl'F moment of inertia, in a moment of inertia of tube cross section, in.a structural constant, dimensionless (Equation 7-2) equivalent effective unsupported length of the tube, in. coefficient of thermal conductivity of tube wall, Btu/hr-ft-'F kr = thermal conductivity of fluid, Btu kn : thermal conductivity of foreign deposits inside of tube, Btu/hr-fi-'F kso : thermal conductivity ofdeposits on outside of tube, Btu/hr-ft-'F L = tube length or span length of tube, ft LMTD : logarithmic mean temperature difference, "F LTTD : lesser temperature difference between shell and tube-side fluids, 'F / : typical dimension of body immersed in fluid, n rir = mass flow rate, lb-/sec mt : mass density of tube metal, slugs/ft3 NB = number of baffles Nna : baffle damage number, dimensionless Nco = critical damage number, dimensionless (Equation 7-39) Np, : Nusselt number, dimensionless : : P: p: q: Np. Nr" r= Prandd number, dimensionless Reynolds number, dimensionless axial force, lbl tube pitch, in. rate of heat transfer, Btu/hr radius of gyration of tube, in. (Equation 7-2) Greek Terms : 6: p: ct factor of effective tube resistant area, dimensionless deflection or displacements, in. dynamic viscosity of the fluid inside tube, lb./fthr p* = dynamic viscosity of fluid at tube wall, lb-/ft-hr uB : Poisson ratio for baffle material ut : Foisson ratio for tube material or : frequency of a given mode, Hz p = density, lb*/ft3 d"1 = allowable stress for tube, psi o" : allowable tube compressive stress, psi, for the tubes at the outer periphery of tube bundle (Equations 7-1 and 7-2) o, : minimum yield stress of tube material at design temperatue, psi : f sum of structural damping and the fluid damping, dimensionless REFERENCES l. Heat Exchangers, Howeli Training Company, 2. Houston. Texas. 1975. Snndnrds of the Tubular Exchanger Manufacturers Association (TEMA), 6th Edition, Thrrytown, New York, 1978. F. L. . "What's the Difference Between TEMA Exchanger Classes," Hydrocarbon Processing, 59, June p. 92, 1980. Ludwig, E . E., Applied Process Design for Chemical and Petrochemical Plants, Volume 3. Second 3. Rubin. 4. The Mechanical Design of Shell-and-Thbe Heat Exchangers Edition, Gulf Publishing Company, Houston, Texas. 1983. 5. Small, W. M. and R. K. Young, "The Rodbaffle Heat Exchanger," Heat Trans. Eng., I, ro. 2, Oct. Dec. (1979), p. 21. 6. Skrotzki, B. G. A., "Heat Exchangers," Power, June, 1954. 7. ASME Boiler and Pressure ry'essel Code. Section VItr Division 1, American Society of Mechanical 8. 9. Engineers, New York. Colburn, A. P., Ind. Eng. Ch.em.,35, pp.873-877, 1933. Kern, Donald Q., Process Heat Tlansfer, McGrawHill Book Company, New York, 1950. 10. McAdams, W. H., Heat hansmission, Third Edition, McGraw-Hill Book Company, New York, ll. 1954. Jakob, M. Heat Transfer, Yol. l, John Wiley & Sons, New York, 1959. 12. Grimson, E. D., "Correlation and Utilization of New Data on Flow Resistance and Heat Transfer for Crossflow Over Tirbe Banks i 'Tiansaaions of the ASME," Yol.59, pp. 583-584, 1937. 13. Engineering Data Book, Wolverine Division of UOP, Inc., A Signal Company, 1959. 14. Thorngren, John T., "Predict Exchanger Tube Damage,' Hydrocarbon Processing, I*l,l. 49, rc. 4, p. 129, r97o. 167 15. American Institute of Steel Constrtclion, Mantal of Steel Construaion, Eighth Edition, AISC, Chicago, trlinois, 1980. 16. Timoshenko, S., and J. N. Goodier, Theory ofElastr:ciry, Second Edition, Engineering Societies Monograph, McGraw-Hill Book Company, 1951. 17. Coit, R. L., C. C. Reak, and A. Iohmeier, "Design and Manufacturc of Large Surface Condensers-Problems and Solutions," American Fower Conference, April 1965. 18. Blevins, R. D., Flow-htduced Wration, Van Nostrand Rheinhold Company, New York, 1977. 19. lbmbsganss, M. W., and S. S. Chen, "Tbntative Design Guide for Calculating the Vibration Response of Flexible Cylindrical Elements in Axial Floq" Argonne National Labomtory Report ANL- ETD.7l-{r/, l9r. 20. Kays, William M. and A. L. Lofron, Compaa Heat Exchangers, Third Edition, McGraw-Hill Book Company, New York, 1984. 21. Miller, K. A. G., 'The Design of Tirbe Plates in Heal Exchangers," Proceedings of thz Institwion of Mechanical Engineers, \bl. lB, pp.215-231. 22. Ctovier, G. W. and K. Azrz, Thc Flow of Complex Minures in Pipes, Robert E. Krieger Publishing Company, New York, 1977. 23. Metzner, A. B. and J. C. Reed, AICLE Joumal, I, p.434, 1955. External Loadings on Shell Structures where In a book about the mechanical design of process sysit is impossible to ignore the phenomenon of external loadings on shell structures. Such loadings occur when piping is flanged to pressure vessels and the vessel nozzle is exposed to loads induced by the piping, and when vessels are erected and the force of gravity induces loads at the lifting lugs. We have already discussed external loadings in the design of piping supports in Chapter 2. Vessels require a simiJ.ar analysis, but the phenomenon is different because in a vessel the loadings are more localized. particularly in a large vessel. In the case of external loadings on vessel nozzles one must consider primary stresses induced by internal pressure and secondarv stresses induced by the external loadings. In the design of the lifting lugs only secondary stresses need to be considered, since vessels being lifted almost never have internal diameter of the branch diameter of the header Also. \\'RC 197 and WRC 107 do not consider the case of erternal ioading combined with internal pressure. Current studies are being made to accomplish this task. Stress induced by internal pressure at the nozzle-shell intersection are extremely complex, so an analytical solution is impractical. Discontinuity stresses at the nozzleshell juncture are caused by the change in geometry from the nozzle shell into the vessel shell. Consequently, a stress concentration factor, ko, must be applied when using the following expression for internal pressure stress: "n pressure. The two "standards" that are most widely accepted for external loadings on pressure vessel nozzles are the WRC (Welding Research Council) Bulletin 107 [1] and the WRC 297 l2l. The latrer is an expanded version with more curves to cover more cases, but it is only for cylindrical shells. Neither WRC 107 nor WRC 297 are considered standards per se. Therefore, one must take the results of the methods outlined here and add the primary stress, which is the internal pressure stress. The reader is cautioned that the WRC 297 Bulletin is under evaluation at the time of this writing. Shell theory was used to develop the WRC 297 , and the results are being compared to finite element studies currently being made. The reader is especially cautioned to use the Bulletin when the ratio of the dianeter of the branch to the diameter of the header is between 0.5 and 1.0. exoressed P(ID)k" (8-1) 2t where P ID I kP : : = : internal pressure, psi inside diameter of shell, in. shell thickness, in. internal pressure stress concentration factor, dimensionless Values of \ are far too exhaustive to be listed here, but are available in a work by Forman [3]. For many years reinforcing pads have been used for external loadings and it has been accepted practice to assume that such pads remove discontinuity stresses at the nozzle-shell juncture. While this is true, one must realize that the reinforcement decreases the flexibility of the nozzle-shell attachment. As shown in Figure S-la, the nozzle with the reinforcement will have maxirnum membrane stresses occurring at the nozzle-shell juncture (assuming the circumferential bending stresses are negligible compared with the membrane stresses). As Figure 8-1b shows that as the reinforcement thickness increases, mathematically as 0.5 < db/DH < = : db DH tems 1.0 169 170 Mechanical Design of Process Systems c r tiryrcJtl F----'1 M-'x'i€m5'mm'n'|ll ll I r, --------|B w> 1.6s(arf. r5 ll HI __-____1---r I I l | I --'_;J II tN_ i R-r Figure 8-1. simple schematic of maximum combined stress disribution, as supported by field tests and finite element studies. the maximum stress shifts towards the edge of the pad, and as the ratio of the reinforcement pad to the shell thickness approaches a "critical value," the maximum stress induced by external loading occurs at the reinforcement edge-shell juncture point, shown in Figure 8lc. Considering this it would intuitively appear that a tapered pad would ideally be the best in application, especially for thick pads (pad thickness relative to shell thickness), as shown in Figure 8-1d. The disadvantage of such a pad would be the increased difficulty and expense to fabricate such a pad. Analytical, finite element studies, and field experience bear the previous facts out. The width of a pad, from the nozzle edge to the pad edge' should not exceed 1.65VRT. Beyond this range a pad has been shown to be ineffective. Pads can be even dangerous on thin-walled shells. In many instances, adding a t/z-in. pad to a nozzle on a thin- walled pipe, such as Schedule 55 (0.083 in. on a 4-in. pipe), is prohibitive. Such a pad could very easily transier the maximum loading to the pad edge as shown in Figure 8-1c, resulting in crack propagation or even ruptuie. Caution should be taken in working with thinwalled shells, where the flexibility of the shell is often sufficient to decrease induced stresses from external loadings. LIFTING LUG DESIGN The design of lifting lugs can become an arduous task one is not familiar with the erection of equipment. Lifting lugs must be designed to withstand the stresses inducad from all the loading conditions; allow lifting and if setting the equipment in one operation without readjusting oi re-rigging the crane or other equipment' and proteit equipment and personnel. The lugs must not interfere with vessel components, such as platforms, ladders, or piping. advantage to lifting lug design is that only secondary stresses must be considered-primary stress, such as internal pressure stress, can be ignored. We can assum€ that the vessels are not lifted while they are pressurized. Thi Consequently, the AISC Manual of Steel Constructi.on (unlike [4] can be used in which the factor of safety is 2: I ASME's 4:l). The vessel is to be considered as a simply supported horizontal beam. All non-shell components, head, ladders, etc. are considered as concentrated loads. The total erection weight is the sum of the concentrated loads and the distributed loads of the shell weight and internals. Various types of lifting lugs are shown in Figure 8-2. Lifting and'election procedures are shown in Figure 8-3 Techniques for designing the lugs are given in the following examples. EXAMPLE 8-1: LIFTING LUG DESIGN At{D LOCATION and tube heat exchanger is to be onto an offshore structure' The exa dock lifted from lbs, which is the total erection 158,750 weighs changer to locate and design the lifting is objective weight. The chocker length and minimum the lugs, and determine angle. chocker maximum A 96-in. ID shell Mechadcal Design of Process Systems 172 t 1T A norizontal It + lili .l J\ U + "1" or "W" beam Figure 8-3. Lifting lug and erecting procedure (moments induced by lift load at choker angle d can be avoided with a spreader bar or with the lug design in Figure 8-28. c spreader bar rig avoids €xcessive bending moments on lilling lugs First, we construct a free body diagram, as shown in Figure 8-4. Each lifting lug is located such that the point of lift is located on a hypothetical vertical line that passes close to or through the centroid of the ellipsoidal head, shown in Figure 8-5. Summing moments to zero and solving for the reactions we have GDt. : 0 : -Rnt46.542) + Rr and Rr. : : (2,283)(40.7 (2,094)(46.7 + (346x44.000) A = 16.50in.,B E : 6.50 in. Hole diameter Lug width : : Wr : = : (4.50 + : 4.50in., D : 0.125) mmlmum 3a : 3(4.50) wL _ 13.50 = 1.688 88 75,888.874 lb For lug supporting the fulI vessel weighing 158,750 lb, referring to Table 8-1 we write a 6.50in., C : : 4in., 4.625 in. 13.50 in. : minimum Lug Thickness, t1 s) + (346)(2.542) 5) + (1s1,587)(23.27 r) 75,698' 126 lb : tL : Larger of w _ 1.6ao, in. r/ use 1.75 in. 158,750 (1.6X4.625X38,000) = 0.565 in. 174 Mechanical Design of Process Systems For lug material SA-516-GR 7O, o, Table 8-1 Anchor Shackles : * - (". " | (?.,)[' n tl H: R": where, ll /\ D' ,\ -) *({* \2 50.0 + 1.75 n tl |l "["-( H: 1"b lvt Pin Dia. D (in.) (in.) (in.) (in.) (in.) rh trys rlz shd tllrc ,1, tl" t1o ,t" 1 1tl4 lrl^ 71rc 5/s 3/c r'lrc lrl, 2rltu ltlrc ZIz lh ls llrc rlz 5/a 3lc 1ls Yt^ 171rc | 33lq 111/to 1Vs 4r1o tt3lrc ltlc 43h Ztlta 13/e rr-r" stlo 2tls lvz -/" lrlz 1t/" 2 53lq 2tlq 27lt 1 7rl" 3tlc 3?'1" zrh qu" tou it, -9V^ i1o tluz 4lz lslt 15 3t/z 15Vz 4118 5t/z Safe Lilting Load-|9! | 4.00 Lslrc le/rc |1ha 4,500 6,400 8,700 2tla 23lg 25lL 3 1I = I' : greater of RR or R; for horizonal vessel reaction at lug when lifting at skirt and lug end 5(19.690) in. (75,888.874) lb ll. (38,000) t13 50)2 in' + ln.' : 1.079 in. < 1.75 in. Lug thickness is sufficient '4OO ___J3_5W 351rc 35la 16'500 Minimum Weld Size 2!,59q u,w 33,600 R[0.47 44,800 56,000 67 '2w 81,ooo 6tlz 100,800 63/q 125,000 t where o,* : lTtlz 6tlz 4tlz 7)lz 200,000 181/z 6tt/rc 43/q 73lc 224,N0 313,600 448,000 0.45(h/w)] ra : allowable shear stress in weld weld minimum yield (7s888.874) stress/ in tension I ot . o.ot rr2jry\l \ir.roo1 [o (0.30)(70,000)(13.50)(0.707) r79,200 41lt + re(wr)(0.707) 50,000 6tlq 5tlz where R R 2,200 2,900 23lq 6 6t/+ 3 33/q r, ) *. or w' 1,675 lrlrc 16l lz 21 + n JO - 19.690 in. .79-91'100 r3/rc 451rc 2 211+ 5 5Vq 2tlz 13 3tl+ 50-00 6. 50 Check lug thickness ft+l ,l* - ")']" insulation thickness shell outside radius, in. (b) round Pin lttn Itl, ;f ;' lug height, in. t:? f-et r q* ,1" 38,000 psi Lug Height (assume 2 in. fireProofing) (a) screw Pin THWP, = r* = 0.426 in. minimum Actual weld size : t*u : 0 3q* External Loadings on Shell : r*a Larger and twr where f t, ot ,, -_ I t, = = : Ds: du: H: Kp: L.: A,B,C,D,E vessel thickness, in. 1.75 in. > tv, so that - 0.0625 = 175 NOTATIOil ,t,u in. >h In this case, tL t*" t/ro in. Structures 1.688 constants (Figure 8-6) header diameter, in. branch diameter, in. 8-l) internal pressure stress concentration constant (Thble factor, dimensionless minimum chocker length, ft Ml= moment resolved about the left Mr: For each side of weld end (Figure 84), ft-lb moment resolved about the right end (Figure 8-4), ft-lb t-,:l'688:0.844 --2 since t*" > > t*, A a/+-in. weld is sufficient Choker Angle (0) o : arctan [----tlt' I -, l3w(H.A.;ll U: "r*rI (38,000x13.50)(1.75F 3(1,58750.00) (rn.uno * r6.s0 + 4t0) 0:4.905" R" I.: 12 sin d , : t" : minimum choker lensth 50.00 12 rin (4.90t A = 16t/z in., B = 61/z in., C = 4!z in., D = 4 in.. E = 6t/z in. = '+6'/rl n Because of height restrictions, the lug had to be lowered from 19.690 in. to 11.00 in. Thus, we now have the following: I l3.soxl.7sy I lrrtst.zso.ooy {rt.oo * ro.so * 4ll zll " .:qrt.grt-l (38.ooox \ t 0 : 6.327' and LC: 12 sin (6.327) = 37.807 ft Figure &6. Detail of choker and shackle. 176 Mechanical Design of Process Systems P RL R" RR t t1 t* wL : : : : constant (Thble 8-1) reaction at left side (Pigure 8-4), ft-lb shell outside radius, in. reaction at right side (Figure 8-4), ft-lb = shell thickness, in. = lug thickness, in. : : weld size, in. lug width, in. Greek Symbols o,* : : 0= 7A minimum weld yield stress in tension, psl allowable shear stress in weld, psi chocker angle, degrees REFERENCES t. Welding Research Council, Welding Research Council Bulletin WRC 107 bcal Stresses in Spherical and Cylindical Shells Due to External Inadings, Match, New York, 1979. z. Welding Research Cotncil, Welding Research Coun' cil Bulletin WRC 297, Incal Stresses in Cylindical Due to External Inadings on Noales-Supplement to WC Bulktin No. 107, New York, August, 1984. J. Forman. B. Fred. Incal Stresses in Pressure Vessels, Second Edition, Pressure Vessel Handbook Publishing, Inc. Tirlsa, OK., 1979. A American Institute of Steel Construction, Manual of Steel Constructior, Eighth Edition, AISC, Chicago, Illinois, 1980. 178 Mechanical Design of Process Systems Example-Spherically Dished Horizontal (a) Head A spherically dished head with a I l4-in. { OD is spun from 1-in. plate. Determine the partial volume of 10 in. of liquid. From vessel head manufacturer's catalog we determine the following: IDD R:'2 e: L: Figure A-2. Partial volume of vertical hemispherical (B) Partial volume of horizonral hemispherical head. : p 16.786 in. (Figure A-5), l14 o\ " - -)/t.'"'= 159.43" 108 - : : 108 in. 56.0in. 2.78 16.786 : 91.21 in. head. -_T---T -+l itv ln' tl tf I PARTIAL VOLUMES OF SPHERICALLY DISHED HEADS -- J___ --.-{,>-- _ Horizontal Head The partial volume of a horizontal head (Figure A-3) is (A-3) Figure A-3. Partial volume of spherically dished horizontal neaos. Vertical Head The partial volume of a vertical head (Figure A-4) is ., v=' nv(3x2 + -vr) 6 atl P"l x v----i\:-7lTv (A-4) -v----T -<--E--------i-:--rllDD ot I .. .v) y: nv2(3o 3 (A-5) Figure A-4. Partial volume heads. of spherically dished vertical Appendix Yr A: Pressure ry'essel Formulations 179 = 6.786" Flgure 4"5. _ V : --i86at - lV(r08, .,- v?ro8r - 5-dF IJ (9t.2r)(562 38,893.21 in.3 - 6.7862) = 168.37 gal t\ Itr t\ t\ ti Example- Spherically Dlshed Vertical ll Head ;;=*--:-__T, For the same head above, determine the partial volume -_- of a head of liquid of 9 in. x : u - 55.456 in. zr(9)[3(55 416)'? + 9'z] in.t = = A.874 "' 6 64.4 gal End View of Horizontal Head PARTIAL VOLUIIES OF ELLIPTICAL HEADS Figure A-6. Partial volume of horizontal elliptical head. The exact partial volume of a horizontal elliptical head (Figure A-6) is as follows: .. (IDD)q (A-6) Venical Elliptical Heads Volume of top portion @ of Figure A-7 is -a Y' '" 2 l"l' - 3(rDDFl v,.' = 'Ri' (A-7) I Volume of bottom portion . , 2r(IDD)R,2 rRl I O - "-----: lw 2( is u3 I 3(rDDll (A-8) Figure 47, Partial volume of vertical ellipticat head. 180 Mechanical Design of Process Systems Horizontal Head Example A Find the partial volume of a 2: I (R;/IDD = 2) elliptical head that is 108-in. OD. The level of the liquid is 35 in., and the head is spun from l-in. plate. vertical head IOR - ?rl O\ IDD -- '"-______:rr:', = 26.50 in. KR From Equation ,4-6 and Figure A-8 we have the followlng: IDD -x y = (IDDI a vm7 --tl'6R, a= 138.80" =2.42 v _ ( 19.0)(2.42t !463r- * 6(53) V : 17,512.94 B {Iqy-rr horizontal head in.r:75.81 gal Vertical Head Example For some head above, determine the partial volume for a vertical head with 19 in. ofliquid. Using Equation A-8 we have the following: c ., _ 2a'(IDD)R1'? vertical knuckle region o v _ 2?r(26.s0x53.01 _ 1(5i.0) 6 V= Y :76,641.06 in.3 : 77,951.81 in.3 n 2 [,o t--" _ trq.or, ] 3(26.s0),.j 13i0.75 in.3 331.78 gal H=IDD-KR D horizontal knuckle region Figure A-9. Partial volumes of torispherical heads: (A) vertical, (B) horizontal, (C) vertical knuckle region, (D) horizontal Figure A-8. knuckle resion. Appendix A: Pressure Vessel Formulations PARTIAL VOLUIIES OF TORISPHERICAL HEADS For Figures A-9 and A-10, : Vo : Vk KR = volume volume radius knuckle dish knuckle Figure A-1o. : IDD : y p= height of liquid inside depth of dish inside dish radius For vertical heads (Figure A-9c) the knuckle-cylinder Dartial volume is v*: ?rtJ + 4ry2 + (A-e) r,2; The partial volume ofthe dish region of a vertical head is ?ry(3x2 + y2) .,vD_-6- (A- l0) The total partial volume in a verticil head is nH Ty(3x2 + y2l ,. +. -----6-------:,, vu : -6- (ro' + 4rM' + ri') (A-ll) whereY=IDD-KR Horlzontal Torlspherical Heads Partial Volume of Dish @ (Figure A-11) VO: o ./(p, -y-il.t V(pt-7F_L(Ri,. yi,) = JZ | ,o_,r., Volume of Knuck-Cylinder Region @ (Figure A-12) uo = "[# + Ri- KR) + (R,- KRr] end view of dish volume Flgure A-11, Sketch for example partial volume calculation of horizontal torisoherical head. (A-13) The total partial volume for a horizontal torispherical head is as follows: V1 : V6+ V6 - . .vG, - R-iT L(Rr2 "lry + Ri- KR) + (& - KR),] wherel: p _ IDD - yi2) (A-14) Flgure A-12. 182 Mechanical Design of Process Systems Horlzontal Head Exampte A 102-in. S OD flanged and dished (torispherical) ) head made to ASME specifications (KR 0.60p and KR > 3th, tr, = head thickness) is spun from l-in. plate. The head is horizontal and the liquid level is 35-in. determine the partial volume. From the vessel head manufacturer's catalog and Figure A-12 we determine the following: : p R, 96 in., KR ltut = :z : 6.125 in., IDD = 50in.. L = 96.0 - : The head is vertical and the liquid level is 18-in. Determine the partial volume. From the vessel head manufacturer's catalog we determine the following: p : R, l?R trl 5l = '-" - 2=-"'-' = 67.50 in.; x : 17.562 in. 17.562 = 132 in., 67 .50 KR : IDD 3 in., - (3f - H2lo 5 = : 20.283 in. 66.446 in. 78.438 in. For knuckle-cylinder region, From Equation A-14 we have vr : Q.532) _ (78.438X50' - ls) | + ro: ,4%t_ 1s+ _\@6r:50it (5o.oo - 6.12s) Vr = 34.093.44 in.r = r- 67.50; 11 J?r' + (s0.00 - 6.l25fl 'J h Yv 147.59 ga. : 138-in. d OD F&D (flanged and dished) head nor made to ASME specifications is spun from I l/z-in. plate. 120.283 - Ri = r.= 67.50 +,[email protected] (3.0 * KR:67.50 = ob.u; + 15.0)l r(I'1 .283)[3(64.500)'? : - 3.00:64.50 2.283 in. : 146,893.558 in.3 + (17.283)2] 6 vv:31,247.726 in.3 + Vv - +() 19,4\ + 4(66.0), + (64.5011 = " -;-"-'l(67.501 b Vertical Head Example A = in. r /,'' <1r, 14(6.125) [ Ri : 115,645.832 in.3 635.903 gal I Appendix A: Pressure Vessel Formulations INTERNAL PRESSURE ASME FORMULATIONS WITH OUTSIDE DIMENSIOI{S Cylindrical Shelt Longitudinal Joint .PR - oE + O.4P oEt - R 0.4t Circumterential Joint r= PRo 2oE + '1.4P 2oEt - 1.4r ^ Ro 2:1 Ellipsoidal Head ^ r=2oEPDo + 1.8P 2oEt - 1.8t Do Sphere and Hemispherical Head - '-2rE+0,8P 2oEt - 0.8r R. ASME Flanged and Dished Head when UR = 164s s 0'885P1 r =0.885L = oE + 0.8P When PLM t= 2oE+P(M-0.2) UB < - 0.8t 16ry3 2oEt ^ ML-(M-0.2) Section PDo r= - 2 cos o(oE + 0.4P) ^ 2SEt cos d Do - 0.8t cos o 183 184 Mechanical Design of Process Systems INTERNAL PRESSURE ASME FORMULATIONS WITH INSIDE DIilENSIONS Cylindrical Shell Longitudinal Joint PRi '-rE-O.6P Ri + 0.6t Circumferential Joinl t= PRi ^ 2oE + O.4P 1-\ i-r-----T;-',-il /l\ 2oEt Ri - 0.4t 2i'l Ellipsoidal Head 2oEl ^ Oi + 0.2t Sphere and Hemispherical Head {,;ft \<=]li - }<T-t"._ 2oEt R + 0.21 ASME Flanged and Dished Head when UR = 1 6?3 P=0.885LoEt+ 0.1t oc-v.tr I Ft When UR pt FOR VALUES OF M < 164s tu 2^tr1 SEE SUPPLEMENT -./L- #+\ \-__=-2, F--- q--l LM + 0.2t \ Conical Section PDr 2 cos d(oE F.-t p - 0.6P) 2oEt cos =Di + l.2l coso d Appendix A: Pressure Vessel Formulations 185 Supptement for ASME Formulations 't. For a cvlindrical shell, when the wall thickness exceeds one half the inside radius or P > 0.385dE, the tormulas in ASME Code AoDendix l-2 shall be used. For hemisoherical heads without a straight llange, the efficiencv ot the head-to-shell ioint is to be ussd it il is less than lhe efficioncy ot the seams in the head. For elliDsoidal heads, whsre ths mtio ot the maior axis is other than 2:1. retsr to ASME Code Appendix 1'4{c). 4. To use the fomulalions lor a conical seclion in the table, the halt apex anqle, d, shall not exceed 30o. ll d > 30o' then a soeci;l analysis is required per ASME Code Appendix 1-5(e). 5. Foian when ASME flangsd and dished haad (torispherical head) used: Ur< 164r the tollowing values ot M shall be Values ot Factor M Ul 1.00 1.00 M Ur 7.00 M 1.41 ' 1.25 1.03 7.50 1.44 '1.10 1.13 8.00 8.50 9.@ 9.s0 1.46 1.48 1.50 1.52 The maximum allowed ratio: M= '('. 1 2.25 1.75 1.08 2.00 '1.06 1.50 L-r = 2.50 2.75 3.00 .15 10.0 1.54 1.17 10.5 1.56 1.18 '| 1.0 1.58 1 D When L/r > 162/3 3.25 1.20 11.5 1.60 3.50 4.00 1.22 1.25 12.O r3.0 1.62 't.65 4.50 1.28 14.0 1.69 5.00 1.31 15.0 1.72 5.50 1.34 16.0 1.75 6.00 6.50 1.36 1.39 16?s 1.77 (non-ASME Code construction), the values ot M may be calculated by Appendix B National Wnd Design Standards A standard is a collection of current practices, past experiences, and research knowledge. Standards that are developed by consensus groups (e.g., ASTM, ANSD, trade associations (e.9., AISC, ACI), or government groups (e.g., HUD, CPSC) carry more authority than other standards because they reflect wider ranges of materials. The ANSI A58.1-1982 is a collection of information that is considered to be the state-of-the-art in the desien of buildings and other structures. Local and region-al building codes adopt portions of the ANSI srandard for their own use. These local and regional codes are developed to represent the needs and interests of their respective areas and are written in legal language to be incorporated into state and local laws. Because these building codes are regional or local in scope, they often do not include everything in the ANSI standard, which is national in perspective. For this reason, one must be certain that a local code written for one area is applicable to the site being considered. The ANSI standard does not have as much authoritv as the ASME vessel codes. and, unfortunarely. does not have a referral committee or group to officially interpret the document. Therefore, one must rnake decisions based on past experience and accepted methods of design. The ANSI standard (Paragraph 6.6, p. 16) states that in determining the value for the gust response factor a rational analysis can be used. A note below the paragraph states that one such procedure for determining the gust response factor is in the standard's appendix. The note at the top ofthe appendix (p. 52) states clearly that it is not a part of the ANSI 458.1 miminum design standard. What all this implies is that one may follow the guide of the ANSI standard's appendix or use another rational analysis, which includes another wind standard. Thus, one care use another standard for design purposes. 147 One of the most widely accepted international standards is the Australian Standard 1170, Part 2-1983, SAA Loading Code Part 2-Wind Forces. The Australian Standard I 170 is more applicable to the process industries because in it are shape factors for geometries that are more common in that industry, e.g., circular shapes. However, before applying the shape factors of the Australian standard to the ANSI or any other national standard, one must be very careful to correctly convert the factors. This is because the codes have different basis upon which these factors are determined, and a direct application of other parameters is not possi ble. This is discussed later after we discuss the basis for the various standards. CRITERIA FOR DETERMINING WIND SPEED Wind is caused by differential heating of air masses by the sun. These masses of air at approximately one mile above the ground circulate air around their centers of pressure. At this altitude, the velocity and direction of the wind is almost entirely determined by macro-scale forces caused by large scale weather systems. Below this gradient height, the wind is modified by surface roughness, which reduces its velocity and changes its direction and turbulence. A secondary criterion, except for extreme wind conditions, is the temperature gradient, which affects the vertical mobility of turbulent eddies and therefore influences the surface velocitv and the eradient height. Therefore. the exact nutur" of the suriace wind at any point depends, first, on the general weather situation, which determines the gradient wind and the temperature gradient, and, second, on the surrounding topography and ground roughness which, together with 188 Mechanical Design of process Systems the temperature gradient, modify the gradient wind to the surface wind. Wind motion is lurrher complicated by rhe rorarion o[ _ the earth. which induces additional forces that cause the alr movrng across the earth's surface to be subiected to a force at righr angles ro the wind velocity vecior. These additional forces are known as Coriolis iorces. Each country has adopted its own standard for measur_ ing wind velocity. The U.S. National Weather Service and U.S. codes use the fastest-mile wind speed, which is defined as the arrerage speed ofone mile ofair passing an anemometer. Thus, a fastest-mite wind speed of 120 mph means that a "mile" of wind passed the anemometer dur_ ing a 30-second period. Other nations, namely Australia and Great Britain. use the two-second gust speed. This is based on the worst 2-second mean as measured bv a cuo anemometer. The mean gust speeds are recorded over a period of time such that a mean recurrence interval is de_ termined. The mean recurrence interval is the reciprocal of the probability of exceeding a wind speed of a'given magnltude at a particular location in one year. The risk. or probability. R. thar the design wind speed will be equaled or surpassed at least once in the life ofthe tower is given by the expression R:l-(l-P,)" where P" : n: annual probability of exceedance (reciprocal of the mean recurrence interval) life of the tower or stack The risk that a given wind speed of specified magni_ tude will be equaled or exceeded increaies with the Deriod of time that the tower is exposed to the wind. Values of risk of exceeding design wind speed for a designated annual probability and a given design life ofthe structure are shown in Table B-1. _ For example. if rhe design wind speed for a tower is based on an annual probability of 0.02 (mean recurrence interval of 50 years) and the projected tower life is 25 years, there is a 0.40 probability that the design wind Table B-1 Probability of Exceeding Wind Design Speed 0. l0 0.05 0.01 0.00s r 5 0.100 0.0s0 0.010 0.005 0.410 0.226 0.049 0.025 l0 15 25 speed will be exceeded during the life of the structure. The United States and Australian wind codes use rhe 50_ year recurrence interval. The instrument for measuring the wind in the United States, Great Britain, and Australia is the cup-generator anemometer shown in Figure B-1. This device is oper_ ated by rhe wind striking rhe cups, which drive a small permanent alternator. The indicator, which incorporates a rectifier, is simply a volrmeter calibrated in miles oer hour. [n most recent cup-generator models the generator output is used to activate a pen-chart recorder w-hich oro_ vides a record of continuous wind speed. WIND SPEED RELATIOIISHIPS As stated previously, another method can be substi_ tuted for the appendix in ANSI A59.1. What this means is that another code could be used instead of the appen_ dix. To do this one must be careful to utilize the correct conversion factors between standards. To accomplish this we refer to Figure B-2. For a 100-mph fastest mile wind speed in ANSI A58. I we wish ro determine the equivalent fastest mile wind speed for a 2-second gust using either the Australian or British code. From Fis-ure B-2 we read from the ordinate 1.54 for 2 sec. Knoiins that one mile of wind moving ar 100 mph will pass thi anemometer in 36 sec, we read 36 sec on the curve and arrive at V,/V366 1.30. Thus, the equivalent fastest : Pr = 1-(1 - PJ" PA Figure B-1. Cup generator anemometer mile wind speed is I 54t : tffil (100y rnp6 = 118.4 mph " I 50 100 0.651 0.794 0.928 0.995 0.999 0.401 0.537 0.723 0.923 0.994 0.096 0.140 0.222 0.395 o.634 0.049 0.072 0.rr8 0.222 o.394 for a 2-sec gust. For I l0 mph, the values becomes V: (l.l8x1l0) mph = 129.8mph n Appendix B: National Wind Design Standards 189 110 Figure B-2. Ratio of probable maximum wind speed averaged orer t seconds to hourlr mean speed. Thus, the gust code 1. if l8 factor would have to be used in the 2-sec that code were to be substituted for Appen- dix A of ANSI A58.1-1982. Similarly, the Canadian code we must convert to ob tain an equivalent fastest mile wind speed from the mean hourly. The mean hourly implies that the rvind moves an :verage of 100 mph across the anemometer in a period of 1.600 sec. Reading Figure B-2 we have V,/V,,o, : 1.9. Thus !! : 1.3 o.ros rvhich yields an equivalent velocity of 76.9 mph. With the Canadian code one must use 0.769 in use of shape constants and the various other parameters when using rvith ANSI A58.1. A comparison of the major wind codes is given in Thbles B-2, B-3, B-4, and B-5. A-A verl restricted category in which the rvind speed is drasticalll reduced. Most petrochemical and power facilities do not fall within this category. The wind force is reduced because the structure is considered to be among many tall structures. One example would be a ten-story building in downtown Manhattan, New York, where the taller buildings would block the stronger air currents. Category B-A classification that encompasses some tall structures, but not enough to block the majority of wind gusts. An example of this category would be a tower in the midst of a large petrochemical facility where there were other towers that would block some of the wind force. A forest surrounding a tower is another example. Category C-The most common classification for petrochemical applications. This category is open terrain where the tower would receive full impact from the wind with minimum ground resistance to the wind. An example of this category would be an open field or an Categorl alrport. ANS| A5A.r-r982 W|ND Category D-A classificarion for wind moving over water. A beachhead, in which there is flat beach up to a CATEGORTES In the ANSI A58.1-1982 there are four wind categocategories are described as follows: ries-A, B, C, and D. The row of buildings would be rn Category D. Miami beach, from the ocean front up to the facade of hotels, is a good example. Behind the hotel fronts would be Category C. Another example of this classification would be a tall vertical vessel on an offshore structure. 190 Mechanical Design of Process Systems Table B-2 Maior U.S. and Foreign Building Codes and Standards Used in Wind Design Code or Standard Australian Standard I170, Part 2-Wind Forces British Code of Basic Data for Design of Buildinss (cP3) Wind Loading Handbook (commentary on CP3) National Building Code of Canada (NRCC No. 17303) The Supplement to the National Buildins Code of Canada (NRCC 17724) ANSI A58.1- 1982 Uniform Building Code Edition 1983 Address Standards Association of Australia t972 80 Arthur Street/North Sydnev. British Standards Institution 1974 Building Research 1980 Establishment National Research Council of Canada National Research Council of Canada 1980 t982 1982 1982 Canada Ottawa, Ontario KIA OR6 Canada 1430 Broadway Southern Building Code Congress International Building Officials and 1984 London, WlA 285, England Building Research Station Carston, Watford, WD2 7JR, England National Research Council of New York, New York 10018 1983 rev. Basic Building Code 2 Park Street Standards Institute International Conference with N.S.W. Australia British Standards Institution American National of Building Officials Standard Building Code Standards House Code Administrators International, Inc. 5360 South Workman Mill Road Whittier, California 9060 I 900 Montclair Road Birmingham, Alabama 35213 17926 South Halsted Street Homewood, Illinois 60430 Table B-3 Reference Wind Speed Beletence Averaging time Equivalent reference wind speed to fastest mile 100 mph Australian British 1 2-3 second gust speed I18.4 1 2-second gust speed 1 18.4 Canadian I Mean hourly 76.9 United States 1 Fastest mile 100 Appendix B: National Wind Design Standards 191 Table B-4 Parameters Used in the Maior National Standards Parametel Australian 1983) (sAA, Brltlsh (BSr, re72) Canadian (NRCC, 1980) Unlted States (ANS|, 1982) Wind Speed 4 3 Yes None Yes Yes Terrain roughness Local terrain Height variation Ref. speed Wind Pressure Pressue coefficients Yes Yes None Yes 2-sec gusts z-sec gusts Mean hourly Fastest mile tbles in Tables, includes figures Figures and Tables, figures and notes Gust speed Reduction for large area Dynamic consideration Gust speed None Gust effect factor Gust effect factor Gust response factor Area averaging Dynamic consideration not included Dynamic consideration Dynamic consideration for h/b appendix includes figures tables in commentaries Gusts Magnitude Spatial correlation Gust frequency > 5 for h/b > 4 in. or for for h/b > 5 h>400ft Analysis procedure This standard is consid- Overall a very good ered by many the best code, its weakest part for us€ in the process is the lack of dynamic industries. Figures and tables are easy to read. The standard actually provides the user with equatrons to curves. The analysis procedure is straight-forward. consideration. An excellent wind Although the appendix standard. The analysis procedure is straight-forward and the docu- is technically not considered a part of the standard, it contains figures difhcult to read, ments-code and namely Figure 6. For supplement conmany structures the tain tables and fig- data extend beyond the ures easy to read, limis of the curves in Figures 6 and 7. In the method in the appendix, one must assume an initial natural frequency, resulting in an iterative process. This method is extremely difficult in designing petrochemical towers without the use of a computer. 192 Mechanical Design of Process Systems Table B-5 Limitations of Codes and Standards Code or Standard Australian Standard I170, Part 2 1983 National Buildinq Code of Canada (NRCC, r980) British CP3 United States ANSI A58.I Uniform Building Code Basic Building Code (BOCA, 1984) Standard Building Code, 1982 (SBCCI, t982) statement ot Limitation "Minimum Design Loads Location Title on Structures" "...EssentiallyaSer Guide to the Use of the Code of Minimum Regulations . . ." ". . . Does Nor Apply to Buildings. . . Thdt'Are of Unusual Shape or Location Section I (Scope) For Which Special Invesrisations May Be Necessary . . ." - "Minimum Design Loads . . ." "Specific Guidelines Are Giyen For. . . Wind Tunnel Investisations ... ForBuildinss.. . Havin--s Irregular Shapei. . ." "The purpose . . . is to provide Section 102 "The Basic Minimum Wind Speeds Section 912.1 TitIE Paragraph 6.1 minimumstandards.._" Are Shown in Figure 912.1 . . ." "The Purpose of This Code is to Provide Minimum Requirements .. "The Building Official May Require - Evidence to Support the Desisn Pressures Used-in rhe Designof Structures Not Includedln This Section." Preface .', Article 1205.2(a) 194 Mechanical Design of process Systcms PROPERTIES OF PIPE * The tollowinq lormulds C're used lhown in the toble: in ihe computotior ol the volues i weight ol pipe per toor (pounds) weighl ol wcter !'€r toor (pour&) squdr€ leet outside iurloce per toot Bqucre leet ilside surloce p€r toot inside qrea (squqre inch*) olea of Inetdl (squcte hches) momert ol inertid (inch6s.) i tbo fsrridc steels rlay b€ qbout S% les., @d tbo dultesitic stoh. l6ss ste€ls dbout 2/o qred'ler th@ the values lhown in this tqbl€ which dre bdsed o! weights lor carbon steol. 10.6802(D-r) 0.3{05d : = r schedul€ Du.Ebers 0.2618D 0.2618d Stotdord weigbt pipe ond schedule 40 dle the sqme in dll sires througb lo-inch; Irom l2,iach through 24-iach, stondqrd weight pipe hcB a wdll thicble$ oI %-inch. 0.78sd 0.78s{Dr-d) 0.049r(Dr-d.) Ertro Btlong eeight pipe (r|td sch€dule gO q!6 the sdme in sll siz6! lhrough 8-inchr trom 8-irch thlough Z4-irch, ert ci sttoag weight A^n; sectio! boduluB (inchest) rodius oI glrotion (illches) = 0.0982(D.-d.) = o.zs pipe hds c wdll rhjcLdess ot %-irch. D l ozlp- Double enrd stloEg weight pip€ bas no cor*ponding scbedule nu.Eb6r. A, = dreo of Estcrl (Equa.e nocles) d = inside dida€ter (iach€6) D = outsids didnete! (bchos) R, = lodiu! ol gFotior (irches) t : pip€ wdU thicloess (inchss) DoEinol piF rize % 0.405 % 0.540 thick- b 40 80 ;; % 0.840 std std l0s 0.049 40s 0.068 0.0740 0.0568 0.095 l0s 0.065 0.410 0.1320 40s 80s 0.088 0.364 0.1041 0.119 0.302 0.0716 ss 0.065 0.710 l0s 0.(E5 0.396 0.2933 40 t; {0s 0.091 0.54S 0.493 80 xs 80s 0.t26 0.423 0.1405 0.065 0.710 o.6't4 0.622 0.546 40 80 ;; XS 40 80 ;; xs 0.466 o.2s2 0.u99 0.065 0.920 0.655 0.2011 l0s 0.083 0.884 0.6t4 10s 80s 0.1l3 0.I54 0.2t8 0-s21 o.?42 0.614 0.434 0.533 0.432 o.2521 0.333 0.435 0.570 0.718 1.185 1.103 1.097 0.945 0.864 0.719 0.083 40s 80s 0.109 0.147 0.187 ;;; xs 0.308 l0s 40s 80s t60 xxs r% {0 ;; J.660 80 xs 0.t{0 r.380 xxs r% l0s 0.0r395 0.1716 0.01197 0.00586 0.00730 0.00862 0.0285 0.01737 0.02160 0.02554 0.2150 0.2159 0.2090 0.0120 0.0285 0,01431 0.0341 0.0407 0.0478 o.0527 0.0577 o.2750 0.2692 0.2613 0.2505 o.2102 0.2409 0.2314 0.2157 0.1943 0.1607 37 0.344 0.344 0.344 0.310 0.2872 o.2716 0.2s20 0.2134 0.1570 0.06s t.?70 2.461 0.t09 1.682 0.37s 0.613 0.197 0.497 0.1271 0.1215 0.1146 0.00378 o,275 0,273 o.275 0.275 o.275 o.275 1.534 0.00437 0,00525 0.01230 0.0660 1.107 0.00088 0,00106 0.01032 0.671 1.057 in 0.00331 0.1765 0.1628 0.1433 0.63r gYrd- 0-00600 0.538 1.160 I UorL 0.00I22 0.I859 0.896 0.8b lus, 0.002?9 0.220 0.220 o.220 0.220 0.220 0.220 0.250 0.382 r.496 r.283 0.0321 lodiu! 0.0572 0.04s1 0.0310 0.1295 0.1r06 0. lb a6clioE Erodu. 0.330 0.425 0.535 o.t77 0.t77 0.t220 |'roEeDt ol inertio. 0.3ts o.t427 0.3{{ 0.3{{ designctioD 0,0246 0.0157 0.t77 0,434 0.434 0.434 0.434 0.134 0.434 1.27a 0.186 0.245 0.538 0,423 0.568 0.739 0.326 U.53I 0.669 40s 0.0s04 0.070s 0.0563 lbf 0.1859 r.839 1.530 lt 0.0794 0.341 t.442 per 0.220 1,076 0.109 It il|3id€ 0.141 0.2818 0.065 Bq 0.I4t 0.s22 1.049 0.957 0.815 wdl ihicla€ss ANSI835.19 stainless sloel piF,e scbedule du.Dclors 0.1073 0.0955 0.599 0.133 0.1?9 0.250 0.358 55 ,:: 0.1479 0.r06 0.2553 0.113 0.4s4 0.639 0.836 r0s 160 1.900 0.065 0.109 0.2961 0.r06 0.106 0.1582 0.1246 0.1670 0.2173 0r9{ l0s 836.10 steel pipe rtoEinql "q.tt.. ouardo 0.141 0.1583 0.1974 0.2503 0.320 0.383 0.504 xxs 40 80 0.19t0 b: ANSI lr'6ight weight ol wcler , | auddc.€! sur{dc6, Fr It, p€r lt, |I | 0.0970 0.12s0 0.1s74 0.3ss9 0,357 0.304 0.2340 0.1706 160 I 0.0364 0.0548 o.0720 0.0925 836.10 steel pipe schedule Dumb€rg e |3cr'l|r" I pertr 0.307 0.269 0.215 xxs .1.3r5 cleq, ldred, . I _ 3q.In. in- 160 1.050 inside didm- io"ia. |l -.tot in. xs 80 % o.675 wcll Bchedul€ oulside diclmeter, ll|" o: ANSI 0.t011 0.0827 0.0609 0.17t 0.rs47 0.851 0.1316 0.0ttl0 1.0€8 0.10I3 0.02010 r,301 0.0710 0.0216 0.022\3 0-t2125 0,684 0.857 o.2aa2 0.02451 0.2661 0.02970 0.0370 0,0448 0.0527 0.0579 't.7t4 l.l3t t.414 1.937 2.441 0.2301 0.1875 0.1284 0.0541 0.858 0.478 1.404 0.{09 0.1t04 0.2810 0.0760 0.ll5l 0.443 0.42A 0.407 0.387 0.361 1.679 0.374 0.311 0.I056 2.811 0.2281 3.659 0.t221 o.1252 0.1405 0.1329 0.1605 0.1900 0.2137 0.1038 0.1605 0.1948 0.2418 0.2839 0.1250 0.1934 o.2346 0.2913 0.312 1.r07 o.797 1.805 0-7al 0.361 2.273 2.997 0.648 0.2t92 0.349 0.343 0.334 2,t72 0.401 0.l9sl 0.0467 0.0566 0.0706 0,0853 0.1004 0.0500 0,0757 0.0874 0.378 0.1594 0.1628 0.1547 0.335 0.304 0.2346 5.2t4 0.458 0.2732 0.341 0.41I 0.469 t.274 1.067 0.I580 0,{40 2.085 0,962 0.2469 0.1663 0.2599 0.32r 0.30{ 0.42t 0.564 0.550 0.540 0.524 0.506 0.472 0.649 0.63{ tCt,kne\) ,'f ITT Ctinkll. Appendix C: Properties of PiPe 195 PROPERTIES OF PIPE (Continued) noEitrol prpe qumber' outside diomelet ia. thick- srd xi 40s 8os xxs 2 2tl 0.154 0.218 0.343 0,436 0.s62 0.687 2.875 80 ";; xs 40s 80s 160 )o(s .''. 1; ;;; 80 3.500 160 10s 3h 40 80 i;xs 80 4'JU) xs 5.563 D-622 0.541 1.411 0.822 0.622 0.822 0.622 0,622 0.508 0.442 0.393 0.328 0.262 5.O22 1,280 0.868 0.731 7.444 9.029 0.971 1.163 0.979 0.76S I.312 1.I01 t0.882 0.533 0.311 L.442 1.2140 1.5130 t2110 0.753 0.?s3 0.753 0.753 0.753 0.753 0.753 0.?s3 0.709 0.6s0 0.646 0.608 0.556 0.464 0.3s9 0.334 2.499 2.361 2,016 1.837 1.535 0.710 0.988 0.4s4 1.530 1.064 1.925 1.339 13.70 15.860 1.067 l.ss8 t1-729 0.554 2.872 3.0890 3.2250 0.873 0.s53 0.803 3.03 4.33 7.58 3.78 1.301 3.6r LazZ 1.154 10.25 tl-32 2314 18.58 1.801 1.431 2-226 2.476 3.43 1.136 0.687 0.602 0.537 o.171 3.02 3.90 5,03 5.39 t.724 0.75S 3.20 2.864 7.O73 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 1.021 t.o47 1.004 1.463 1.047 0.984 3.41 4.91 2.680 3.68 a,721 1.047 t.o41 0.92S 0.881 12.51 1.047 0.7t6 22.850 3.8S 2.S30 3.92 6.40 2.1s0 2.556 3.199 3.641 0.083 0.120 3.334 3.260 3.068 2.900 2.626 2.300 2.050 8.73 8.35 7.39 0.89r r.s00 2,5,13 0.r20 0.188 0,237 0.337 o.437 0.500 160 0.62S )o(s r.075 o,z6s2 o,420 0,561 s.2t2 0.674 0.800 0.925 4os 80s 0.499 1.276 t20 xs 0.3rs 1.582 1.455 t.275 0.109 0.134 0.258 0.375 0.500 80 r.715 2.638 3.653 1.826 0.531 ;; ;;; 0-622 0,622 0.472 2.184 0.226 0.318 0.636 r0s 0.787 0.7s0 0.875 1.000 3.834 3,760 3.548 3.364 2.72A 4.334 4.260 4.L24 4.026 3,826 3.626 3.S00 3.138 3.152 2.900 2.650 5.34S 5.29S 5.(X7 1.813 4.563 4.313 4.063 3.813 3.553 6.6r 5,12 4.15 3.299 11.10 9.89 8.89 5,845 r.704 1.2?4 2.224 3,02 1.2L 5.4t 6.317 1.178 14.7S 11.25 13.357 t2.73 It.50 2.547 3.17 4,41 r0.33 s.521 s.28 7.80 6.602 5.513 0.817 0.802 o.741 0.755 o.129 0.703 0.6710 0.6410 0.t23 1.525 40s 80s :o,s t,229 1.001 0.58I 1.60d t.771 0.I20 r60 r.251 0.508 0.598 0.6470 0.6670 8.6?8 2.945 4.03 4.663 10s 120 1.774 0.{12 0.588 0.565 4.19 4.24 3.55 0.2I6 40s s0s l.5m 0.326 0.39r 0.I57 1.039 0.083 ;; ;; 1.689 I.939 0.623 0.50s 0.310 0.246 o.724 0.300 0.437 0.600 0.725 0.850 IGS o.176 tio|1. inJ in.. 7.7tO 2.635 2.469 2.323 2.L25 80s xrs 0.{97 lus, lb 0.483 0.568 0.6140 0.6340 2.r09 0.083 1,qn 2.551 rodiue gYrc- o.4tz 1.885 0.083 0.120 0.203 0.274 0.3?5 0.552 0.675 0.800 40s xi; 2.247 rnodu- 6.40€ I.{29 80s lt. a6ctioE ol wsler oI p€r It, in€diq, 1.859 r.406 0.950 0.567 0.283 {0s per w€isht 0.882 0.765 0.608 1.I00 xs suatcce, EurIqce, pe.Il po. ft rrreight 3.631 1.338 ;; ;; It itrlide 2.7t8 0.400 3.96 3.65 3.36 2.953 2.210 rq 0.3s3 0.350 0.288 o.223 0.281 2-245 2.157 2.081 lt outsido o,42r r.058 0.850 0.600 eq 0.497 0.497 0.497 0.497 0.497 0.799 1.767 0.109 ;; rD. 2,036 0.06s l0s rq. 1.500 5'S xxs 3q. in. 1.6r0 0.650 160 metol 0.200 los 80 iriide 0.I45 0.52S .: 2.375 diqa- in. 160 L90{) inrid€ !646. b q 40 80 1% wcll rchedule rir. 6.283 6.62 8.10 9.294 12.385 2.175 3.531 5.793 7.661 I0.01 zt-447 24.0s'l 9.r! t.178 l.ll5 1.178 1.082 1.178 r.054 10.79 1.178 1.002 14.98 1.178 0.94S r.178 0.916 0.900 0.825 0.759 0.694 r8.96 21.360 1,178 1.178 10.384 1.r78 t.178 8.560 0.792 o.111 r.041 1.208 t.t96 1.094 1.0,17 6.50r0 3.7t50 1.0140 6.8530 3.9160 0.9810 5.01 4.81 4.28 1.960 2.756 4,19 6.28 s,8d80 0,980 1.38s L.312 5.800 5.51 4.98 4.48 4.160 1.378 2.394 3.14 4.9240 1,337 1.307 1.2100 2.811 t.249 1.562 3.96 5.8500 L.762 2.6000 3.21 4.27 1.549 123 11.65 t2.17tO 4-O2 13.27 21.54 31,613 35.318 3.38 2.864 15.29 2.391 t7.?130 1.399 1.386 6.35 7.77 9.73 6.95 8.43 l{.62 16.66t0 1.868 1.456 2,285 4.30 t.456 1.4s6 r.321 18.19 6.ll 1.456 1.260 20-74 t.89 I6.35 1.456 1.t95 27.O4 14.6r 7.95 9.70 1.456 1.129 32.96 t2.97 I1.34 1.455 r.064 38.5S 7.(x) 6.33 s.62 rt.4l3 12.880 l.{s6 0.998 0.933 43.8t0 {.951 36.6450 17.7s1 4.232 39.lll0 1.156 2.I4S0 2.2430 0.988 0.975 0,947 0.924 0.894 0.844 0.8140 0.7860 1.103 22.44 22.02 20.01 1t.328 0.68t 0.549 0.5200 0.4980 15.17 20.68 25.74 30.0 5.6760 5.90 6,79 7.4050 7.8720 2.494 3.03 5.15 7.13 9.25 10.80 1.5250 t,510 t.177 1.445 1.1250 t.116 1.37{ 1.3380 r.3060 1.920 1.878 1.839 1.799 1.760 I2.10 13.1750 11.0610 1.6860 1.5s20 196 Mechanical Design of Process Systems PROPERTIES OF PIPE (Continued) pipe Biz€ schedule in. wall inside thick- diom- l0s 0.109 6.407 32.2 0.134 6.357 0.219 6.187 3t.7 30.r00 5.761 28.89 26.07 40 sia 40s 0.280 80 xs 80s 0.432 tItetol sq. in. rn. b 6 inside 3q. rL aq lt outside sq ft inBide surrcc pe! It per lt weighl per It, lbf 5.37 r3.98 ll.8s 3.58 1.664 9.29 t3.74 14.40 4.4I0 4.35 t.734 t.734 1.620 22.6600 6.8400 1.588 15.020 18.97 r3.100 5.58 12.51 28.\4 8.s0 8.40 I.734 1.508 28.57 It.29 t2.2s 2.I95 L440 36.39 I0.30 40.5 49.6 14.98 2.153 1.358 5S.0 66.3 r7.8I 2.r04 20.03 72.r190 21.7720 2.060 2.0200 76.5970 23.t240 1.s850 5.50r 23-77 10.70 5.189 4.897 18.83 15.64 1.734 1.734 1.734 L000 L t25 4.62S 16.792 t7.662 t.734 r.211 45.30 s3.16 60.076 4.37S Is.02s 19.429 t-734 1.t45 66.0S4 0.109 4.407 9,91 8.329 2.180 r3,40 0.219 8.187 2.258 2.258 2.258 2.258 2.258 2.25A 2.258 2.25A 2.2A1 0.I48 2.916 3.94 2.150 19.640 2.t27 2.1t3 22.36 24.70 28.55 r.282 8.17 7.284 24.07 23.59 22.500 22.48 8 20 0.250 8.125 s4.s 52.630 51.8 8.625 30 0.27',| 8.07r 51.2 0.322 7.991 0.406 50.0 47.9 10.48 0.s00 7.813 7.625 45.7 t2.78 100 0.593 7.439 t20 0.718 7.18S I l{0 t7.44 2.25a 2.258 1.882 0.8I2 7.001 43.5 40.6 38.5 19.93 8.625 2.2s8 L833 160 0.906 6.813 2t.9? 2-2s8 1.784 74.69 15.80 1.000 6.625 6.375 23.942 26.494 2.258 2.258 t.?34 81.437 90.1r4 14.945 r.669 2.744 2.728 2.70 r8.70 24.63 2.683 28.04 a;; 80 XS 4;; 80s l0s ;; 30 5.800 6.58 8.40 14.96 2.089 2.045 1.996 L948 22.t8 18.84 t21.4 28.t4 2.847 17.60 140.6 32.6 2.807 r6.69 1s3.8 35.7 2.117 38.5 2.7 4A 4r.0140 2.7I90 2.68I0 13.838 10.250 9.25 0.307 r0.r38 2.815 2.815 2.81s 2.654 34.24 10.020 82.s 80.7 78.9 2.623 40.48 )0.750 80 100 120 2.938 50.87 60.63 0.250 xs 2.962 2.953 2.S09 0.219 60 I3.39 t4.6S r6.81 2.578 36.9 36,2 35.8 35.0 l0 63.4 24.52 2.815 l.9l ll.s000 r05.7 2.815 10.07 3.00 2.9700 sr.3200 19.80 5.49 7.24 l 8.2I 20.58 4.52 0.365 0.500 0.593 3.0r 35.4 88.8 85.3 ;,; 6.13 20,79 86.3 2.815 26.4S 21.69 r0.420 r0-312 83.52 2.304 2.295 2.2700 2.245 35.64 43,39 t0.482 0.134 0.t 65 40 40s 80s 34.454 3L903 luB, r.677 0.562 40 60 inertia, tb 1.734 0.7I8 I0s per It, rddius gyration, in. 1.734 160 0.864 oI 2.231 2.733 t20 xxs w€ighl 37.4 177.t320 r90.62I0 44.2020 63.7 76.9 I1.85 14.30 3.75 3.74 100.46 r8.69 3.72 I13.7 21.I6 3.7r 137.S 160.8 25.57 29.90 3.69 34.1 9.750 s.564 '14.7 16. t0 2.815 2.5S3 54.74 32.3 7t.8 2t2.0 39.4 3.53 t8.92 2.815 244-9 9.314 68.I 45.6 3.60 22.63 2.815 248.2 0.843 53.2 9.064 64.5 3,56 26.24 2.815 0.87S 27.t4 2.815 2.36 L000 t.125 28.0 27.6 324 9.000 64.33 76.93 89.20 92.28 31.1 0.718 2.504 2.438 2.373 8.7S0 60.1 30.6 2.815 2.:91 104.13 26.1 368 8.500 2.815 2.225 37.3r 2.815 2.16 t26.42 428.t'I 1.500 7.750 47.r5 3.52 3.50 3.47 3.43 3.39 43.57 2.8I5 2.03 148.19 24.6 23.2 20.5 399 8.250 56.7 s3.45 34.0 1.2s0 60.3 62.04 58.4 74.3 79.66 478.59 89.04 3.31 0.156 12.438 rzt-4 t22.2 12.390 r20.6 19.20 7.11 3.24 52.2 I40.S 0.2s0 !2.250 u7.9 22.t3 3.34 3.21 3.34 3.17 43-77 19.1 191.9 248.S 30.1 12.0S0 ll4_8 5r.l 0.330 9.84 r2.88 20.99 24.20 33.38 52.7 0.180 3.34 3.34 0.375 12.000 I 3.14 49.S6 4S.0 279-3 11.938 llt.9 3.34 0.406 14.58 1s.74 0.500 u.750 3.34 3.08 0.562 I1.626 106.2 2t-s2 3.04 362 401 11.376 r0t.6 56.7 62.8 0.687 26.04 3.34 3.34 48.5 47.0 46.0 47.1 19.24 53.53 65.42 73.16 300 108.{ 4.45 4.44 4.42 4.39 4.38 4.37 4.33 2.978 88.51 44.0 0.7s0 0.843 0.87s 1r.250 99.40 .28.27 3.34 2,94 96.2 43.1 475 510.7 11.064 96.t 41.6 562 t20 3.34 2.897 2.88 07.20 t0.9 4I.l 578,5 1.000 10.750 l{0 36.9 3.34 2.8t4 10.500 4l.l 3.34 642 70r 1.250 10.250 45.16 150 r.3t2 35.8 755.5 10.126 3.34 3.34 2.749 2.68 25.49 39.68 53.6 39.3 r,125 95.00 90.8 86.6 82.50 80.5 31,5 32.64 3.34 I1.000 2.651 4D.27 34.9 781 140 I60 l0s ;i 30 40 t2 ;; 12.750 80 I00 ;;; 4;; .-. 80s t3.l 41.1 3.34 3?.S 333.46 39.0 43.8 ? 4.5 80.1 90.7 4.31 4.27 4.25 4.22 4-21 I09.9 4-t7 4.I3 118.5 122.8 4.09 4.01 100.7 3 '1' Appendix C: Properties of Pipe 197 PROPERTIES OF PIPE (Continued) aoniaal pipo riz. rchedule outtide woll iDsid€ thicL- diqn- inside metal h. sq. it!. 11646, iD. b Frlt 13.688 147.20 6,78 3.67 3.58 145.80 13.580 141.80 3.67 3.67 3.57 0.2r0 0.219 r3.562 144.50 8.16 9.10 9.48 to 0.2s0 t3.s00 143.I 10.80 ;; 0.281 13.438 141.80 l2.tt 140.5 139.20 t3.42 ;; 40 0.312 0.344 0.375 0.437 ;; 80 100 13.312 13.250 13.126 137.9 14,76 16.05 I35.3 18.62 19.94 0.469 13.082 1s4.00 0.500 0.ss3 0.625 0.750 0.937 13,000 t32-7 12.8I4 129.0 24.94 12.750 t27.7 t22.7 26,26 12.500 woisht trrr fL tb trlo|ne|''t ol modu- i|'ertiq, luB, tioD. iD.. in.t i!- aectiorr rcdiu6 9Yra- 3.55 23.0 27.1 30.9 32.2 3.67 3.53 36,71 62.1 3.67 3.52 4t.2 6I.5 285-2 40.7 3.50 45.68 60.9 3.48 3.4J 3.44 s0.2 s1.57 63.37 67.8 50.3 3r4 34{.3 14.9 49.2 58.7 s8.0 429 456.8 55.3 1-79 72.09 57.5 484 69.1 84.91 55.9 562 80.3 s8s 81.1 4.18 4.14 4.73 4.69 4.63 1.58 4,53 4.18 3.67 3.57 3.42 3.67 31.2 weight 3.67 3.67 12,t28 3.40 3.35 3.34 3.27 3.17 r62.6 63.1 62.8 130.73 150.67 30.9 225.1 t2.2 4.47 36.S 4.86 4.85 59.7 89.28 106,13 2t8,2 4.90 4.88 1.87 194.6 53.2 s0.0 47.5 45.0 27.8 53.3 61.2 687 94.2 825 117.8 tr21 132.8 146.8 159.5 4.84 4.8s 4.82 1.80 1.093 1.2s0 It.8l4 109,6 44.3 I1.500 103.9 50,1 3.67 180 1.406 lI.l88 98.3 55.6 3.6'r IS.670 I92.90 8.21 i; 0.16s 0.188 0.250 15.624 r5.500 191.70 188.7 9.3{ t2.3? 1.19 4.19 0.312 1s.376 185.7 15.38 0.37S 1s.250 182.6 15.000 14.688 t76.7 4.19 3,93 60 0.500 0.656 18.4I 24.35 4.IS 4.I9 4.10 4.09 4.06 4.03 3.99 4.19 80 0.843 14.314 160.9 40.1 4.19 100 1.03r 13.938 1s2.6 48.5 {.19 120 1.218 1.437 13.564 144.5 13.126 t35.3 65,7 4.19 4.19 3.85 3.75 3.65 3.55 3.44 1.593 12.814 129.0 72.1 4.I9 5S 0.r65 17,670 4.71 4.63 106.2 368 40.8 6.31 l0s 0.188 t7.624 I7.500 245.20 243.90 4.',1L 4.61 36 105.7 4t7 46.4 5.30 41-39 59.03 104.3 5{9 61.0 6.28 102.8 75.S 6.25 70.59 t01.2 678 807 89.6 8.23 82.06 93.15 r04.75 99,9 93r 103.4 6,21 98.{ 1053 117.0 6.19 97.0 rt72 130.2 120 140 20 30 40 l0s ;; xs t40 t60 ;; 30 ;; 80 169.4 t7,34 4.71 0.375 17.250 233.7 20.76 4.71 230.4 227.0 223.7 24.11 4.71 4.58 4.55 4.52 4.48 21.49 4.71 {.45 30.8 4.71 4.71 4-42 4.32 4.22 0.437 17.126 0.500 17.00 0.562 16.876 0,750 0.937 16.500 213.8 204.2 40.6 s0,2 1.7r 16.126 193.3 61.2 4.7 r 182.6 4-71 4.7 | 4.7 ! 3.89 3.78 140 1.562 r60 1.781 14.438 163.7 71.8 80.7 90.7 0.188 I9.634 302.40 I1.70 0.218 19.564 300.60 0.250 0.375 r9.500 r9.250 30 40 0.500 0.s93 t9.000 18.814 60 0.812 I8.376 18.2s0 80 0.875 1.031 100 1.281 17.438 298.6 291.0 283.5 278.0 265,2 261.6 252.7 238.8 1.375 s; 2.929 237,r r5.688 r5.250 r4.876 l0 ts 240.5 r.r56 20 4. 3.01 u.376 r00 I20 l0s 3.09 9.24 r0.52 13.9{ 0.2s0 0.312 20 20 20,000 rurlqce, lt ingide per lL rurldce, lbt per lL 13,624 l{ 18,000 sq 0.188 t1.000 t8 3q. It outside 0.1s6 l0s 16.0U) iD- sq 17.938 173.8 23.t2 30.6 36.2 48.9 52.6 61.4 s.21 5.24 s.24 s.24 5.24 t10,22 I89.12 42.8 I0l7 28 32 83.5 25? 8S.0 292 42.05 81.8 80.s 384 52.36 62.58 42.71 10r.50 79.1 36.5 48.0 473 562 59.2 ?32 9t.s ?0.3 136.45 73.4 89.7 ll57 114,6 164.83 66.1 1365 170.6 58.5 I?60 220.0 1894 236.1 933 192.29 223.81 245.11 138.17 92.7 t70.75 88.S 1834 4.ll 207.96 2180 3.9S 244.14 274.23 83.7 79.2 75,3 203.8 242.2 2499 z'17.6 2',150 308.5I 7 r.0 3020 306 335 168.3 40 131.0 574 5.12 46 r30.2 663 5.ll s2.19 78.60 129.5 126,0 1I 104.I3 5.24 4.97 4.93 5.24 5.24 5.24 5.24 5,{8 5.43 194.5 5.14 s.60 5.59 5.37 5.21 5.17 5.12 6.10 6.01 s.97 5.90 5.84 5.77 7S? 7S-7 7.00 6.99 6.98 l4 lll.4 6.94 t22.8 t457 6.90 r22.91 120.4 1704 145.7 170.4 4.8r I66.40 115.0 6.79 178.73 Ir3.4 2257 2409 225.? 4.78 4.70 4,57 208.87 256.10 109.4 2772 240.9 277.2 103.{ 3320 332 5.0{ 57.4 198 Mechanical Design of Process Svstems PROPERTIES OF PIPE (Continued) nominol pip6 rire wcll schedule b 20 20.ooo in. iD. 16.500 16.064 227.0 213.8 202.7 2r,624 367.3 t.968 s.24 5.24 s.24 4.45 4.32 296.37 341.10 4.21 379.01 17.18 0.37s 2t.250 354.7 25.48 0.500 0.625 346.4 339.2 33.77 5.76 322.1 41.97 50.07 58.07 5.?6 0.875 21.000 20.750 20.s00 20.250 80 l.t2s I9.750 306.4 13,7A 5.76 r00 1.37s 19.2s0 291.0 276.1 8S.09 5.76 104.02 5.76 30 xs 0.750 ;; 18.7S0 330.r ?.70 l0l0 91.8 87 153.7 1490 lls 135.4 7.69 7.65 150.2 1953 t77.5 7.61 t43 146.6 2t8-2 1?0 143.t 2400 2829 3245 434 18.65 5.76 5.76 5.99 s.96 5.92 5.89 6.17 5.83 5.78 140.80 156.03 t76-2 3140 26t.4 174.3 172.4 3420 285.2 37I0 309 r88.9 I152 96.0 216 238.11 168.6 4256 4650 s670 354.7 t73 8,07 6850 571 7830 8530 9460 719 788 7.95 7.47 7.79 7.10 41.{ 6.28 6.28 6.28 398 45.9 50.3 54.8 436.1 16.29 388.6 63.54 70.0 6.2S I42.1 6.28 150 19.314 293 159.4 6.28 0.2s0 2S.s00 t0 0.3I2 25.376 0.37s 510.7 505.8 500.7 490.9 0.625 24.500 0.875 24.250 24.000 23.7s0 20 std 20 30 xs 6.54 6.48 2S6.36 158.3 367.40 429,39 149.3 141.4 483.13 541.94 t34.S t27.0 388 8.18 8.15 22t.4 1646 126.6 s.l0 88 2t9.2 r59.7 9.08 I03 217,1 2076 2479 3259 4013 4744 2t2-8 190.6 9.06 250.7 308.7 9.02 8.98 8.93 s.89 8,85 8.80 6.41 202 6.81 235 452.4 6.8I 6.35 6.28 267 20s.6 204-4 200.2 r96.1 443.0 87,91 6.81 6.22 299 ts2.t 594.0 71 92 2s1.3 2098 2601 149.8 185.8 9.81 2S5.0 22t-A 9.77 520.8 94.98 252.6 248.0 243.4 238.9 234.4 230.0 225.6 3l0s 530.9 21.80 z',t.t4 32.54 43.20 53.75 64-21 74.s6 84.82 1.20 0.875 r.000 1.r25 27.500 27.376 27.250 27.000 26.750 26.500 28.250 26.000 2s.750 0.375 0.500 0.625 t0s 6.81 6.81 r55.8 8.22 8.41 6.81 0.750 l0 6.68 6.64 55 8.29 a.z7 8.25 49.82 0.3r2 xs 6.81 186.24 1316 59.49 69.07 78.54 0.250 30 6.8r t7t.I? 188.0 471-4 461.9 1.000 std 19.8S 25.18 30.19 40.06 5.48 5.33 s.20 5.06 63.41 481.1 1.t25 l0 8.35 8.31 7.07 16I.9 126.3 0.750 8.10 212.5 231-0 310 26.000 109.6 7.t5 1943 326 0.500 t07.2 2550 2840 1s.876 20 45t 7.31 7.23 183.8 1.812 25.250 2s.000 24.750 119.6 7.39 180.1 178.1 2.062 2.343 srd 351 403 4?58 5432 6054 s4.62 406 87.2 108.1 t26.2 125.49 4 344 303 7.47 6,09 21.83 36.S 365 40i29 7.52 295.0 366.3 432.6 493.8 550.3 602.4 6.O2 425 140 L2l8 1.53t 132.8 237 -2 6.r5 t20 80 5.04 4.91 I97 2Sl 6.28 6.25 6.28 6.28 6.28 5.28 6.28 6.28 6-28 100 5.56 5.50 5.43 5.37 5,30 5,17 4.78 415 382 6.41 157.4 23.500 23.250 23.000 22.816 22.750 22.626 22.500 2s.564 22.250 22.064 21.s64 20.938 20.376 0.968 459 't.71 0.250 0.8?5 6.56 6.48 80.4 l0 ;; 422 885 132.68 0.218 376 1s8.2 118,55 402 4220 4590 5l 26t.6 0.750 98.3 92.6 87.9 14.92 247.4 0.687 tb 69.7 17.750 io 9yra. lion, in. Eroduinerlid, lus, 756 r8.250 0.62s rqdiur oI r59.t r.875 0.562 per lt, lnoEent rection 44 2.t25 0.375 n eight 12.88 140 160 0.500 tbt perlt 363.1 ;;; lt lt per 2r.500 20 sq lreight in8ide gurlqce, surlcce, per Il, 0.250 30 30 30.000 lll.s lt oubide 21.564 XS 2A 87.2 Bq 0.188 0.218 20 28.000 I00.3 17.000 120 28 aq rr'" 1.750 160 metdl sq in. 1.500 l0 24.000 inside 140 I0s 22 inaide dicm- r20 5S 22.004 lhick- 588.6 583.2 572.6 562.0 s51.5 541.2 0.250 29.s00 683.4 23.37 0.3I2 29.376 477.8 29.19 0.375 0.500 29.250 29.000 28.750 672.O 34.90 660.5 46.34 649.2 57.68 0.62S 7.t7 '1.33 7.33 7.G) 7.33 7.85 7.85 7.85 7.8s 7.8s lll ?.13 7.07 7.00 t17 6.34 2tg 6.87 183 253 288 6.74 323 7.72 7.69 7.66 7.59 7.53 79 99 119 158 !96 296.3 293.7 291.2 286.2 281.3 364.9 5458 419.S 6149 473.0 6813 524.1 4085 5038 5964 6855 714D 8590 9.79 23 1.8 359.8 426.0 490.3 6t3.6 9.68 9.61 9.60 s.55 9.51 t72.3 2t3.4 10.52 3201 3823 254.8 10.18 s033 6213 335.5 I0.43 4t4.2 10.39 258S 10.50 n-. Appendix C: Properties of Pipe 199 PROPERTIES OF PIPE (Continued) nominol schedule pipe size oulside wcll thick- inside dicm- irBide sq. in, didmeteL metal Bq. in, sq It sq It outside inside weighl pe! ft, lbt weight per It !(rdiug ol ilrerlio. lb lus, gvrqiion, per It per rl 7.46 234 276.6 271.8 137 | 491.4 10.34 272 84S4 566.2 10.30 310 2E',t.O 9591 639.4 10.26 347 242.2 10653 t0.2 t0.22 in.3 0.750 0.875 28.500 637.9 68.92 30 28.250 620.7 80.06 7.85 7.85 30.000 I.000 28.000 615.7 9t.Il 7.85 7.39 7.33 l.l2s 27.',750 6D4.7 r02.05 7.85 '1.26 0.250 31.500 '179.2 24.93 8.38 8.2S 85 337.8 11.22 3I.02 8.38 8.21 106 335.2 3l4 t 38gl 196.3 773.2 243.2 11.20 766.9 37.25 8.38 t27 332.5 4656 291.0 11.18 7 54.7 49.48 8.38 B.l8 8.l l 168 321.2 383.8 u.l4 473.6 I1.09 40 l0 0.312 std 0.375 xs 0.500 31.250 31.000 7 32 30 0.625 30.750 7 42.5 61.59 8.38 8.05 209 321.9 6140 7578 32.000 40 0.688 s0.624 736.6 67.68 8.38 8.02 230 319.0 8298 518.6 11.07 0.750 30.500 730.5 73.63 8.38 7.98 250 316.7 8990 561.9 I1.05 0.87s 30.250 8.38 8.38 7.92 7.85 10372 648.2 lr.0l 30.000 85.52 s7.38 291 1.000 718.3 706.8 33t 306.4 I I680 l0.ss l25 29.?50 694.7 8.38 7.',19 371 301.3 I3023 730.0 814.0 0.250 0.312 33.500 881.2 26.50 8.90 8.1',| 90 382.0 3173 22t.9 33.376 33.250 874.9 32.99 8.90 8.7 4 1r2 379.3 4680 2',t5.3 IL33 I t.9I 867.8 39.61 8.90 8.70 sssT 329.2 11.89 33.000 s5s.3 52.82 8.S0 8.64 t79 370.8 7385 434.4 r 1.s5 841.9 65.53 72.00 8.90 8.57 365.0 I1.80 3M.l 587.8 I 78.34 LS0 8.54 8.51 9124 9992 535.7 8.90 223 245 266 359.5 1082s 637.0 11.76 20 L t0 st; 20 34 34.A00 XS 0.62s 40 0.688 32.7s0 32.624 0.750 32.500 0.875 32.250 829.3 816.4 91.01 8.90 8.44 310 3S4.1 12501 735.4 tt.12 1.000 32.000 804.2 I03.67 8.90 8.38 353 348.6 l4l t4 830.2 t.125 3t.750 791.3 lI5.I3 8.90 8.31 395 343.2 15719 924.7 I1.67 I1.63 0.250 35.500 s89.7 28.11 L42 9.29 96 429.1 4491 24S.5 t2.84 0.312 35.376 982.S 9.42 9.26 lIs 426.1 12.62 3s.2s0 s75.8 L42 9.23 143 423.1 5565 6654 309.1 0.37s 310.2 12.59 0.500 35.000 962.1 34.95 42.D\ 55.76 9.42 9.16 190 417.l 8785 488.1 12.55 30 0.625 34.750 948.3 69.50 9.42 9.10 236 4lt.t 10872 504.0 12.51 40 0.750 34.500 934.7 83.0I 9.42 9.03 242 405.3 12898 7I6.5 12.46 0.875 920.5 96.s0 9.42 399.{ I4903 82',t.9 907.9 109.96 9.42 8.97 8.90 324 I.000 34.250 34.000 374 393.6 I6S5I 936.2 t2.42 I2.38 1.125 33.750 a94.2 123.19 9.42 8.89 419 387.9 18763 t042.4 12.34 0.250 0.375 41.500 1352.6 32.82 tt2 586.4 r28 339.3 14.?3 1336.3 4S.08 10.80 t320.2 65.18 t0.99 10.73 s79.3 s't2.3 I0627 I4037 t4.7r 0.s00 I67 222 506.r XS 668-4 t4.67 1304.r 81.28 10.67 276 565,4 1288.2 1256.6 97.23 r0.99 I0.99 330 558.4 427.3 985.2 14.62 14.59 128.81 10.99 10.60 10.47 17373 20689 1.000 41.250 41.000 40.7s0 40.500 40.000 10.99 10.99 10.86 std 438 544.8 210a0 39.500 39.000 t225.3 160.03 t0.99 10.34 1194.5 190.85 10.99 10.21 s44 649 531.2 517.9 33233 39181 r2s9.5 rs82.5 14.50 1.250 1.500 1865.7 14.33 20 36.000 10.92 30 l0 36 0.375 0.500 109.0 2i 42 30 42.000 40 XS 0.62S 0.750 835.S 7 I.78 14.41 200 Mechanical Design of Process Systems INSWATION WEIGHT FACTORS To determine the rveight per foot of any piping insulation, use the pipe size and nominal insulation thickness to find the insulation l.eight factor F in the chart shorvn belorv. Then multiply fl by the density of the insulation in pounds per cubic foot. Nominal Insulation Thickness Nominal Pipe Size 2rt" 1%" I 1% 1% 10 12 .051 .066 .080 2 214 3 .09r .r9 .10 .17 .24 .21 .24 .!7 .31 ,41 .30 .39 .34 .38 .45 t2 .50 .46 .44 .66 .59 .68 l4 .70 .78 .88 .90 1.0r 16 18 .6{ .87 l.t2 20 24 .70 .83 .96 1.13 1.44 .58 .56 .58 .64 .80 .93 .70 .68 .78 .83 .81 .s7 .88 .97 .71 .83 1.17 1.07 1.34 1.24 1.37 1.49 .96 1.10 1.04 1.20 1.34 1.13 1.36 1.54 t.12 1.1I 5t4" .59 .63 .o.t .34 .43 .30 .38 .36 .34 4%" .40 .39 .48 .47 .31 .29 .29 .21 4 10 3%" .23 ll l4 3% 6 8 Example. For 4" pipe rvith 4" nominal thickness insulation, f : .77. Il the insulation density is 12 pounds per cubic foot, then the insulation rveight is .77 X 12 : 9.24lb/lr. 1.99 1.52 1.74 r.s9 1.57 1.81 2.01 2.07 2.29 2.40 2.80 3.16 1,64 1.92 1.50 t.7s 1.77 2.10 2.09 2.44 2.24 2.34 2.58 2.82 2.50 2.62 2.88 3.14 3.06 3.54 3.40 3.92 LOAD CARRYING CAPACITIES OF THREADED HOT ROLLED STEEL ROD CONFORMING TO ASTM A-36 Nominal Rod Diameter, in. Root Area of Thread, sq. in. Max, Safe Load, lbs. at Rod Temp. of 650'F % .068 lz V+ % .126 .202 .302 .419 610 1130 1810 1 .1ya, ry4 .693 .889 1y4 1.293 2 1.144 2.300 2l+ 2 3.023 3.719 2y4 4.619 3 3r/t 3 5.621 6.124 ?.918 27t0 3770 4960 6230 8000 11630 15?00 20700 21200 33500 41580 50580 71280 3 v Appendix C: Properties of 1tt WEIGHTS OF PIPING MATERIALS Pipe 2O1 prpo r.Brs, o.D. {? t-2 {.J-r' z ? z B {\ {;\ f,.-l ,4L, E=:r L+! !-r__--, {--J--r \.lJ Temperature Range "F FiberSodium s$ z i sr_r_u$ NJM {N:IS 4 z /.4 F 4l z /> Soldface tvoe is weieht in pounds. Lighifice type b6neath weight, is weight fa.ctor Ior insulation. Insulation thicknesses and \.reichts are based on averase conditions and do not constiiuie a recommendation for specific thicknesses of mrterials. Insuhtion iveights are based on 85/, magnesia and hvdrous cdcium silicate at 11 lbs/cubic foot. The listed thicknesses and rveights of combination covednq are the sums of the inner laj'er of diatom{Lcecus earth at 21 lbs/cubic fooi end the outea layer at ,N. 11 lbs/cubic foot. Insulation rveights inciude al,]O\llnces lol wIIe, cemen!, can- vas, bands and paint, but not sbecial surface 6nishes. - To find the weight of covering on flanges, valves or fittings, multiply the \r'eight fuctor by the @ +€ nCI tsO * 16 h cu. ft. den-.ity. SJrr weight per foot of covering used on straight pipe. Valve \reights are approxi- m:Lte. When possible, obtain veights from the nranufacturer. Cast iron valve Neights are for flinged end valvesi steei weights for rvelding end valves. All ftanged fitting, flrnged valve and flcnge $eights include the oroDortional Ncieht oI bolts or siulli to make up all joints. 202 Mechanical Design of Process Systems lYn" z F PIPE r.660" o.D. WEIGHTS OF PIPING MATERIALS w' 4\ z di F t_L_, Tempcrature Renge Fiber- 'F Nom. Thick.,In. Sodium Nr$ is \eight in t)pe benexth is weight factor for Boldface .ty"pe pounos. Lrghflace weight. Insulation thicknesses and weights arc based on averaqe mnditiors and do Dot constituie ts-ts$ {l.-.-tis z F ,41 /A # ,N z Jrtd -J a recommendation tr @ IrtJ @ FsO specific combination coverinq are ihe sums of ihe inner layer of dia- 2l lbs/cubic foot and the outer laycr at tomaceous earth &t 1l lbs/cubic foot. Insulation weiqhts include al- lowances for wiri, cement, can- vas, bands and paint, but not special surface @ for of materials- Insulation lveights are based on.85/p magnesra ano nl drous c3lclum silicate at 11 lbs/cubic foot. The listed thicknesses and neights of thicknesses fi nishes. To find the weieht of coverine on flanges, vatvds or fittings] multiply the weight factor by the \aeight per foot of covering used on straight pipe. Valve rveiqhts are loproxi-dbtain mate. When possible, lreights from the manuf&cturer. Cast iron valve weiqhts arc for flanged.end valves; stiel weights lor weldrng eno valves. All flanged fitting, flanged valve and flange weights include the proportionrl weight of bolts or studs to makc up all joints, * 16 lb cu. ft, density. ] Appendix C: Properties of .IVEIGHTS OF PIPING X{ATERIALS Schedule No. {,1 t2 nuj >f\ i t /> LLP tij e i -1/ 40 80 Wall De,<igna.tion std. NS lhickness-In. Pipe-Lbs/Ft lVatcr-Lbs/Ft .145 .200 .281 .400 2.72 3.63 4.86 6.41 .88 .77 .61 .41 .8 1.1 1.4 I.E .6 .3 .7 .3 L.R. 90" Elbow S.R. 90' Elbow L.R. 45" Elbow Tee 4, .E 1 .2 .2 2.5 3.L 3.7 .6 .6 .6 5.4 Latera.l 1.3 .6 q--- 1_ -0 dti Reducer ,2 c"p .7 .2 .9 .2 .2 .5 .7 .7 .3 .3 .3 Temper&ture Range Nlaqnesia 'F \om. Thick., In. t00-199 200,29e 300,3c0 .100-.199 ;00-it)9 000-0119 ;00-;,1,1 s00-sf)1r 1t00-!r!9 11000-1099 1 I \)t .84 .84 1.35 2 2 214 !: Caliium Siili.crp Lbs,/Ft { Combina- \om. Thick.,In. 2tt Lbs/Ft, 1.t0 z Fiber- Nom. Thick., In. Sodium LbslFt PressLrre ,MS A rtr za| lg tsrj_ri} {rrTs ..4 a /:) Z tt!4\ - ?41 | /A 3,\ 1.07 Ratiig 250 SIip-On 1.5 7 1.5 \eck S.R. 90" nlbow lltn FrO * 16 h G:rt{! I)tessure Seal Borrrret-(-irte Pressurc Seal Ilonnet Giobe cu. ft. density- r.85 3.50 3.5 1.5 10 3.7 I 7 5 4.52 4.s2 4.52 21 ; 2)1 3 3 3 1.20 1.20 5.62 5.62 5.62 2\l 2% 3 3 4.76 4-16 3.50 6.16 000 900 r500 9 l9 l9 1.5 9 1.5 1.:) 1.5 I \2 l2 l9 l9 34 1.5 1.5 1.5 1.5 1.5 *eights 9 1.5 9 t9 19 31 r 9 10 l0 1.5 1.5 1.5 t2 23 26 3.8 3.9 l9 t7 20 5.6 19 1.5 rveight is insulation. tl pc bene&th rveight iactor lor Insul&tion thickncsses rnd based on :rverage and do not constitutc conditions^te rocommcnd&tion for spocilic of m"rtorial-q. Insulation Neishts :rre bstxl on 85f6 mrgnesia ud hrrlrous lrrlcium 3l l 46 !-.. , ,,,,1,i ^ f^^r Tl- listcd lhiclinesses orxl \\'cights of combinltion covering rte the sums of the inner l.rver of dirtomaceous errth at 21 lbs .ubic foot anrl the outcr hl cr at 39 23 30 70 5.8 6 70 1.2 .l.il 125 40 45 .t.2 t70 4.2 30 35 40 I 4.1 .1.1 6.8 tlpe is weight in pounds. Lightfi.ce thicknesses 4 ll 2500 1.5 t.5 9 Roldf.rcc 400 8 1.5 3.5 Flanged tsonnet, GLrlrc or Angle Irlanged Bonnet 1.8s 3.47 300 Ilanged lJonnet Clheck ++I 1.5 L.R. 90' Elbow Tee 2 3 blecl i j;0 L5 Lap Joini Rlind 1.01 1ta Casl lron 125 45'Elbow j=<l s k3J 1.07 1% 1100-L:00 tl i 2.52 1 ps' Screled or \Yelrling erce xxs .2 .6 l/2" r.eoo'o.D. 203 160 _5 .2 Pipe 5 42 1.9 l0 t.2 11 ltls/cubic foot. Insuhtion \\'ci,ahts inrluclc cllouanr:rs for \\'iro, ccmcnt. ernvlt'\, brnds llnd l)rint, but not st'ccirlsrrrf,,rc ti n rs)'cs. Tu lin,l tlLe \, iHl,t .f,1,v, ring on flugcs, vrlvos or fittings, rveight f.|rtor l)y thc rvcight lrcr fooi of covcrir)g uscd or) strLright pipe. \'.rlvt} \ 0iJahts lrre appro\i- multiplt thc mcte. \\'hcn lrossiblc, obtrin rveights f|om the munuf:rcturer. (iust iron vrlvc \!eights:Lro for lhnged cnrl vxlves: stecl $eighls for \eldins end vrlves. ,\ll firLneed fittins, flrnjaed vrlvc ond 1|Lngc *cights includc iho I)r'otxJrtional \!1'ighi, of bolts or studs to make ur) !.lL joints. ioints. 2O4 Mechanical Design of Process Systems 2" ptpn z',s,, o.D- wErcHTS oF pIprNG MATERTALS Schedule No. A 40 80 Wall Designation std. XS Thickness-In. Pipc-Lbs/tr 1, .154 .218 .343 .436 5.02 7.41 9.03 I4'ater-Lbs/Ft 1.46 L.R. 90" Elbow q t!-/ S.R. 90' Elborv F !w t/> L.R. 45' Elbow zf. A^ 'HJ .5 .5 1 1.3 .2 Tee .6 .6 Lateral 5 1.4 7.8 \i/ crp Nom. 2.9 .5 .3 r.1 1.6 1.8 .6 .6 1.6 1.9 1.2 t,2 ,+ .+ 1.4 1.2 .3 .5 Temperaiure Range "F z I 1.5 .2 Reducer xxs 1.2E .E !_l--__, 160 Thick.,In. Megnesia Calcium Lbs/Ft silicate 100-199 200-299 300-399 400-499 500-5s9 600-699 700-7c9 800-899 900-9s9 I I L% 1.01 1.01 t.7l 2.53 2.53 Nom, Thick., In. * uomDlnx; tion Lbs/Fb z Fiber- Nom. Thick.,In. Sodium Silicate Lbs/Fb Pre-ssure psl sffi O Z ,h d-ir SIip-On '|1'elding Neck 6N_l-M Lap Joint ryi:-s Blirrd ,-{l t?.4 E II' Y ll_______.rl ru ",1.{l 3m +<f rc I I 1% 1% 1.26 1.26 1.26 2.20 2.20 Cast Iron or trLrlS 2t4xJ i rlt E,N e /9S z Scre* ed Rating I L.R. 90' Elbow 45" lllbow 2% 3 3 3 3.48 3.48 4.42 4,42 4.42 2% 2% 3 3 3% 4.28 4-2E 5,93 5.93 7.80 2 2 4.57 3 3 5.99 5.99 150 300 400 600 900 1500 2500 9 6 9 ll ll 32 32 4E 10 13 t3 3l 3l {E type is weieht in weigii. is yreight factor for Boldface pounds. Ligh[flce type bineath lnsul&llon. 1.5 9 12 4E 1.5 6 10 4-8 l0 3l t2 3l 1.5 19 35 3.8 3.8 3.8 3.8 1E 27 22 4.r 3l 4.1 4.1 14 l6 3.4 3.4 23 37 83 4,2 Gat€ 6.9 7.1 Flanged Bonnet Globe or Angle 30 7 64 Flanged Bonnet Check 26 7 5t 190 4 4.5 5 40 3.8 for specific combination coverins arl the sums of the inner Iajer of diatomaceous eerth st 21 lbs/cubic l1 los/cuorc loo!. on EO 45 4 recommendation thicknesses of materials. I-nsulation weights are based on.85/, magnes,a anct nydrous c&lctum silicate st 11 lbs/cubic foot. The listed thicknesses and weiqhts of 129 40 30 a Insulation weishts include allowances for wird, cement, canvas, b&nds and paint, but not 3.9 41 3.8 49 fnsulotion thicknesses and weights a,re based on average COnOrtlons ancl do not constitute foot and the outet layer at 73 6 I'langed Bonnei 235 4.5 60 300 4.2 5.8 Pressure SeaI 150 Pressure Seal 165 3 Bonnet-Clobe 4.57 3% Steel 1'ee Bonnet-Cste 214 250 16 S.R. 90' Elbow 1000-1099 1r00-1200 2% special surface finishes. To find the weisht of coverins flanqes. valvds or fittincs] weisht factor by tle wergnt.per too! ol coverrng usecl on srrargn! prpe. V&lve weishts are aooroxi-dbtain muhipltth! mete. When possible, weights from the rnanuf&cturer. C&st ircn valve weiqhts are lor flanged,end valves; sGel weights IOr Welolng eno valves. All flanged fitting, flanged valve and flange weighls include the proportional weight of bolts or 6tuds too make up uD all s.ll joints. ioints. 16 lt cu. ft. density. ' nr Appendix C: Properties of WEIGHTS OF PIPING MATERIALS 2.875'o.D. Pipe 2/2" 2o5 Ywn A (.!-f z w F fl\ F-:l z F---i -2t" J ' /-\ !-L-t (--r..} \.u Temperature Range z I ) z 'F Magnesb, Calcium Combina- tion FiberSodium ,ffi 9+ i ${lit$ N-ls$ N () z I /A) ,4"1 ,N z g!4 l-{ .t @ +€ flt' ) |<IJ * 16 lb cu. ft. density. type is seight in \r'eight is weight factor for Boldface pounds. Lightfece type beneai,h insulation. Insulation thicknesses and weights are besed on everage conditions and do not constitute a recommendatioD for specific thicknesses of materials- Insulation weights are based on 85/6 magnesia and hydrous cclcium silicate at l1 lbs/cubic foot. The listed thicknesses and rveights of combination covering lrre the sums of the inner laver of diatomaceous earth at 2i lbs,'cubic foot and the outer l:r|cr at lbs/cubic foot. Insulation weights include allowances for wirc, cemcnt, canvrs, bends rnd print, but, not special surftce linishes. To find the rveight of covering on flnnges, valves or fittings, multipiy the \reight factor by the weight per foot of covering used on straiqht DiDe. 11 Valve *eiftrts are approximate- When possible, obtain weights fronr the manufrcturer. Oast iron valve weiehts ere for flanged end valves; stiel weights for *elding end valves. AII flanged fitting, flenged valve and Iiange \\eights include the proportionel iveight of bolts or studs to rnake up all joints. 206 3 Mechanical Design of Process Systems tt "tpr B.boo" o.D. WEIGIITS OF I'IPING NIATERIALS rt? 8 z F F z B uf /\ {_0 {l} L:-I -{\ fl-\ ri\ {----fr \iJ l z cnrpentLurc Rcngc "F Magnesia Calcium Nom. Thick., In. F z (--oDlbi tron r- FiberSodium weight ${rn$ Insulation ihicknesses and weights are based on average Njs a /A -11 z is weight in ffi qN z Boldface type ,N /9N 49!S pounds. Lightface type beneath is weight Jactot Jor insuLation. conditions and do not constitute recommendation for specific of materials. Insulation $eights are based on 85/p magnesia and hydrous calcium silicate at ll lbs/cubic foot. The listed thicknesses and weights of thicknesses cornbinetion covering are the sums of the inner layer of diaiomrceous eerth at 21 lbs/cubic foot and the outer la] e. at 11 lbslcubic foot. Insul{rtion Ncights include al- for \\'irc, cenrent, canvas,.bands- and prlitrt, but not lorvarrces suf tace hnrshes, speclsL - t<t @ 0 J{ a Fs3 To iind the ueight of covering on flanges, vs,lves or fittings, multinl\' the weishtfactor bY Lhe weighi irer foot 6f covering'used on straight pipe. Yalve weiehts are aDDroxi-dbtain mete. Wben- possible, weights from the ma,nufacturer. Cs.st iron valve weights are for flanged end valves; steel weights for rveldinq end valves. All flanged fitting, flanged valve and llanee weiqhts include the Drooortion;l weriht of bolts or siudi to meke u[ all joints. * 16 lb cu. ft. deDsity. fl Appendix C: Properties of WEIGHTS OF PIPING MATERIALS 4.ooo" o.D. Pipe 3/2" 202 ewy {f (.-!-f z /'h t4J F tij z &>", f,l-\ ri\ Temperature Range'F z Celcium F Combina- z \om. Thick.,In. tion FiberSodium Boldface z J in ffir$ 4(|l_M \Yeights are based on average conditions and do not constitute lr, rccommendxtion for specific thicknesses of materitls. Insuletion \Yeights are b.r,sed on 85% magnesir and h\'drous calcium silic&te at 11]bs./cubic foot. The listcd thicknesses and leights ol combin.rtion covelir)g lLIe thc sums of the inner hler of diltomrceous earth lt 2l Ibs,/cubic Nls TNN / z F ,11 -4 N /> 1 1-<J ' type is \leight poun,ls. Lightfece tl pe beneath neiglt is Beight insulation. fscLor lor Insulation thicknesses and foot end thc outer l:ryer at ll lbsrcubic foot. Insulation weighis include allorv:rnces for \rire, cemcnt, .r,nvas, b0nds and l)l!inl, but not spccitl surfrlce linishes. To find the $eiglrt. of covering on llrnges, volves or 6iiings, multit)l]'the weieht frctor bv tho @ ff1 weight per foot of covcring uscd on straight pipe. +<J flangcd cnd valves: steel ueights for *eltlirrg end valves. rc 16 lt cu. fr. density. Vrlve weights irrc appro\i- matc. \!'hen possiblc, obtrin neights from the mxnufs(iturer. Cut iron valve s'eights are lor lll flarrged 6tting, fir.ngerl valve lnd flrnge seiglrts include thc proportional rveight of bolts of studs to make up all joints. 208 Mechanical Design of Process Sl stems 4" ptpn 4.boo' o.D. WEIGHTS OF PIPING MATERIALS \\'stcr-Lhs/l t /a) tu z k o &? h 1: ,t {l\ tr;:I tr:JI /\ \JJ 'li,mtx'nrluro z trlagnesia Calcium ComLirur- I rngo "I \om. 'l'hick., In. Nom. T)rick.,In. iioIl IiberSodium NrS z {Nj+ln} N_ts rx:w ,.'Nl 7 / F ,41 ,l) Boldface type is weight in pounds. Lightface tvpe bene&th rveight is \reight fsctor Jor insulation. Insulation thicknesses lnd weights are based on average conditions and do not conslitutc a recommendation for specific thicknesses of mgterials. Insulation weights are based on 8596 magnesia and hydrous calcium silicate &t 11 lbs/cubic foot. The Iisted thicknesses and \reigllts of combinstion covering are the sums of the inner layer of diatomaceous earth at 21 lbs/cubic foot and the outer ieter'at N z /\ 1 ll Ibs/cubic fooi, Insulation weights includc allowances fo wire, cement, canvas, bands and paint, but not speciel surlace 6nishes. - To find the weighl of cover;ng F<3 3 @ fi\ +<l F<U on flanges, velves or fittings, multiply the weight frcior by the seight per foot of covcring uscLl on str{righi pipe. Vrlve weights are approrimate. When possible, obtoin $eights from thc mxnufacturer. Cast iron valve Ncights are for flanged end valves i steel $eights for rveldinq end valves. All flanged fitting, flrnged valve and flangc wcights includc the proporbionxl \\eiglrt of bolts or studs to mrke up all joinbs. I 16 li cu. ft. density. Appendix C: Properties of WEIGIITS OF PIPING MATERIALS Schedule No. ul ,a g.I/ zf\ F ! li E4\ o f'+ 3 4/4- 40 80 Wall Designation std. XS Thickness-In. Pipe- Lbs/ Ft, .258 t4.52 Water-Lbs/Ft 8.66 14.7 1.3 21 L.R.,90" Elbow 9.8 13.7 .8 S.R. C0" Elbow L.R. 45' Elborv .8 7.3 .5 20.78 7 120 160 .500 .62'r 27.M 32.96 38.55 7.09 6. J3 5.62 .89 r 0.2 15.6 .5 .5 t7 .7 .5 43 26 39 1.2 1.2 1.2 Laterel 3l 50 2.5 LJ---.D Reducer 6 .4 E.3 .1 \tJ cop .7 .7 t4.2 .4 {---J--r Nom. Thick.,In. Z Sodium Silicate 9 F- Lbs/Ft B tion Lbs/Ft Nom. Thick., 85% !Iagnesia Calcium Lbs/Ft ,ffi O -'r- Screu ed or '|r,\'elLling 2.92 2.92 I I 2.34 2.34 i50 20 32 l8 1.5 1.5 +<i ft. 3 3tl 3ti 4 4 7.01 9.30 I1.8 I1.8 14.9 14.9 2% 2% 3 3 4 4 9.31 9.31 14.31 14.37 t.5 l 58 94 80 5 73 1.5 100 1.5 162 1.5 259 1.5 rvcight 713 103 162 293 \reights.rre brsed on rverage 49 1.5 7l 32 1.5 98 168 1.5 50 39 1.5 1.5 l3 t23 t 78 205 4.3 1.lr 172 1.5 268 435 4.8 5.2 104 1.5 pounds. Lightf.rce type benerth is rveight factor ior insulrtion. Insuiation thicknesses and condirions and do not constitute rocommendrtion for specihc of materials. lnsuhtion wcights rre brsed on t5% mrgnc-.ia antl hydrous crlcium rot. The silicatc at 11lbs,/cubic foot. righrs oi listed thickncsses 3nd rreighls 3 thicknesses combination covering lrre lhe dieof the inner later of dirtomrceous errih rt 2I lbs cubic -cums 3.3 3.8 3.8 90 t45 ll9 t72 179 304 6.5 0.4 6.4 6.8 7 138 264 150 3r0 7.9 4.3 4.9 455 5.5 Flanged Bonnet Globe or Angle 138 )47 ls5 2t5 515 Flanged Bonnet Check llE 210 110 7.6 E 4.3 8 is $eight in 1.5 5 1.5 I.5 Boldf&ce type l 98 density. 2ra 2|rc/..) 66 {ilobc 10.4 1500 E3 Bonnet 10.4 s00 51 Pressure Seal E.41 600 t2a Pressure Scal 8.41 400 9l Bonnet-Cate 6.90 300 1.5 Cet,e - FdJ JiLII ;hJ 4 Stecl 250 105 Flanged Bonnct 4 3.76 2.34 1.5 Tee 1-{ 11,.i 68 45" Elbow Y 1,t; Casi, L.R. 90' Elbow Et\ 3rl 4.08 | 1100,1200 3r/t, 2% 2ra 2 S.R. 90" Elbo* ,an 16 lb cu. 1.86 37 /,$ .7 22 Blind rc 1% Ncck El:::lr$F E II' 1 125 Lap Joini /a 1l .7 00-199 200-20s 300-399 400+s9 500-599 000-699 700,;9c 800-Ec3 900-999 1000-1009 18 3,\ ' Rctiltg N-l,Ns 0 F | z Pressure psr Slip-On i sli19 ll In. Nom. Thick.,In. 5" pge 1.3 t9.E Fiber- O.D. 209 xxs Tee Tcmpereture ll.enge "F 5.56:J" Pipe rl er foot end the outer irl t23 5.2 165 5 1E5 665 615 6 1340 7 on llenges, !lll\'fs or littings, rnc )r DJ bl th. muitiplt thc \reight fsctor 350 350 3.1 soecial surfxco linishes. co\,enng 1o hnd tlrc $Lrglrt ol coverlne 950 6 5 Di Dt 415 4 5 ll lbs/cubic foot. .lurie rlInsulation \\0ighis inclurie lorvances for \\'ire, cement, crnnoi vns, bends xnd p.rint, hut not 350 130 560 6 1150 7 520 3.8 865 4.5 280 4 450 4.5 lng used rveight per foot o[ covering on,str.riqht t,ifo. x||ro\l\'!ive \\'.rqh is rrc approximrtc. \\-hen possiblc, oblarn weiglrts fronr the mllnufrcLurerC.rst iron vrlve rvcishis l|re fol \reights fluged end vrlves;steel \reightl for $cLdirrq end vlrlvcs. flanged ,\ ll fianee(l fittiDs, flanged include vol\c .rn.l ILrngc wprgl,tsr includ€ bolts tl,c t,rol,ortionxl \eight of bolt! ll joints up all ioints. or siuds to make up 2'10 Mechanical Design of Process Systems 6" pr"" 6.625, o.D. WEIGHTS OF PIPING X{TTERIALS \\'eter-Ils/Irt z '. z F u/ AX w {T\ LilI t---1 \JJ Tempcraturc Ilange "F z Magnesia Calcium t z Combinst)on Fiber* Sodium Boldface sq-,$ z #r|& N-S dISrsS z -Xl t# rA kL ,N z /> lt' '{ l-dl .| @ ru 1-<i rc type is weight in tleight iactor for trpe benea,th oounds. Liehtiace ' iveight. is Insulation thichnesses and weights are based on average conditions and do not constitute a recommendation for specific thicknesses of materials. Insulation weights are based on 85% masnesia and hvd.ous calcium siliate at 11 lbs/cubic foot. The listed thicknesses and weights of combinstion covering &re the sums of the inner layer of diatomaceous es,rth at 21 lbs/cubic foot and the outer layer at l1 lbs/cubic foot. Insulation $eights include aIIowrnces for \aire, cement, can- vas, bands and paint, but not special surface finishes. To find the weight of covering flanges, valves or fiLtings, multiplt; the weight fxctor bl the rveight per foot of covering used on straight pipe. on Valve ueights xre sppro\imete. When possible, obtrin weights from ihe mrnuf&cturerClst iron valve ueights are for flenged end valvcs; steel weights for rveidinq end valves. All flanged litting, flanged valvc 3nd nlnge Ncrgnts Incluoe tLe DrotJortional $cieht of bolts ot stud" to mrke up all joints. * 16 lb cu. ft. density. ,qR Appendix C: Properties of WEIGHTS oF PIPING MATERIALS 8.625. Pipe o.D. 8'' 211 "T"e t'- 2 i. z B r_!j w {t} E:I ,4\" A F--l-r \tJ Temperature Range 'F Magnesia 2 Calcium F - z Combina,- tron Nom. Thick.,In. FiberSodium ffi$ 2 F a 7 Neight. is veight Jactor lor Insulation thicknesscs cnd \reights are based on average $\ a is conditions and do not constitute A recommendation for specific of materiols. Insulation rveights are based on 85% magnesio and hJ'drous calcium silicate at 11lbs/cubic foot. The Iisted thicknesses aod $'eights of combinetion covering are the /A foot and the outer la]'er at A egilq thicknesses sums of the inner layer of diatomaceous earth at 21 lbs/cubic 11 lbs/cubic foot. Insulation rveights include al,lowances lor wDe, cemenl, c&nvas, bands and paint, but noi soecial surface finishes. ' d - j.43 t4r\ +<i FsO | tlpe js Neiaht in ffi d <,fs$ z Boldfnce pounds. Lighilirce tvpe bineeth 16 lb cu. ft. density. To find the weight of covering on flanges, valves or frttings, multiply the weight f&ctor by the Neight.per folt of covering used on slrarghl prpe. Yalve rveights are approximcte. lYhen possible, obtcin lleights from thc manufrcturer. Cast ilon valve weiehts are for flanged end valves; sGel \\'eights Ior seldinq end valvcs. AII flcneed fitting, flanged valvc and llangc rveights include tlrc nroDortioDrl \eiqht of bolts or stu,li to make ut all joints. 212 Mechanical Design of Process Systems 10" z (, z prpn lo.zbo, o.D. IVDIGIITS OF PIPING tr{ATDRIALS Ih fl\ L:J .4'4^ L:!-l_, \]J lrmpcr:rturc lirnge'F z Magnesia Calaium F P z Combina- \om. Thick., ln. iion FiberSodium (, ffi$ qFl rr$ N-|s ryrTqJr Ai z Boldfece /AJ !. ,-11 z ,N /> tHt'{ lN' @ ff1 +<i f<o t{pe is l\'eight in pounds. Lightface t1'pe benerth *eight is rveight foctor ior insulation. Insulation thicknesscs \Yelding Neck and rveights are based on average conditions and do not constit,ute a recommcndetion for specific thicknesscs of materials. Insulation weights are based on 85/o magnesie and hl drous crlcium silicate at 1l lbs/cubic foot. The listed thicknesses and weights of combination covering are the sums of the inner layer of diatomaceous earth at 2I lbs/cubic foot and ihe outer lsyer at 11 ibs/cubic foot. Insr-rlation Neights include allowances for vire, cemeni, can- vas, bands and !B.int, but not spacirl surfrce 6nishes. To find the weight of covering on ffanges, valves or fittings, multiplt' the $eight frctor b! tLe lieight t'er foot of covering used on streight pipe. \'rlve \rcights ere approri- matc. \Yhen possiblc, ol)irirr ciglrts from thc nrnnufrcturcr. (lxst iron vrlYc \\'ciglrts arc for lllngcrl cnd vrlrcs: stcoi teights fol lcldilg cnd vrlves. rr -\)l fl.rngcd fitting, flnngcd !'rlvc :!nd l]3nge \\'eights include tlru prolroriioDxl scislrt of l)olts or studs to mrkc up:rlL joints. * 16 lb cu. ft. derxity. Appendix C: Propenies oi rz.lso'o.D. WEIGHTS OF PIPING MATERIAI,S Schedulc )io. | 20 {,) IJJ f4 (_!-f . 2n^ F flIT Eji1 o -: -t i3tr-/>" t- d_l\ .330 43.8 49.7 L.R. 90' Elbow S.R. 90" Elbow L.R. .406 .500 49.6 53.5 65.4 49.0 48.5 47 .O .375 100 120 12" .687 .843 1.000 EE.5 t07 .2 r25.5 44.0 4 r.6 39.3 .562 46.0 l-J! 139.7 t58 t51 3 3 80 2 104 2 60 7E 181 167 360 3 1.o Calcium silicate ,s| Combina;z iron FiberSodium ,ffi ;+ z 5.4 33 44 30 3E ,| Reducer 9,1 '| E9 1.5 900-999 1000-1099 1100-1:to 100-199 200-299 300-399 400-49S 500-5s9 600-699 700-799 800-E99 Nom. Thick., In. 1)4 114 2 2t/4 3 3 3rlt 4 4 4% Lbs/Ft 6.04 6.04 8.13 10.5 t2.7 12,1 15.r 17.9 17.9 20.4 20.4 3 3% 4 4 414 1)i 17.7 21.9 26.7 26.7 31.1 3l, r 2\/r, 216 4 4 5 c 14.20 14.20 24.& 4.64 32.& 32.40 Nom. Thick.,In. Lbs/Ft Nom. Thick.,In. Pressure Rating psr Screwed or Slip-On Cast 250 71 r37 1.5 1.5 a4 a lAl S.R. 90' Elbow /..4 L.R. 90' Elbow A,N I /}! 45' Elbow z@ 600 900 1500 | 72 | | 1.5 | 88 I 1.5 I 164 1.5 261 3EE 820 1611 434 1.5 843 1.5 1919 1.5 433 902 1573 1.5 163 1.5 212 164 ta7 286 1.5 1.5 1.5 475 t474 261 1.5 453 345 509 669 El5 5.2 5 5.2 485 624 6.2 6.2 6.2 6.2 235 383 2E2 6E4 6.2 4.7 1124 4.8 5r3 754 7.4 943 1361 r92E 8.3 a.7 s.3 1420 5.5 215s 7 2770 7.2 4650 8 1410 7.2 2600 8 3370 8 1975 2560 45r5 6 7 7.8 1015 5 Fhnqed Bonnet Globi or Angle 808 1200 7t0 1410 9.4 9.5 5 Flanged Bounet 674 ll60 560 Checlc 9..1 9.5 densrty. 6.2 4.5 635 4 Bonnet-Globe I.D 469 8.5 Pressure SeaI t.5 1775 159E 720 705 l.c 92E 414 1298 Bonnet-Gate 5.8 2500 1.5 4.3 4.3 6E7 Pressure SeeI 1.5 209 7.8 Flanged Bonnet Gate r.o lllE r.5 | 1.5 265 5 Tee fi. 400 r44 341 177 403 IP '{ 300 72 | 96 | 150 1.5 | Lap Joint Blind l1/r, 1r/1, ffi 125 Welding Neck {N * 16 lb cu, 1rt t% Lbs/Ft '$$js E l 273 1E0 Lateral #rils , ; 2.5 2.5 cap z 9 3 119 r32 Temperature Range "F Pwr: 1{0 45" Elbow Tee 213 XS sid. Wall Designation Thickness-In. | .250 33.3E Pipe-Lbs/Ft 5l .10 Wsier-Lbs/Ft 80 60 40 30 PiPe 214 Mechanical Design of Process System: 14" ,trr. 14'o.D. WEIGHTS OF PIPING ]IATERIALS {.f z |. z t /) fl\ fJJ t -t c---r---l \L"J Tcmpcrature Range z Alagnesia Calcium 'F Nom. Thick.,In. Nom. Thick.,In. F t Conlbination z 1 l\'pc is Ncight in *eight is lYcight lactor for Boldlace ffi pounds. Lightface tl pc l)eneath S{r-rM $eights are based on lverage insulation. N]s {N z /.4 --ll /,4 z ,N i> Insulation thicknesses and conditions and do not constitutc a recommendation for spccific thicknesses of rnaterials. Insulation $eights are ba-sed on E5% magnesia and hvdrous cak.ium silicate at 11lbs/cubic fool. The listed thicknesses and lreights of combination covering Lire the sums of the inner l&\'er of diatomaceous e:irlh at 21 lbs/'cubic la] er at foot and the outer 11 lbs/cubic foot. .{l Insulation \reights include alfor lvire, cement, canvas, bands and ptint, but not ru To find the leight of covering on flanges, valves or fittings, multiplt the weight fcclor b]'the MeiAht pcr foot of covering used on strnight pipe. 0, @ 0 +<i FSO lorvances special su ace finishes. Valve s eights are spnro\imate. When possible, obtain weights from the mrnufscturer. Csst ilon velve Neights are for flanged end valves: steel weights for rveldine end valves. All flaneed fitting, flanged valve cnd flonge $eights include the nroDortiorrrl \\'cigl,t of holts or sludi to mrkc up all joints, * 16 lb cu. ft. density il - Appendix C: Prop€rties of WEIGHTS OF PIPING MATERIALS re" o.o. Pipe 16t' 215 plpu tl A. vz z ; lJj i\ w {T\ 1-5:I J,1 E=_:ir t fl\ \iJ .+r Temperature Ra.nge z 'F l 100-1200 I\Iagnesia Calcium F Combina- z tion !'ih.rSodium z Boldfxce tvDe stjjs Insulrtiod thicknesses and weiqhts are bascd on averase conditions and do not constituie & recommend&tiol for spccific thicknesses of materials- Irrsuhtion weights ere bosed on 85% magnesir and hydaous cnlcium silicate &t ll lbs/cubic foot. The listed thicknesses &nd \yeights oi A combiortion covering are the sums oI the inner layer oI diatomaceous earth at 2l lbs/cubic .A 1 Lighifirc tt pe benesth is rveight factor for insulation. $$l.M z rveielrt in teight qr\ssF z is S$ pounds. foot and the outer layer at rr rDs/cuDLc ioot. A Instrlati<.rn weights irclude al,low&nces Io! $alrc, cement, ca!! 4!B vas, bands and pcint, but Dot, specilll surlace fi nishes. To find the weight of coverbg on flanges, v&Ives or fittings, @ t i[I multiply the weight frctor by the r eight per foot of covering used on str&ight pipe. Flenged Bonnet @ t4 * 16 lb cu. ft. density. Valve Neights are approximatc. When possible, obtrin weights from the m.nuf&ciurer. Cllst iron v.rlvc \reights:rre for flanged end valves: steel $eigh6 Ior rvelding end valves. All flcnged fitting, flanged vclve and flangc wcights include the prot)ortionul Neighi of lrclr,s or studs to make up 3ll ioinis. 216 Mechanical Design of Process Sy:,rems 18" plpr 18" o.D. WEIGI{TS OF PIPING MATERIALS LLl z F z E f^ ('4r fl\ H' UL, c.=-=I IA \JJ 'fcnpcnturc ll z Magnesia Calcium tCombin.r.- Dgc 'I,' Il,s / Iit \om. Thir,k., In. tion Fiber- \om. Thitk., In. Sodium ffi z ffi Nl$ si)\r'|\s Z F /'a IA rA ,N z /$ 4444 is lcicht in t5 pe b-enerth reiglrt. is \cjght fschor for Boltlface tvne pounds. Lig)rifrce Instrlation thicknesses aod rvciglrts flrc l,rsr:d on r,vcrrge conditions ltnrl do not (oustituta a r-ccommcndrtion for specific thicknesscs of matcricls. Insulation \reights ore bascd on 85/o magncsia and h-Ydrous calcium silicrte at 11 lbs/cubic foot. The listcd thickncsses and rveights of combination coveljng are the sums oI the inncl hver of diatomaceous eorth at 21 lbs/cubic foot and the outet laver at 11 lbs/cubic foot. Insulation s'cights include alIolanr:cs for \rirc, cemcnt, conves, b:rnds and print, but not spccial sur'Iace finishcs. To find ihc \lcight of covering on flanges, valvcs oa fittings, multit)l]'the xe;ght factor by the a @ iln +<t rc \eight pcr foot of covering used on stroight pipe, Vrlvc \rriqhts rre aptrroxi-dt,tain mate. \l'hen possil,le, lscights from the m$nufacturer. Cast iron valve \yciqhts are for flanged end velves; st-eel \\eights Ior welding end valves. All flanged fitting, flanged valve and flange scights include thc proDortionrl \\ci(lrt of bolts or si,udi to meke up all joints. * 16 lb cu. ft. deDsity. :: Appendix C: Propen:* 1VEIGIITS OF ]'IPING }I.\TDRI,\LS 20,,o.D l- 21 20" e-,rz l{t) Pip€'-Lbs./I,t \\'at.r 3;9 Lbs/ I,t Ll 9 '17 &Jj z F i: z Ih \-.1-_t {l\ -'t r'-: F4 ,!^ !*J----! 'Icmpcraturc Renge "F z 300-3c3 100+cc i00-;9u 1000-6e0 I{agnesia o Calcium 2a.l F Combina- z 4l.: tion 43.r Fiber- {-1- 1 \om. Thick.,In. Sodium 1-1.03 Pressure ffi z psr Rnting sm$ N+s gr(\i.x$ z F (, z g J /A /41 /,+ A\ /> €4!4 @ fln l'langed tsonnet Globe or Anglc J-<f rc * 16 lb cu. ft. deDsity, (last.Ir('n | ll25 l2s is r..r: : .: rir)f I :..,: \l{ttglrL. ls \\etglll Iri-: : ::: Illsulrtion thi|krrts... :: vc;ghts uc brsc(l 0r ,,. :. ::corrditiols urrtl iIr rror ,,.:.-:.:::r! rccommrr{lxti(,n a,)r .-- l tlti< kncsscs of mritli,.l: I: --.-tiorr rveiehts rLn' 1,,,.t i :. :i I nNgncsil rLnd lrr,ir ru. -:-sili(rtc lri 11 lLs r ui,:. : - . listc(l tLi( knciscs ,t:. i , :: , ::conrl)in$tion co\'!f:r:: .. :: sums of t))r inncr -.:.,: : ,tolnxceous rtLrtlr :,i l: .: i - : fooL oniL tl)c a';:.: - . : -: ll Ibs r:ulric fooi IusulLtion r, r::.:. :: -loNrurccs ior r|ir,. vrLs, blnrls:i'l:,1 :.:.: - : : sp( ( lrLL :Llr 1t1.. :.: :, . . Roldfrrce tYpe poun(ls. Lighthcc \lrgllt l)ff iL_'r: .: ' I : _. onstfrLigi,:r: f. \_rtlvc Li,:::.:. .:. .. nlrtr'. \\ '.1: \fi{)its ir,r:r :].- r.. , (,Lst ir,:r'. .... : -- .- :.fl:LrLgcrl i r: i iot $r:Lli:-ir::- .. : .. .\ll :l:,r..r. : : :: : _' : vrh-c rrri i ::.,::r': r. ::r -. tlrc prorl:l:,:.1- .:: : :: or studi i1r ::r:i: .: ; ,.- .: 218 Mechanical Design of Process Systems 24" prpr. 24" o.D. \T UIGI I1'S OF I'IPI\G }IATEITIALS \Y.ltcr-Lbs/It ui Z F z e f>< w {T\ trJ-t -/A J]\ t___-l____-! Icnrpcrlturc llongc 'F Magnesia z Calciun F p Combinction z FiberSodium ffi z qN trs Njs EN,fr\l z :: d ,N z /D Boldfsce troe is weicht in pounds. Liehifl.ce tvDe b;neath - rreight'iactor for Insulation thicknesses and $'eights are based on averaqe ireight. is conditions and do not, constitule a recommendation lor specific of materials. lnsuhtion ucights are bused on.85/e m3gnesla ano nyorous cstclum silicate at ll lbs/cubic foot. The listed thicknesses and lr'eiqhts of combinotion covering arl the sums of the inner layer of diatomaceous earth at 2l lbs/cubic thicknesses foot and the outer lsyer at ll lbs,/cubic foot. tt, .rl IH l=<[J @ e ++J rc * 16 lb cu. ft. density. {: I}zAppendix C: Properties of WEI(IHTS OF PIPING MATERIALS z F F a za" o.o Pipe 26t' 219 prps Llj /\ Iit {1\ E--I t J'\ z -:I !-I_' \"J Temperature Range 'F Ilagnesia z Calcium brUcate o F 3 combina3 tion 3;m::;FiberSodium Boldface type is weight in pounds. LiEhtface type beneath weight is weight factor ffi z for insulation. Insulation thicknesses and weights are based on average conditions and do not constitute a recommendation for specifrc thicknesses of mat€rials. Iosulation weishts ate based on 85% magndsia and hvdrous calcium silicate at 11 l6s/cubic foot.The listed thicknesses and weights of combination covering are the sums of the inner layer of diatomaceous earth at 21 lbs/cubic s.{-n$ N-is fFq.s | z F ,41 AI foot and the outer layer at /r+ 11 lbs/cubic foot. Insulation weights include ,N allowances &"f n' !l u:-Ji ing on flanges, t<t rc ft. v-alves or fit- covetlngused on siralghl plpe. Valve weights are approxi- mate. When possible, obtain weights from manufacturer, Cast ilon valYe weights are for flansed end valve€i steel weishts Ior weldineend valves. A'il flane€d fitting, flanged +<i 16 Ib cu. cement, tings, multiply ihe weight factor by the weight per.foot of @ fi) * fo! wire. canvas, bands and iaint, but not special surface ffnishes. To-find the weiqht of cover- valve and flange weiRhts in- clude the propo-rtionaf weight of bolts or studs to make up deDsitt'. all joints. 220 Mechanical Design of Process Syslems 28" prpn 28- o.D. WEIGHTS OF PIPING MATERIALS W /4 {.J-f F Ih t-+J {1} trJ:I B \IJ Tempelature Range "F nlagnesia Calcium Combina- tion FiberSodium ffi$ ffi ds]-s iN z F F z ,-a A tr' .{ B---Jl t=<3 @ 0 +<i rc * 16 lb cu. ft. derBity. Boldface type is weight in pounds. Lightface type beneath weight is weight factor for insulation. Insulation thicknesses and weights are based on average conditions and do not co[stitute a recommendation for sDecific thicknesses of mate- rials. Insulation weights are based on 857, magnesia and lrydrous cjrlciuJn silicat€.at 11 lDs/cuorc root. I ne lrsteo [nlcknesses and weights of combination covering are the sums of the inner laver of diatomaceous earth ai 21 lbs/cubic foot and the outer layer at 11 lbs/cubic foot, Insulation weights in€lude for wire, cement, allowances canvas, bands and paint, but not special surface finishes, To find the weight of cover- ing on flanges, valves or ffttings, multiply the weight factor by the weight per foot of covering usedon straight pipe. Valve weights are approxi- mat€. When possible, obtain \reights from manufacturer. Cast iron valve weights are steel weishts forweldinsend valves. A-ll flanged fftting, flanged for flanged end vslves; valve and flahge weights in- clude the proportional weight of bolts or studs to make up all joints. Appendix C: Properties of WEIGHTS 0I' PIPIN(} MATERIALS Bo" o.D. Pipe 30" 221 prpe u-f Ih fl\ E-I F z 4',q E::l ' L--r-----U \L/ Temperature Range 'F Ilagnesia Oalcium t tlon Fiber SodiLtm ffi z E lr-'$ Nls CI-]-\} Boldface type is weight in pounds. Lightface type beneath weight is weight factor for insulation. Insulation thicknesses and weights ale based on average conditions and do not constitute a recommendation for specilic thicknesses of mate- rials. Insulation weights are based on 859t magnesia and hydrous caicium silicate at 1l lbs/cubic foot. The listed thicknesses and weights of combi_ nation covering are the sums of the inner layer of diatomaceous earth at 21 lbs/cubic foot and the outer layer at 11 lbs/cubic foot. Insulation rveights include allorvances for wire, cement, canvas, banCs and paint, but not sDecial surface finishes. To_lind the u'eight of covering on flanges, valves or fit- z tinss. multiDl\.the weieht factoibl the rieight per-foot of covering used on straight piPe. Valve weights are approxF G @ CD+ * 16 lb cu. ft. density. rrt mate. When possible, obtxin weiqhts from manufacturer. Cist iron valve weights are for ffanged end valves; steei weights lor weldingend valves. All flanged fitting, flanged valve and flange weights include the proportional weight of bolts or studs to make up all joints. 222 Mechanical Design of Process Systems 32" prcn sz, o.D. WEIGHTS OF PIPING MATERIALS tu? tg z f\ l_p {T\ 7 ! LJJ- 4',4 {-r-, lr-f-r \L/ Temperature Range .F Magnesia Calcium z Silicate { uomDlna5 llon FiberSodium Boldface type is weight in pounds. Lightface type beneath weight is weight factor ,@$ 3* for insulation, Insulation thicknesses and 3 tute a euls weights are based on average conditions and do not consti- fsls speciflc thicknesses !J:!i.\\! ,-11 z F tr z /A .A A of materials. Insulation weights are based on 857. magnesia and hydrous calcium silicat€ at 11 lbs/cubic foot.The listed thicknesses and weights of eombination covering are the sums of the inner laye! of diatomaceous earth at 21 lbs/cubic foot and the outer layer at 11 lbs/cubic foot. Insulation weiEhts include t"{3 allowances for w-ire. cement. eanvas, bands and paint, but not special surface finishes. To find the weieht of covering on flanges, valves or fittings, multiply the weight factot by the weight per foot of m weights from- manufacturer. Cast iron valve weiehts are for flanged end vatves; steel t€ valve and flange weights include the orooortional weieht 4!4 @ lt lecommendation for +<i * 16 lb cu. ft. density. covering used,on straight pipe. v alve wergn!s are approxlmate. When Dossible. obtain \ eights f or .!rrelding end valves. All flanged fitting, flanged of bolts oi all joints. stluds to make-up \ Appendix C: Properties of WEIGHTS OF PIPING MATERIALS s4" o.D. Pipe 223 34" *trc G /.^ u-/ b /-i\ z F I z rT F 2,1 c_=_=r -r "t\ {---t-r \IJ Temperature Range "F 2 Magnesia Calcium { tion z FiberSodium ffi z { ffi Njis N z 3 a" z -l) /A AI // N /> @ m +<i rc * 16 lb cu. ft. density. r- for insulation. Insulation thicknesses and weishts are based on average conditions and do not constitute a recommendation for sDecific thicknesses of mate_ rials. Insulation weights arq based on 857, magnesis altd hvdrous calcium silicat€ at 11 l5s/cubic f oot. The listed thicknesses and weights of combi- +.{ 3 Boldface type is weight in pounds. Lightface tYPe beireath weight is weight factor nation covering ale the sums of the inner layer of diatoma- at 21 lbs/cubic foot and the outer layel at ceous earth 11 lbs/cubic foot. Insulation weights include for v/ire, cetnent, allowances canvas, bands and paint, but not special surface frnishes' To find the weisht of coverine on ffanees, v-aives or fittinles. multi6lv the weiqht fac- tor"bi the iveight per-foot of coverrng usecl on slralghl plpe. Valve weights are approxi- mat€. When possible, obtain weights from manufacturer. Cast ilon valve weights are for flanged end valves; steel weiehts forweldinsendvalves. A'il flanged fitting, flanged valve and flange weights include the proportional weight of bolts or studs to make up all joints. 224 Mechanical Design of Process Systems 36" "t"u s6" o.D. z F EI 3 WEIGHTS OF PIPING MATERIALS W uj f\ w {T\ t=l _/A F--i A \iJ Temperature Range'F I\{agnesia Ctllcitm, Nom. Thick., In. Fiber- Nom. Thick,, In. Sodirm ffi z 6{fliN$ N-S {raT,s ,tA z F 4t /A z /t\ l|' tl p6l .lk{ l-<J lli'l +q] @ * 16 ]b cu. ft. derNity. Boldface type is weight in pounds. Lightface type beneath weight is weight faetor for insulation. Insuiation thicknesses and ['eights are based on averag:e conditiods and do not consti- recommendation lor specific thicknesses of mate- tute a rials. Insulation weights aae based on 85% magnesia and hydrous calcium silicate at 11 lbs/cubic foot. The listed thicknesses and weights of combi- nation covering are the sums of the inner layer of diatoma- at 21 lbs/cubic foot and the outer layer at ceous earth 11 lbs/cubic foot. Insulation weights include allowances for urife, cement, canvas, bands and paint, but not sDecial surface finishes. To-find the weight of cover- ins on flanees. valves or fittirigs, multiply the weig-ht factor by the welgrr! per lool or covering used on straight pipe. Valve weights are approxi- mate. When possible, obtain weiahts from manufacturet. Cast iron valve weights are for flanqed end valves; steel weichts iorweldineend valves, A-ll flanged fitting, flanged valve and flange weights include the proportional weight of bolts or studs to make up all joints. D Appendix D Conversion Factors 225 226 Mechanical Design of Process Systems Alphabetical Conversion Factors TO CONVERT INTO MULTIPLY BY A Abcoulomb Statcoulombs Sq. chain (Gunters) sq feet acres acres actes acres acre-feet acre-feet cm cm in. In. meler meter ampere-hours arnpere-hours ampere-turns ampere-turns/cm ampere-turn5/cm ampere-tutns/cm ampere-turn5/in. ampere-turns/in. ampere-turns/ In. ampere-turns/meter ampere-turns/meter ampere-turns/meter Angstrom An8stron un un it it Angstrom unit amps/sq amps/sq amps/sq amps/sq amps/sq amps/sq Btu/min Btu/sq ftlmin .4047 10-: 3.259 x cm meter cm In. coulombs faradays gilberts 1Cl' 6.452 10. 0.1550 6.452 x 10-. 3,600.0 0.03731 2.540 r00.0 amp-turns/cm amp-turns/meter grlberts/cm 39.37 0.4950 amp-turns/ in. 0.0254 3937 x 10-' Acre (US) .0247 ft of water (at 4'C) 1x 10-ro 1x 10-. | I19.60 o.o247 | 100.0 1.495 x 101 .007348 76.0 33.90 29.92 1.0333 In. of mercury (at 0"C) kgs/sq cn kgs/sq meter l0,332. pounds/sq jn. t4.70 tons/sq ft 1.058 B Barrels (U.S., dry) Barrels (U.S., dry) Barrels (U.S., liquid) barrels (oil) oars bars cu. tnches quarts (dry) 8al tons gallons (oil) bars arrnospnetes dynes/sq cm kgs/sq meter bars bals Baryl Eolt (US Cloth) pounoS/sq In. Dyne/sq. cm. Meters BTU Liter-Atmosphere 8tu ergs Btu Btu Bttr Btu t'(U Btu graln-caloneS horsepoweahrs ioules kjlogram,calories 8tu Btu/hr foot-lbs krlografi-meters kilowatt-hrs foot,pounds/sec horsepower kilowatts waIls watts/sq in. Cubic Cm, cu ft 0.0700 3.929 x 0.2931 12.96 0.02356 0.01757 l0 ' t7.57 o.r22r 1.818 x 10' 1.2445 cu In. 2,150.4 cu meters o.03524 laters pecks pints (dry) quarts (dry) 4.0 64.0 32.0 105.0 31.5 42.0 0.9869 105 !..020 x lcr. 2,089. 14.50 1.000 10.409 1.0550 x 10'o 778.3 252.0 3.931 x l0-l 1,054.8 0.2520 107.5 2.928 x o.2t62 c Candle/sq. inch centares {centiares) Lamberts sq meters Fahrenheit glams Ounce fluid (US) centiliters 0.01257 ncn Meter l\4 icron or (i.,lu) Kilometers Ton/sq. inch cms of mercury toot-lbs/sec B.T.U. {mean) Lambeats centiglams Centiliter Centiliter Centiliter 0.3937 0.01 Astronomical LJnit Atnospheres norsepower-hrs watts Calories, gram (mean) Candle/sq. cm Centigrade t.257 amp/turn5/cm sq. yards acres sq meters gram-cal/sec MULTIPLY BY I0 I amp{urns/in. amp{urns/neter gilberts/cm I Bucket (Br. dry) bushels bushels bushels bushe,s bushels bushels bushels tNt0 1,550.0 |.257 gilberts/cm /hr Btu/man 43,560.0 neler Btu 8tu/min 1.562 x 4,840. In. Btu /hr Btu/hr Btu/min I x 1Cl' 4,O47. Ares ares atmospneres atmospheres atmospneres atmospheres atmospneres atmospheres atmospheres 10 43,560.0 sq mete6 sq mrles sq yards cu feet gaflons amperes/sq amperes/sq amperes/sq amperes/sq amperes/sq arnperes/sq 10ro 160 Rods Square links (Gunters) Hectare or sq. hectometer Acre 2.998 x TO CONVERT 10-' centimeters centimeters Cubic inch m meters es mallimete6 m ils yards centrmeters centimeter-dynes cm-grams centimeter-dynes meter-xgs po!nd.feet centimeter-dynes centimeter-grams cm-dynes centimeter-grams rneter-kgs poundJeet centimeter-grams centimeters of mercury atmospheres centimeters of mercury feet of water centimeters of mercury kgs/sq meter centirneters of mercury pounds/sq tt centimeters of rnercury pounds/sq in. centimeters/s?c feet / min centameters/sec centameters/sec feet/sec kilometers/hr centimeters/sec centimeters/sec centlmeters/sec centimeters/sec centimeters/sec/sec centimeters/sec/sec xnotS l0-' lO-. 1,094 x 10-I 1.020 x 10-! 1.020 x 10-l 7.376 x 10-r 980.7 10-5 7.233 x 10-5 0.01316 0.4461 136.0 27.85 0.1934 1.1969 0.03281 0.036 0.1943 mete6/min miles/ hr miles / rn in centarneters/s€c/sec feet/sec/sec kms/hr/sec meters/sec/sec centimeters/sec/sec miles/hrlsec Chain Chain Chains (surveyors' or Gunter's) Inches meters Cords Cord feet Coulomb coutomos .6103 0.01 3-281 x 0.3937 10- 5 0.01 6.214 x 10.0 centimeters centimeters centimeters Circumference 0.01 liters feet kilometers circular mils 1.0 (C'x9/5)+32 2.705 inches 10 3.142 .4870 drams centrmeters cent,meters circular mils circular Inils 3.9685 x o.02237 3.728 x l0-r 0.03281 0.036 0.01 o.02237 792.00 20.12 yards sq clns sq mils Radians sq Incnes 22.O0 cord feet cu. teet 8 Statcoulombs faradays 5.057 r 10-. 0.7854 6.283 7.854 x 10-' l6 2.998 x 10' 1.036 x 10-' I Appendix D: Conversion Factors 227 (Continued). Alphabetical Conversion Factors TO CONVERT coulombs/sq cm coulombs/sq cm coulombs/sq in. cou,ombs/sq in, coulombs/sq meter coulombs/sq meter cubic centimeterc cubic centirneters cubic centimeters cubic centimete6 cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic feet cubic feet cubic feet cubic cubic cubic cubic cubic cubic feet feet feet feet teet feet cubic feet/min cubic teet/min cubic teet/min cubic teet/min cubic feet/sec cubic teet/sec cubic cubic cubic cubic cubic cubic cubic ctibic cubic cubic cubic inches inches inches inches inches inches inches inches inches meters rneters cub,c meters cubic meters cubic meters cubac mete6 cubic meters cubic meters cuDrc meters cubic yards cubic yards cubrc yards cubic yards cubic yards cubic yards cuorc yards cubic yards cubrc yards/min cubic yards/fiin cubic yards/min I INTO coulombs/sq in, coulombs/sq meter coulombs/sq cm 64.52 10. coulornbs/sq meter coulombs/sq cm coulombs/sq in. cu feet cu inches cu mete6 cu yards Sallons (U. S. liq.) 1,550. l0-. 6.452 x t0-l 3.531 x 10-' 0.06102 10-. liters pints (U.S. liq.) quarts (U.S. liq.) bushels (dry) cu cms cu inches cu meters cu yards gallons (tJ.S. iiq.) liters pints (U.S.liq.) quarts (U.S. liq.) cu cms/sec gailons/sec liters/sec pounds of water/min million gals/day gallons/ min cu cms cu feet cu meters cu yards ga onS liters mil-feet pints (U.S. liq.) quarts (U.S. liq.) bushels (dry) cu cms cu feet cu tnches cu yards gallons (U.S. liq.) liters pints (U.S. liq.) quarts (U.S. liq.) cu cms cu feet cu rncnes cu meters gallons {U.S. liq.) liters pints {U.S. quarts (u.s.'iq.) liq.) cubic ftlsec Sallons/sec liters/sec ULTIPLY 8Y 1.308 x 10-' 2.542 x 0.001 2.113 x 1.057 x l0-! lO-' 10-! 0.8035 - 2A32O.O Gram days decrgrams seconds grams deciliters tlers oecrmelers degrees (angle) degrees (angle) degrees {angle) meters quadrants radrans seconds oramS oramS otams Dyne/cm oyne/sq. cm. Dyne/sq. cm. Dyne/sq. cm. t,72A.O o.02832 0.03704 7.4a0s2 dynes dynes dynes dynes dynes dynes 2432 59.84 472.0 0.t247 0.4720 IN?O MULTIPLY 8Y fadians/sec 0.01745 revolutaons/min 0.1667 2.778 x revolltions/sec gtams r0.0 liters 10.0 10.0 meters 10 ounces (avoidupois) 0.r371429 ounces (troy) 0.125 cubic cm. 3.6967 1.7714 Srams grains ounces 27.3437 0.0625 Erglsq. millimeter Atmospheres Inch of Mercury at 0'C Inch of Water at 4'C grams .01 9.869 x 10-' 2.953 x l0-' 4.015 x 10-' 1.020 x 10 I 10-' JOUTeS/Cm joules/meter (newtons) kilograms poundals pounds oynes/sq cm bars EII Etl Cm. 1 ' 101.020 x 10 6 7.233 r 10-5 2.248 x 10-' 10-6 62.43 0.646317 448.831 5.787 x 10-. 1.639 x 10-' 2.143 x 10-5 4.329 x l0-3 0.01639 1.061x 105 0.03463 0.01732 106 5C.lt 61,023.0 1.308 264.2 1,000.0 Em, Pica Ern, Pica 2,1r3.0 1,057. 7.646 x IO' 27.O Dyne ergs ergs Btu dyne-centimeters foot'pounds erSs ergs ergs ergs Srarn-calo es erg5/sec cm/sec t2.74 l0-1. kilowatFhrs O.277ax watt-houts Btu/min farads Faraday/sec faradays faradays Fathom Iathoms microfarads Ampere {absolute} ampere-hours coulombs feet leet centimeters teet feet leet feet ol water feet of water leet of water l0-rr 1.0 Joules Kg-carofles Kg-melers Sram-cm5 ft-lbs/sec feet feet 1.000 9.480 x 7.367 x 10-l 0.2389 x 10 1.020 x 10 ! 3.7250 x 10-r' 102.389 x l0 -rl 1,020 x 10-' kg-calories/min kilowatts 202.0 764.6 1,615,9 807.9 0.45 3.367 0.01111 0.01745 3,600.0 - ft-lbs/min 0.7646 0.1 0.1 0.1 .4233 Crn. ergs/sec 46,656.0 1.650 x 86,400.0 114.30 45 Inches Inch *glsec ergs ergs ergs 0 Dalton CONVERI degrees/sec degrees/sec degrees/sec oeKa8rams dekaliters dekamete6 Drams (apothecaries' or troy) Drams (apothecarieS' or troy) Drams (U,S., fluid or apoth.) TO l{eter feet krlometers meters rniles (naut.) miles (stat.) millimeters ' ' I0 t3 0.2778 x 10 -ro 5,688 x 10-, 4.427 x lO-' 7.3756 x 10-l 1.341 x l0-ro 1.433 x l0-' 10-,0 10 9.6500 x 26.4O lcr l0 9.649 x 1.828804 6.0 30.48 3.048 x 10 ' 0.3048 1.645 x l0-. 1.894 x 10 . 304.8 lg mr ls 1.2 x armospnere5 an. of mercury Kgs/sq cm 0.02950 0.8826 0.03048 228 Mechanical Design of Process Systems (Continued). Alphabetical Conversion Factors TO CONVERT teet of water feet of water feet of water teet/m in feet/ min INTO kgs/sq meter pounds/sq ft Pounds/sq in. feet/ min feet/ min cms/sec teet/sec kms/hr meters/min feet/min miles/hr feet/sec feet/sec feet/sec feet/sec feet/sec feet/sec teet/sec/sec feet/sec/sec feet/sec/sec feet/sec/sec feet/ 100 feet crns/sec Foot - candle kms/hr knots meters/min miles/hr males/ rn in cms/ sec/sec kms/hr/sec meters/sec/sec miles/ hrlsec per cenl graoe Lumen/sq. meter MULTIPLY BY 304.8 62.43 0.4335 grains (troy) grains (troy) Srains (troy) giains (troy) Srains/U.S. gal grains/U,S. 8al 0.5080 0.01667 0.01829 0.3048 0.01136 30.48 1.097 0.5921 18.29 0.6818 0.01136 30.48 1.097 0.3048 0.6818 10.764 1.286 x 10-3 1.356 x 10' 0.3238 5.050 x l0-' 1.356 3.24 x 1.0 . foo!pounds Btu foot-pounds loot.pounds foot-pounds foot-pounds foot-pounds foot-pounds ergs foo!pounds foot-pounds/min foot-pounds/min loot-pounds/mjn loot-pounds/m,n foot-pounds/min toot-pounds/sec foot-pounds/sec foot-pounds/sec toot-pounds/sec foot-pounds/sec kilowatt-hrs 3.766 x Btu/min 1.286 x foot-pounds/sec hotsepowel kg-calories/min kilowatts 0.01667 3.030 x 10 -5 3.24 x lO-. 2.260 x l0-5 Btu/hr Btu/min o.o77 17 grarl1-calofles np-nrs JOules kg'calories kg-meters horsepower Furlongs kg-calories/min kilowatts miles (u.S.) turlongs rooS furlonBs feet Sallons garrons galrons Sallons gallons gallons gallons (liq. Br. lmP,) gallons (U.S.) gallons of watef gallons/min gallons/min gallons/min gausses Sausses Sausses gausses gilberts gilberts/cm gilberts/cm gilberts/cm cills (British) gills cu cms cu feet cu Inches cu meters cu yards liters gallons (U.S. liq.) eallons (lmp.) pounds of water cu ftlsec liters/sec cu ft/hr lanes/sq in. weDers/sq cm webers/sq in. webers/sq meter ampere-turns amp-turns/cm amp-turns/in amp-turns/meter cubic cm. liters Sills pints (liq.) Grade Radian drarns (avoirdupois) Grains 0.r383 parts/rnillion l0-' l0-3 l0-' 1.818 x 0.01945 1.356 x 10-' grams/cm Slams/cu cm gr-arns/cu cm Srams/cu cm grams/ liter grams/ liter 10-t 0.04167 17.118 142.56 14.286 980.7 joules/cm joules/meter (newtons) kilograms milligrams ounces {avdp) ouhces (troy) pounoals pounds pounds/inch pounds/cu ft pounds/cu in pounds/mil-toot grains/gal pounds/ gal grams/liter grams/liter parts/nillion grams/sq cm pounds/sq gram-calones gram-calories Sram-catones Stam-catofles Sram-calories gram-calones gram-caloraes/sec gram-centimeters gram-centimeters gram-centrmeters gram'centametels 6tu grafi-centimeters 2.0833 x parts/million oynes Slarns grams grams grams grams g,ams 1.0 0.06480 pounds/million gal Srams Srams Srams Srams MULTIPLY 8Y grains (avdp) grams ounces (avdp) pennyweight (troy) grains/lmp.8al Sralns 1.0 INTO TO CONVERT pounds/cu ft ft foot-pounds horsepowet-hrs kilowatt-hrs watt-hr9 Btu/hr Btu ergs joules kg-cal xg-meters 15.43 9.807 x lo-t 9.807 x 10-! 0.001 1,000. 0.03527 0.03215 0.07093 2.205 x l0-' 5.600 x l0-r 0.03613 3.405 x l0-t 58.417 8.345 o.062427 1,000.0 2.0481 3-9683 x 10-t 4.1868 x l0' 3.0880 1.5596 x l0-. 1.1630 x l0-. 1.1630 x 10-3 14.286 9,297 x lO-. 980.7 9.807 x l0-5 2,343 x 10-3 10 o.125 -' 40.0 660.0 Hand nectares nectares neclograms 3,785.0 23i.0 3.785 x 10-' 4.951 x 10-t 3.785 1.20095 o.83267 8.3453 2.22a x l'-t 0.06308 8.0208 6.452 l0-l 6.452 x 10-, 10-. 0.7958 0.7958 2.02r 79.58 142.O7 0.1183 0.25 .01571 0.03557143 10.15 Cm. acres sq feet grams hectoliters liters hectometers hectowatts henries Hogsheads (British) Hogsheads (U.S.) Hogsheads (U.S.) meters watts millihenries cubac ft. hoasepower Btu/min foot-lbs/min foot-lbs/sec horsepower kg.calories/min kilowatts ho15epower horsepower horsepower (boiler) horsepo',ver (boiler) horsepower-hrs horsepower-hrs horsepower-hrs horsepower-hts norsepower-nrs 1.076 x 100.0 100.0 100.0 100.0 1,000.0 10.114 horsepowet (550 ft lb/sec) horsepower (metric) (542.5 ft lb/sec) watts Btu/hr kilowatts Btu ergs footl bs gram.calol|es JOU leS 103 8.42184 cubic ft. gallons (U.S.) holsepower horsepower horsepower (met.ic) (542.5 ft lb/sec) horsepower (550it lb/sec) 2.471 42.44 33,000. 550.0 0.9863 1.014 10.68 0.7 457 7 45.7 33.479 9.803 2,547. 2.6845 x 10u 1.98 x l0' 641,190. 2.684 r l0' Appendix D: Conversion Factors 229 (Continued), Alphabetical Conversion Factors TO COI{VERT tt{To ho.sepower-hrs horsepower-hrs horsepower-hrs nours houls HundredweiShts Hundredweights Hundredweights Hundredweights Hundredweights Hundredweights kg.calories l(g-meters ilIULTIPLY BY 641.1 kilowatt-hrs qays 2.7X7 x lU o.7457 4.167 x 5.952 x 10-r t12 (long) pounds (long) tons (long) (short) ounces (avoirdupois) (shortl pounos (short) tons (metric) (short) tons (long) l0-r 0.0s t600 100 0.0453592 o.0446429 I inches inches inches inches Inches inches inches inches inches inches inches inches inches inches inches inches inches inches centimeters meIels miles millimeters mils mercury mercury mercury mercury mercury of mercury of of of of ot of water (at of watet (at of water (at of water (at of water (at of water (at International 4'C) yaros atmospheres feet of water kgs/sq cm kgs/sq meter 2.540 2.540x 10-t 1.578 x 10-5 25.40 1,000.0 2.77a x rO-' 0.03342 pounds/sq tt pounds/sq an. atmospheres 4'C) inches of mercury 4'C) kgs/sq cm 4'C) ounces/sq in. 4'C) pounds/sq ft 4'C) pounds/sq in. Ampere Ampere(absolute) InternationalVolt Inte.nationalvolt lniernational volt JOUIeS joules joules ioules joules joules joules/cm ioules/cm joules/cm .loules/cm ioules/cm volts(absolut€) Joules(absolute) Joules Btu ergs footpounds kg-calories kg-meters watlhrs grams dynes joules/meter(newtons) poundals pounds 0.03453 345.3 70.73 5.204 0.03613 .9998 1.0003 l-593 x 10-'' 9.654 x l0' 10-' 107 l0-' lO-' 1.020 x 10. 10' 100.0 723.3 22,44 K kilograms kilograms kilograms kilograms kilograms kilograms kilograms kilograms kilograms/cu meter kilograms/cu meter kilograms/cu fieter kilograms/cu meter kilograms/meter Kilogram/sq. cm. kilograrns/sq cm kilograms/sq crn cm cm cm rneter meter meter meter meter kalograms/sq meter inches of mercury kilograrns/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq mm kilogram-calories kilogram-calories kilogram-calories kilogram-caloraes kilogram.caloaies kilogram-calories kilogram-calories kilogram meter9 kilogram meters kilogram meters kilogram meters kilogram meters kilogram meters kiloliters 0.07355 2.540 x l0-1 0.5781 0.7376 2.389 x 0.1020 2.77Ax INTO HULTIPLY BY 24. pounds/sq lt pounos/sq In. 2,O44. 14.22 9.678 x 10-' 98.07 x l0-. 3.281 x l0-: 2.896 x 10-l 0.2044 1.422 x 10. atmospheres oars teet ot water inches ot mercury pounds/sq ft pounds/sq in. kgs/sq meter l0-' Btu foot-pounds hp-h.s 3,088. 1.560 x 10-1 4,186. 426.9 4.186 1.153 x l0-3 9.294 x 10-r 9.804 x 10' joules kg-meters kilojoules kilowatt-hrs Btu foo!pounds 9.804 2.342 x lO'' 2.723 \ 1O-' 1,000.0 1,000.0 10, 3,281. 3.937 x lO 1,000.0 JOUIeS kg-calories kilowatt-hrs kilolines o.4912 2.458 x 10-! 9.480 x TO CONVERT dynes 980,665. grams 1,000.0 joules/cm 0.09807 joules/meter(newtons) 9.807 poundals 70.93 pounds 2205 9,842 x 10-' tons (lond tons (short) 1.102 x 10-r grams/cu cm 0.001 pounds/cu tt 0.06243 pounds/cu in, 3,613 x 10-5 pounds/mil-foot 3.405 x 10-'o pounds/ft 0,6720 980,665 oynes 0.9678 atmospheres feet of water 32.81 kilometers kilometers kilometers liters centimetels {eet inches kilometers meterS kilometers miles millimeters kilometers kilometers kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hrlsec kilometers/hrlsec kilometers/hrlsec kilometers/hrlsec kilowatts kilowatts kilowatts kilowatts kilowatts kilowatts kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kiiowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs 0.6214 lCl' 1,094. 27.74 54.68 yards cms/sec feet/min teet/sec 0.9113 knots meters/nin miles/hr 0.6214 27.74 cms/sec/sec ft /sec/sec meters/sec/sec 0.9113 0.2774 miles/hrlsec Btu/min 0.6214 foot-lbs/min foot-lbs/sec 4.426 737.6 norsepower kg-calories/min Btu foot-lbs 1.341 14.34 1,000.0 3,413. 3.600 x 10r' 2.655 x 10. 859,850. gram-calories horsepower-hrc joules xg.carofles k8-meters knots knots l(nots knots 1,341 3.6 x lcl. 5bu.5 3.671 x 10' pounds ot water evaporated from and at212'F. kilowatt-hrs \W 3.53 pounds ot water raised frcm62" to 212" F. feet/hr kilometers/hr nautical miles/hr statute miles/hr 22.75 6,080. 1.8532 1.0 1.151 230 Mechanical Design of Process Systems (Continued). Alphebetical Conversion Factors TO CONVERT knols knots INTO yards/hr feet/5ec MULTIPLY BY 2,027. 1.589 L leaSue Light year Light Year lines/sq cm lines/sq in. lines/sq in. lines/sq in. lines/sq in. links (engineer's) links {surveyor's) liters liters liters liters liters liters liters liters liters liters/min liters/min lumens/sq ft Lumen Lumen Lumen/sq. ft. tux miles (approx.) Miles Kilometers 9.46091 x 10" gausses Sausses 0.1550 5.U 5.9 x 10rr 1.0 weDers/sq cm w€bers/sq in. webers/5q meter inches inches bushels (U.S. dry) cu cm cu feet cu tnches cu mete6 cu yards eallons (u.S. liq.) pints (U.S. liq.) quads (U.S.liq.) cu ft/sec gars/sec foot-candles Spherical candle power Watt Lumen/sq. meter foot-candles 1.550 x l0-l l0-' 1.550 x 10-r t2.o 0.02838 1,000.0 0.03531 61.02 0.001 1.308 x 10-r 0.2642 2.r13 1.057 5.886 x l0-' 4.403 x 10-' 1.0 .07958 .001496 10.75 0.0929 tl maxwells kilolines 0.001 megohms megohms fieters centimeters meters metets meters metels meters meters meters metets leet meters/m,n cms/sec meters/man feet/min 39.37 0.001 5.396 ! 10-1 6.214 x 10-' 1,000.0 1.094 1.179 1.567 3.281 meters/mrn meters/min metels/min meters/min meters/sec teet /sec 0.05458 kms/hr 0.06 knots 0.03238 0.03728 mete6/sec feet/sec meters/sec meters/sec mere6/sec metels/sec meters/sec/sec meters/sec/sec kilomete15/hr 5,O kilometers/min 0.06 miles/hr miles/min 0.03728 mete6/sec/sec mete6/sec/sec meterkilograms meteFkilograms meteFkilograms microfarad micrcgrams micrchms anches kilometers miles (naut.) miles (stat.) millimeters yards miles/hr feet/ m in 1Cl. 10u 10. 100.0 3.281 kms/hrlsec rniles/hrlsec cm-dynes cm-grams pound-feet farads glams megohIns 9.807 x liters Microns miles (naut.) miles (naut.) miles (naut.) miles (naut.) miles (naut.) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) mererc 19 I x 10-' feet kilometers 6,04O.27 meters miles (statute) yards centametels 1,853. 1.1516 2,027. 1.509 )( 5,280. 6.336 x feet inches kilometers meterc miles (naut.) yards cms/sec leet/man mil-feet cu inches milliers kiloSrams meters feet/sec kms/ht meters/min miles/min sec/sec feet / sec /sec / kms/hr/sec 10 r.609 1,509. 0.8684 1,760. M.70 8& t,467 26.42 0.1667 44.70 L.467 1.509 meters/sec/sec cms/sec teet/sec kms/min knots/min 0.4470 2,642. 88. miles/hr 60.0 9.425 x 1,000. g|a Ins grams parts/million millihenrie5 henries milliliters liters centimetels feet inches kilometers meters millimete6 miles millimeters millimelers million gals/day mils mrls yards cu ftlsec 0.8584 0.001 1.0 0.001 0.001 0.1 3.281 x 10-. 10-' 1.094 x l0-' 1.54723 anches mils mils kilorneters yaros 2.77Ax cu ft/min cubic cm. cubac cm. oeSrees quadrants radians seconds kilograms kilometers kilowatts 10-t 0.001 6.214 x mils centimeters feet 10-' I x lo-t 0.01543235 2.540 x 8.333 x 0.001 2.540 x myriagrams myriameters myriawatts 1Cl' o.o26a2 0.8684 knots cms 1..'J5 1.609 kms/min milliSrams/litet millimeters millimeters millimeters millimeters millimeters IT.IULTIPLY BY 10-. 10-. miles/hr rniles/h. miles/hr miles/hr miles/hr miles/hr miles/hr miles/h. miles/hr/sec miles/hrlsec miles/hrlsec miles/hr/sec miles/min miles/min miles/min miles/min miles/min miner's incheg Minims (British) Minims (U.S., flu;d) minutes (angles) minutes (angles) minutes (angles) minutes (angles) r00.0 ft/sec /sec ohms micrcliters mils 195.8 3.281 INTO microhms Millimicrons Milligrams milligrams 10-l webels maxwells microhms ohms megaltnes TO COI{VERT t.5 10-t 10-! 10-' lO-' 0.059192 0.0516r2 0.01667 1.852 x 10-' 2.909 x l0-. 60.0 10.0 10.0 10.0 lCr' l0-. N 10-. decibels 10-rl Dynes 8.686 1x105 Appendix D: Conversion Factors 231 (Continued). Alphabetical Conversion Factors TO CONVERT INTO MULTIPLY BY 0 OHlvl (lnternational) ohms ohms ounces ounces ounces 0unces ounces ounces ounces ounces (fluid) ounces (fluid) ounces (troy) ounces (troy) ounces (koyJ ounces (troyj Ounce/sq. Inch ounces/sq In, OHIV (absolute) megohms mtcrohms drams grains grams pounds ounces (troy) tons (long) tons (metric) cu rnches liters grains grams ounces (avdp.) pennyweights (troy) pounds (troy) Dynes/sq. crn. pounds/sq rn. 1.0005 10 . 1@ 16,0 437.5 2a349527 0.0625 0.9115 2.790 x 10-5 2.835 x 10-5 1.805 o.02957 480.0 31.103481 1.09714 20.0 0.08333 4309 0.0625 P parts/mil!ron lViles Kilometers grains/U.S. gal grains/lmp. gal parts/mjllion pounds/million gal Pecks (British) Pecks (British) Pecks (U.S.) Pecks (U.S.) Pecks (U.S.) Pecks (U.S.) pennyweights {troy) pennyweights {troy) pennyweights (troy) pennyweights (troy) pints (dry) pints 0iq.) pints (liq.) pints (lrq.) pints (liq.) pints (l'q.) pints (liq.) pints (liq.) pints (riq.) Planck's quantum cubic inches Iters Parsec Parsec parts/ftillion Poase Pounds (avoirdupois) poundats pounoars pounoars pounoats poundats pounoars pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds p0unds pounds (troy) pounds (troy) bushels cubic inches liters quarts (dry) grarns ounces (troy) grams po!nds (troy) cu lncnes l9 x 10rl 3.084 x 10r3 0.0584 0.07016 8.345 554.6 9.091901 0.25 n.' Erg - second Gram /cm, sec, / ft tt in. R^"n.i</(^ if, pounds/sq inpounds/ sq In. pounds/sq in. pounds/sq 8.809582 8 24.O lo(/<n mptar n.ic,cn in ^^ atmospheres fact w.tEr ^f inches of merclry kgs'sq meter pounds/ sq ft MULTIPLY BY 13.1657 t2.0 240.0 o.a22457 3.6735 x 10 ' 3.7324 x 10-l 4.1143 x 10-' 0.01602 27.68 0.1198 2.670 x 10-' 1.356 x 10' r3,825. 0.1383 0.01602 t6.o2 5.787 x 5.456 x 27.64 2.768 x 1,724. 9.425 x 1.488 10-' 10 ' 10 L0-' 178.6 2.306 x 1Cr' 4.125 x lO 0.01602 0.01414 ' 4.882 6.944 x t0-l 0.06804 2.307 2.036 703.1 144.0 0.05 4.1667 x 0.01671 24.87 4.732 x l0 6.189 x 10-' 0.125 o.4732 0.5 6.624 x 1O 1' ' 1.00 14.5833 oynes 13,826. 14.10 Srams joures/cm 1.383 x joules/rneter (newtons) 0.1383 kilograms 0.01410 pounds 0.03108 drams 44,4423 r. dynes grarns 7,000. grams 453.5924 joules/cm 0.04448 joules/meter (newtons) 4.448 0.4536 kilograms 16.0 ounces 14.5833 ounces (troy) pounoals pounds (troy) t.21528 0.0005 tons (short) l0 5,760. 373.24177 o 10-l 33.60 ounces (troy) grarns grams 'n,lc ^^"nd<r<^ 473.2 cu feet cu lncnes cu meters cu yards gallons Irters quarts (liq.) INTO CONVERT pounds (troy) ounces (avdp.) pounds (troy) ounces (troy) pounds (troy) pennyweights (troy) pounds (troy) pounds {avdp.) pounds (troy) tons {long) pounds (troy) tons (metf ic) pounds (troy) tons (short) pounds of water cu feet pounds of water cu inches pounds of water gallons pounds of water/min cu {t/sec poundjeet cm-clynes pound-feet cm-grams poundjeet meter-kgs pounds/cu ft grams/cu cm pounds/cu {t kgs/cu meter pounds/cu tt pounds /cu in. pounds/cu ft pounds/mrlJoot pounds/cu in. grns /c! cm pounds/cu in. kgs /c! meter pounds/cLr in. pounds/cu ft pounds/cu in. pounds/mri foot pounds/ft kgs'meter pounds/ in. grns/ cm pounds/mil-foot gmslcu cm pounds/sq ft atmospheres pounds/sq ft feet of water pounds/sq ft inches of mercury (n TO quadrants (angie) quadrants (angle) quadrants (angle) oegrees rad ra ns q!adrants (angJe) quarts (dryj 1.571 seconds cu tncnes cu cms cu teet cu inches cu meters cu yalds gallons 3.24 x quarts lliq.) quarts (liq.) quarts (liq.) quarts (liq.l quarts (liq.) quarts (liq.) quarts (1,q.) 90.0 5,400.0 minutes liters 1O5 67.20 946.4 0.03342 57 .7 5 9.464 x 1.238 x 0.25 l0-. 10-l 0.9463 1 R ians radians radrans radians rad W radians/sec radians/sec radians/sec radians/sec /sec €dians/sec /sec raorans/ sec/sec revolutions revoru!ons tevotutons revolutions/min revolutions/min revolutions/min rninutes quaorants seconds degrees/sec revolr.rtions/min revolutrons/sec revs/min /min revs/nrn/5ec revs/sec /sec quadrants radrans oegrees/sec fadians/sec revs/ sec 57.30 3,438. 2.063 x 10r 57.30 9.549 0.1592 573.0 9.549 0.1592 360.0 4.0 6.243 6.0 0.1047 0.01667 232 Mechanical Design of Process Systems (Continued). Alphabetical Conversion Factors TO CONVERT revolutions/min/min revolutions/min/min INTO radians/sec/sec revolutions/min/min revs/sec/sec revolutions/sec revolutions/sec revolutions/sec revo,utions/sec/sec revolutions/sec /sec revolutions/sec/sec oegrees/sec Rod Chaan (Gunters) xoo Meters radians/sec MUI.TIPLY BY 1.745 x 10-r 0.01667 2.778 x 10-. 360.0 6.283 50.0 radians/sec /sec revs/min/min revs/man/sec 3,600.0 60.0 .25 5.029 INTO TO COI{VERT square squate square square square square square square square mrls !nrl5 yards yards yards yards yards yards yards sq cns gra,ns minutes quaoranls radians Kilogram tempemture ("c) +273 Pounds 20 2,778\ lO . 0.01667 3.087 x 10-6 4.848 x l0-l 14.59 32.17 Steradians circular lnils sq feet sq rnches sq miles sq millimeters sq yards acres circular mils sq cms sq inches 1.973 x 10' 1.076 x l0-3 0.1550 0.0001 3.861 x 10-'r r00.0 1.196 x 10-. 2.296 x 10-, 1.833 x l0o 929.O 144.0 0.09290 square Inches square square square square square square square square square square square square square square square square square square square square square square square square square square square Inches Inches Inches inches k'lometers kilofleters kilometers kilorneters kilometers kilometers kalometers meters meters melers meters meters meters meters miles miles miles mrles millimeters millimeters millimeters millimeters rn ils sq mrles sq millimeters sq yaros circu lar mils sq cms sq teet sq millimeters sq mils sq yards acreS sq cm5 sq ft 0.8361 3.228 x 1O-, 8.361 x l0' sq males sq millimeters 3.587 x l0-r 9.290 x lCr 0.1111 1,273 x 106 6.452 6.944 x l0-3 tons tons tons tons tons tons tons tons tons tons tons tons tons tons tons tons tons (long) (long) {long) (metric) (metric) (short) (short) (short) (short) (short) (short) (short) (short)/sq ft (short)/sq ft of water/24 hrs of water/24 hrs of water/24 hrs cns sq feet sq miles sq feet sq xms sq meters sq yards circular mils sq cms sq feet sq inches circular mils 3.861 x 1,973. 0.01 1.076 x 10-r 1.550 x 10-! 1.273 5/9 foot-lbs/min 3.4129 0.05688 107. 44.27 0.7374 watts kg-calories/min kilowatts 1.341 x l0-1 1.360 x 10-! 0.0t 433 0.001 Watts (Abs.) Watts (Abs.) watt'hours B.T,U. (mean)/man. 0.056884 joules/sec. Btu 3.413 3.60 x 10'o walls watts 1.196 640.0 27.88 x 10. 2.590 2.590 x 10d 3.098 x 106 1.0 .003336 toot'lbs/sec 106 10-' ('F) .39370 Volt/cm. Statvolts eags/sec 1Cp 1.8 kilog€ms 1,016. pounds 2,240. tons (short) 1,120 kilograms 1,000. pounds 2,205. kilograms 907.1848 ounces 32,000. ounces (troy) 29,166.65 pounds 2,000. pounds (troy) 2,430.56 tons (long) 0.89287 tons (metric) 0.9078 kgs/sq meter 9,765. pounds/sq in. 2,000, pounds of water/hr 83.333 gallons/min 0.16643 cu ltlhr 1.3349 Btu/hr Btu/min 1,550. sq millimeters sq yards actes 1.0 w watts lO-. ('C) v Volt/ inch Volt (absolute) 10. 7.716 x 10-. 247.1 10x 10.76 x 106 1.550 x 10' 0.3861 1.196 x 2.471 x 10. 10.76 absolute temperature temperature ('F) temperature ('c) + r7.78 temperalure absolute temperature ("F) +460 temperature ("F)-32 temperature ('C) 106 sq mrles sq yards sq 9.0 ,296. T s square feet 't sq inches sq meters feet Scruples seconds {angle) seconds (angle) seconds (angle) seconds (angle) Slug Slug Sphere square centimeters square cent|melerS square centimeters square centrmeters square cen!melers square centimeters square centimeters 6.452 x 10-6 10-6 2.066 x 10-. 8,361. sq Inches acres sq cms Rods (Surveyors' meas.) yards rods MULTIPLY BY horsepower horsepower (metric) watt-hours watt-hours erSs watt'hours gram-caloneS horsepolver-hrs kilogram-calories watt-hours watt-hours watt-hou.5 watt-hours Watt (lnternational) foofpounds I 2,656. 859.85 1.341 x 0.8605 kalogram-meters kilowatt-hrs Watt (absolute) 0.001 1.0002 1Cp kilolines 10, l0-1 -----Appendix D: Conversion Factors Synchronous Speeds syncnronou3 sPc.o Frcqusncy r 120 - T;;Ei;;FIEQUEiICY 60.ycle 50 .y.lc 3600 3000 r800 t 6 8 50 Gycl. 12 171.1 142.9 500 11 | 63.6 136.4 1200 1000 a6 | 56.5 130.4 900 750 375 18 l50 r25 600 300 111 t20 500 250 t38.5 124.6 214.3 133.3 ||t.l 375 187.5 128.6 t l0 l2 600 II 5r t6 150 t8 400 4.3 | 500 56 166.7 5.a o7.l t21.1 103.5 360 300 t50 60 120 100 327 .2 272.7 136.4 62 rr6.t 96.8 2l 300 250 61 2.5 93.7 26 276.9 230.8 lt5.a 66 t0t. 28 257 .1 211.3 t 07. t 58 r 30 210 200 100 32 225 187.5 93.7 72 31 2n.8 175.5 88.2 71 97 .3 8r.l 36 200 166.7 83.3 76 91.7 78 -9 38 t89.5 157 -9 78,9 92.3 76.9 10 r80 150 75 ?0 75 Courtely Ingersoll-Rand Co. 80 I 90.9 05.9 88.2 102 -9 85.7 t00 83.3 2Sg 234 Mechanical Design of Process Systems Temperature Conversion NOTA Thc G.nter .oluh'l of nu|'b.t! in boldfo.. .efeB to the teDperotur. in desreei, either Cenrig.odc or Fohrenh.ir, whidr it ir d.!ir.d to conv.rt inlo lh. olh.rtol.. lf.o.v.rtins kom fohr€nhcil lo Ccntis.ode degr€e!. the equivolent tempe.oiure will bc found in lh.lefi col'r6n, whileil convc.li.s lron d.s.c€i Ccnrigrodc to d.gr..r fobr.nhi.t, thc oniy€r Cenlisrod. -20.6 -16.7 -t6.1 - .l -159.1 -151 -136 -4t8 -2oO 328 -100 -361 -316 -tlo -tto -292 -271 -256 -t50 -lao -r30 -238 -220 -202 -120 -181 -t66 -18.3 -15.6 -50 -67 .0 -58 .0 a5 -49.0 -/2.9 -,40.0 -!l -40 -35 -31.1 -3t .7 -28 .9 26.1 t7 .2 .8 u 5r.8 -8 .9 -8 .3 l4 l5 220 225 t2a I l0 163.4 165.2 I t6 230 235 240 116 155 461 167 .O I l8 7.45 173 25 27 80.6 2.4 8? .,{ a9 3l 81.2 86.0 82.8 32 89.6 7a 75 76 7a ,9 !o 152 168.8 170.6 l2l t72.1 127 129 121 171.2 't76.O 27 .2 27 .S 8l 177 .8 a2 t79.6 28.3 28.9 29 .1 30.0 30.6 83 3t.l ll3 l8l 132 135 138 t{ 3f 98.6 3l 100.,{ 39 40 102.2 104 .0 8.9 /t8 118.,( -4.0 9.1 105.8 to7 .6 109.1 .7 32.2 32.8 33.3 33.9 31.1 35.0 31 35.6 36.7 114.8 37 .2 | 16.6 536 545 554 E5 185 .0 86 186.8 l,a9 154 | 88.6 t60 | 90 .,4 t66 300 310 320 330 t71 3:10 626 611 a, E8 s72 590 608 89 90 192.2 194.0 177 350 662 9l | 95.8 182 t88 360 370 680 .6 99.4 r93 3t0 ,16 201 .2 t99 731 203.0 204.8 201 390 a0o 210 216 at0 420 206,6 208.4 21o.2 212 .0 221 r30 805 L0 aso 150 170 {r0 ago 500 gza 812 92 93 9a 95 95 9A 99 197 r 227 40 .6 t05 221 238 43.3 0 213 219 a9 50 120.2 ,(6.l ||5 122.O 5l t20 t25 218 251 t23.9 18.9 5t .7 257 260 | et-r'r Degreca KeMn,'K:'C + 273.2 518 290 495 .,a 230 239 = 500 509 lt6 100 cent,'.=|et + ,ot -ro 280 2t5 ta2 191 143 9f 113.0 250 233 260 255 270 215 137 I83.2 !4 95.0 -22.0 Desr€e' 26.1 26.7 8.3 10.0 l0 .6 23.9 21.1 25.0 25.6 l]1.2 (ony€rling Ceotigrcdc or foh.enhcil i.lo thc othcr 3cal.r. 119 77 .O 14 15 a6 17 formulor ol lh. .isht hoy oho bc ured 215 25 6.7 .4.0 ttt t02 t04 t07 -3 .9 12 -t0 212 -1.1 5-6 6.1 -t3.0 110 100.0 23 24 10.0 392 ,a0r ,3 {3 383 200 371 210 22.8 96.8 195 t5.4 205 d8.0 69.8 71.6 73.1 75.2 36 t90 I 317 356 93.9 20 93.2 85.0 82.8 l15 117.2 t 338 96.1 72 9t.,( !65 t70 t75 ta0 329 13.6 73.9 76.7 79.1 s2.2 .6 154.4 | 56.2 158.0 159.8 161 .5 fl 34 35 38.2 l{0.0 l4r.8 t20 50.8 2t .7 22.2 LI 71.1 I55 t50 3ll 34.6 | 36.4 150 t 2t.r 0.6 65.6 68.3 55 57 62.6 61.1 66.2 0.0 32.8 r l8 .9 t7 t8 t9 30 293 2e1 149.0 59 70 1.7 l,l5 55 20.6 2l .0 266 8.3 60 .8 6.7 -6.1 r3l t30 t35 ta0 90.6 93.3 t5 /tt -31.0 l, | 5.0 -25 -20 -ll 18.2 50.0 5l 3.9 4.1 -50 9 52 53 61 20.0 -t 03.0 -65.0 -75,0 t6.7 6l 59.0 -75 -55 16. r I9..{ -t l2 .0 -53 .9 -51 .l | 5t 57 .2 -90 91.0 59 60 l5 .6 t0 t3 1.7 2.2 -ro 16.4 60.0 62.8 | t2.a I 12r.2 57 14.1 15.0 lt.6 5t.t 13.3 t3.9 al.0 125.6 127.1 52 53 5a 55 55 39 .2 -10.6 -10.0 -148.0 -t 30.0 -r0 11.7 12.2 3 7 -t2.8 -t2.2 -382 -I00 .l 32.0 1 -13.t -r3.3 -230 -220 -210 -ll0 23 -O 35.6 37.1 5 C.ntlgrod. Centigrode I2.8 2 -15.0 -14.1 -116 -f10 -t34 -129 -123 -I8 -l 12 -107 -tot -96 -90 -8{ -79 -73.3 -67 -S -62.2 -r50 -5 I -rao -r90 Fohrenhcil 0 -tsf -56.7 fo'rnd in the column on thc right. C.ntigrodc -273.17 -a59.f -268 -r50 -262 -aao -{30 -257 -25t -420 -216 -aro -,100 -210 -231 -390 -3r0 -229 -370 -223 -2t8 -360 -350 -212 -3{0 -207 -330 -20t -310 -t96 -190 -3ro -300 -t81 -290 -179 -2t0 -173 -2f3 -f69 -168 -rro -260 -t62 -250 -157 -59.r $ll b. Dcqree' Fohr., 'F = ! 9 fc + .ot -.0 c +32 Degrccr Rcrftlne, ol :oF+459.7 69S v0 748 860 678 896 914 932 3*. Aooendix D: Conversion Factors Altitude and Atmospheric Pressures Kelrq Hs Ab3. -1526 -1373 -5000 ,{500 ,{000 77 75 73 21 35.58 35.00 H9 Abr. PSIA .7 17.15 .229 .209 903 t7.t9 889.0 23 s{.12 87t.3 16.t0 .188 -3500 -3000 t068 71 22 859.5 16.62 .t69 -915 70 2l 33.84 33.27 8,(5.l t 6.34 .r19 2500 -763 68 20 -610 830.6 816 .4 16.06 15.78 l8 3t .58 802.1 -305 65 61 63 32.70 32.11 .129 -2000 -1500 -1000 17 3l .02 757 6l t6 30.17 773.9 59 29 .92 760.O 29.38 716.3 28 .46 733 28.33 719.6 706.6 -1220 15S 0 0 500 1000 t53 I500 .158 2000 6t0 ?500 763 3000 915 l8 3500 1068 17 t000 1220 1373 t4 55 ,4500 12 ll 50 0.95 6000 7000 1.1 l83l 1.3 2136 2111 2716 3,( 3050 23 20,000 1.9 2.4 3.8 25,000 30,000 1.7 5.7 7628 t0,000 t5,000 1.7 7.6 8.5 9.5 40,000 15,000 50,000 55,000 10.1 60p00 ll.,4 20.000 80,000 90,ooo t00,000 t3.3 t5.2 120,000 160,000 180,000 22.8 26.6 30.4 31.2 200p00 37 .9 t,(0,000 't7.1 r8.9 1 5 | t,( 't2 | 21 6 30 t-31 -18 | -41 9153 -66 -70 -70 -70 -70 12,201 13.730 r5,255 t6/81 27.159 30,5t 0 36,612 67,t22 ,(00,000 75.9 94.8 t22,010 -11 -86 I I 500,000 600,000 It4 900,000 132 244,080 tp0o,ooo 189 305,100 1.200,000 1,400,000 1,600,000 228 266 l,8oo,ooo 312 379 2,000,000 30.{ .926 .909 t2.69 .492 .876 2t .90 632_5 609.3 555.7 561.6 5,t3.3 12.23 .78 .s60 23.99 23.10 .3,6 .91 l0 l0 .50 .797 .767 .738 10.t0 .710 .583 319.5 282.1 8.29 6.76 s.16 8.903 226.1 a .37 .307 .060 5.558 't79 .3 3 .17 .211 .192 2r .39 20.58 16.89 13.76 1l.l? l,{l a7.5 68.9 2.135 1.325 ls.273-1 5.200-r -42 2.523-t 9.955-. .406 13.2 8.36 3 I t.113 . .737-t 6 .3-l Courtdy Ins.Boll-Rrd Co- .162 .45 51 16.97-l 3 .26-l 3.5r 3-. 3 .0738 .0158 .0285 .o179 2t.0 r '3 | .05 .651 358-I 5.917-7 r.18-! 6.11 ? 2.53-r 8.92-r .67 L19-1' x | .1-l 1.605 3.56-. t.6r 1 I .50-6 .06-l I 366,t 20 127,110 188,160 2.O-' L2_10 s.08-r 2.08-l 3.8-ro 9.65-' 519,1S0 | .8-ro 1 6r0,200 9 2.31-e .2-tl .30-' .57-' .381 .r5l .7 I .828 2.15 | .69 t.33 51_2 33 Dor6 ,'.m NASA Sr.ndcrd Arh6ph.r.ll9a2l. ond b.'.m.r.r or. opp'orirot. ,o( n.soriy. clri|ld.a ..Tcfp.rorur.3 or. .y!roe. .rnine cla0'l.rirrd. .id o.. round.d r. ev.n iurSlij. lx.sorir. .tpon.nr ,F i!nb.. ol |9oct rh. d.<irol point nutr l. rov.d b tn. |.fi. .T.nr.'orur. .2 l .l 1.375 3.111 2.712 3.290 12.16 129 .O 5.9 . -- .960 12.93 5.1-t I 3.66 .956 .978 .913 | .281 5.816 t2z I -88 .0333 .015 13.t7 -7 -129 | -135 | -93 r4.696 t,(.13 t,(.16 t3.91 13.1r 2.716-' 66 90 .071 .052 68t .2 668.6 656.3 611.1 -2 -3 | -r9 61,020 73,221 79,326 85,128 91,530 56.9 28t t9t 5t,918 at.7 53.t a L -16 12711 ,(8,815 45.5 49.3 280,000 300,000 -62 | -52 -57 | 59 5t | -16 -26 I 48 2A,AOa t5.23 I4.96 | 693.9 7 57 57 70 \ -s7 18,306 21,357 2,{0,000 l -1 6102 220,000 260,000 6 3 1o,679 35,000 8 4l 5000 8000 9000 9 .O t09 .091 26.87 26.33 25.81 25 .37 t0 7 13 27 .87 .9 . r5.5| . 9 .0935 .01 14 235 236 Mechanical Design of Process Systems l! o\ tr IIt I a E 8 E 3 6 E I a ! 6 E R 6 6 6 I 6 E E q o 6 F !-- !$ I :f I t5 5 6 I 9 E .o ?. E: I R 3 8 I E - I 6 o .' Eo arO 6 A 8 b o& -+ 3 6 I 5 o0 IY . rl 6 ? 63' b i3 8 d = F ao o 3 5 P l. o F o z tt UT o c, CO G I It t= oi o9 9p tt sl !aa rrO >! f€ !g €+ eI -+ E; a E E 5€ iE o UllSlInN N3Al9 A'ldll'llll[ -._- ol tr Index American Society of Mechanical Engineers. mass flow in, 1, 3-4, 6, 8, 11 piping,3 angle of internal friction, 3-4, 6-7 angle of friction, effective, 6*7 critical flow factor for, 7 See ASME. API, degrees for hydrometer, conversions, tables of, 92 defined,8T-88 ASME Section VIII Division I joint reliability factor, l13-l14 joint types for tubesheets. I l5 maximum tube joint force, ll3, 157 tube joint load criteria, 113 vessel code, 99, 101 Axial flow compressors aircraft, for, 59 airfoil blades for pitch, 58 size,58 applications of, 44, 58-59 characteristic curve for, 59 operating range of, 49 surge piping factor, 304 pneumatic gases in, 7 pressure vessels, differences stresses 13- 14 wall friction angle, 4-5 Blowers and fans, 59 Bulk solid properties bins, in, 1, 6 bulk density, 3, 6 Beams, boundary conditions for, continuous beams, 142 Bins arching (rathole, l-2, 6) critical dimension for, 3, 12 critical flow factor for, 4 critical hooper dimensions, 6 dead storage, 1-2 critical dimensions of, 3 pressure of, consolidating, 4, 6-7 stresses, hooper wall, on, 3 solids, in, 3 typical values oi 7 yield strength, solid material, 1 flow, erratic, I flushing of, 1 funnel flow in, 1, 6, 8 hoop pressure in, rnaximum, 6 hooper angle, in, truss design, 18-20 limit of, 59 degradation flow condition, 1 design of, reasons for inefficiency, from, 1 segregation, 1 shear stress, 1 solid flow, pressure distribution for, 8 steady flow, consolidating pressure for, 3 structural design, conical portions, rectangular, 17 frame detail, 20 stiffener design, 14-16 hoop force, 16 Centrifu gal compressors actual, or inlet, flow rate, 80 advantages of, 43-44 affinity laws, 50 3 237 3 Mechanical Design of Process Systems anti-surge devices for, 52 diagram of, 53 applications of, 49 compressibility curves for, 81 compressibility factor, significance of, 83 compression process, diagram of, 50 compression ratio of, 50, 80-81 discharge temperature average,80 dependence on ratio of specific heats, 83 frame data, typical, 80 gas, cyclic vibration of, 50-51 noise induced by, 50-51 gas inlet conditions, 50 impeller, 49 types of, 52, 52 inlet parameters, effect of varying. 52 intercoolers, sizing of, 50 mechanical losses of, 82 percentage of power required, 83 mixtures compressibility factors for, 79-81 specific heats for, 79 nncratinc 'arlo" 44 performance curves, typical, 51 polytropic head, 81 maximum per stage, 82-83 significance of, 83 polytropic relations for, 46-50 pressure versus capacity for constant speed compressor, 52 rpm, required, 82 selection of, 79-83 shaft power, required, expression for, 82 single stage, 49-50 specific heat ratio significance of, 83 stages, required number of, 82 standard cubic feet, use of, 52 surge,50 control of, 52 surge limits, 50, 52 temperature, discharge, 49-50 temperature ratio for, 81 volumetric flow, expression for, 80 Centrifugal pumps advantages of, 31 API hydrometer, conversion factors, table of, 92 defined, ST-88 bearings, 34 outboard type, 34 brake horsepower, 34, 36, 70, 9l required,96 shut-off, at, 36 by-pass for, 34, 36 casrngs, horizontally split, 32 vertically split, 32 advantages of, 32 components of, 33 efficiency of, 70 head, total, 36 heat dissipation in, 34, 36 intercooler for, 37 Hydraulic Institute, 68, 71-72 hydraulic requirements of, 34, 36-37 impeller, axial flow pump, for, 32 mixed flow pump, for, 32 vanes of, 32 radial type, 32 volute of, 32 net positive suction head (NPSH) definition of, 34 pressure pads for, 91 Newtonian fluids, 68 non-Newtonian fluids, 68, 79 packtng, 32 performance curves for, 34 typical, 69, 75, 95 pressure drop discharge line, for, 67 -68, 9l, 95-96 friction factor for, 66-67 , 89-91, 93, 95-96 suction line for, 65-66, 90-91,93,95,97 viscosity, effects of, 68, 70-72 seals,32 double seals criteria for use, 32 types of, 35 seal flush, 34 single seals types of, 35 versus double seals, 32 selection of, 70 total dynamic head, application of, 70, 74 types of, 31, 34-35 vaporization of pumped liquid, causes of, 34 viscous liquids, pumping of, 37 correction-factor curves, 37, 38-39 criteria for, 37 equivalent water-performance of, 37 water horsepower, 34, 36 defined, 36 Compression, ideal gas compressibility factor discharge, at, 45 Heat transfer, convection of, air normal to cylindeq 126 mean, 45 suction, at, 45 isentropic (reversible adiabatic), 46-49 adiabatic efficiencY, 46 energy, isentroPic, 46 polytropic efficiencY, 46 principles of, ff 44-48 real gas. compressibility factor. 44 Compressors acfm,59-60 advantages of, 59-60 conversion to, standard volumetric flow, 60 actual volumetric flow. See acfm' flow conditions, sPecifYing, 59 actual, or inlet flow, 59 mass flow, 59 flow, 59-60 flow, conversion to standard volumetric flow, standard volumetric mass 60 principles of comPression, 44-48 scfm, 59-60 specifing flow conditions, 59 acfm, exPression for, 60 actual, or inlet flow, 59 mass flow, 59 specific volume, exPression for, 60 standard volumetric f1ow, 59-60 standard volumetric flow compressibilitY factor, 59 conversion to actual or mass flow, 60 disadvantages of, 60 specific volume, exPression for, 59 'ttandard" condition, defined, 59-60 comparisons of various forms, 60 volume flow, equation for, 59 types of, 43 volume flow, exPression for, 59 External loading on shell structures applications of , l7Q-17 5 "critical value," 170 shell thickness, 170 Hydraulic Institute, 37 Hydraulics API hydrometer conversion factors, table of, 92 defined,8T-88 Internal pressure, stress concentration factor, 169 lsentropic comPression brake horsepower, 48 discharge temperatue, 48 head, adiabatic, 46 heat, mechanical equivalent of, 45 horsepower, ratio of isentroPic, 45 horsepower input for single stage, 45 ideal eas, 45 adia--batic efficiencY, 45 horsepower, isentropic, 45 mechanical efficiencY, 45 overall adiabatic efficiencY, 45 multistage,46 perfect gas, formulations for, 44 real gas, formulations for, 45 isentropic exPonent for, 45-46 relations, basic versus polytropic compression, 47 reversible,48 Jenike and Johanson method, 1-8 Lifting lug design, 170-175 choker angle for, 175 standard designs for, 171 L'Hospital's rule, 165 Ingarithmic mean temperature difference. See LMTD. LMTD, application of, 148-149, 154, 160, 162' t65 correction factot F, 117 -l2l multipass exchangers, variance in, 117 variance in shell and tube heat exchangers, 117 zero LMTD exchanger, 165 Multi-stage reciprocating compressors, 58 Flow of solids, problems of, 1-3 Non-Newtonian fluids, 162 Nozzle reinforcing pads disadvantage of pads, 170 Gas pad width, maximum, 170 Nusselt number, 125-126, 156 Fans and blowers, 59 compressibility tactor, 44 general gas law, 44 specific heat ratio for, 44 universal gas constant, 44, 59 Gear pumps, 37, 40 Petroleum fractions API hydrometer for, 87-88 Plate-fin heat exchangers advantages of, 147 24O Mechanical Design of Process Systems applications of, 99 disadvantages of, 147 illustrated, 149 Kays and London coefficients, 148 thermal shock and fatigue, 148 of, 147- 148 vacuum brazing of, 148 Polytropic compression uses efficiency overall polytropic, 48 polytropic vs. isentropic, 46-47 gas horsepower, 47 head, adiabatic, 47 horsepower, compressor (polytropic head), 48 perfect gas, for, 47 polytropic exponent, 46 polytropic head (compressor horsepower), 48 real gas, for, 47 relations, basic versus isothermal compression, 47 Positive-displacement pumps applications of, 31 brake horsepower, 77 definition of, 31 efficiency of, 77 pump selection, use in, 77 gear pumps, 37 , 40, 78 heat dissipation in, 43 intercooler, 43 temperature switch, 43 net positive suction head. See Pumps. performance curves for rotary gear pumps, 79 pressure drop suction line, 74 velocity heads, 74 pressure protection for, 42-43 priming of, 79 reciprocating pumps diaphragm pumps, 3l piston pumps, 31 nlrrnocr nrrmnc 1l rotary pumps cam pumps, 31 gear pumps, 31 lobe pumps, 31 screw pumps,31 types of, 37 vane pumps, 31 screw pumps, 40-41 vane pumps, 37 Prandtl number, 125,152, 156, 164 Pulsation response spectra compression bottles, 64, 65 typical,65 methods of predicting, 64 orifice plates, application of, 65 piping system excited by, 65 pulsation bottles. See Compressor bottles. pulsation dampener. See Compressor bottles. reciprocating equipment, induced by, 62, &-65 Southwest Research Institute, 64 Structural Dynamics Research Corporation, (scRc), 64 surge drums. See Compressor bottles. Pumps API degrees, defined, 87-88 calculation sheet for, 36, 70, 77 flow capacities of, 34 head, friction, 40 static discharge, 40 static suction, 40 total discharge, 40 total dynamic, 34, 40 total static, 40 total suction, 40 Hydraulic Institute, 68, 7 | -72 inline, nozzle loadings for, 61 lift static suction, 40, 42 for water maximum recommended, 43, 77 theoretical, 43, 77 total suction, 40, 42 motors, NEMA frame dimensions, 73 NPSH definition of, 34 pressure pads for, 91 priming of, 79 pump Hydraulic Design, calculation sheet, 36, 70,77, 93,95-96 pump selection guide, 32 of, 3l of, 31 types uses velocity heads, effect on pumps, 40 Reciprocating compressors adiabatic compression, work required for, 58 adiabatic exponent, 53 adiabatic expressions for, 44-46, 53 adiabatic process, 57 applications of, 43, 84-86 clearance capacity, effect of, 55 clearance pockets, 43 stop valve, 53 volumetric efficiency, effects on, 56 compressibility factors discharge, 58 inlet, 58 fr lnder compressor horsepower, factors affecting, 53 compression ratio, 58, 84 compressor bottles. See Pulsation response spectra. cylinders, size of, 86 cylinder displacement, 86 diatomic gases, 57 discharge temperature, 85 efficiency, volumetric, 86 Neerken equation for, 86 gas temperature, exPression for, 58 horsepower, theoretical, 58 parameters affecting, 58 horsepower per million curves, 85 correction factors for, 85 intercoolers for, 84 multiple staging of, 58 advantages of, 58 compression ratio for, 84 cylinder size, 58 cylinders, number of, flywheei, effect on, 58 torque, effect on, 58 operating range, 44 piston rod diameter, 86 polytropic exponent, 57 Chlumsky recommendations for, 57 pressure-volume diagram, 56 ratios of clearance volume to volume swept by piston,57 reciprocating compressor cycle, 53, 55 58 re-expansion process, 57 schematic of, 87 volumetric efficiency curves for determining, 57 expression for, 53, 57 for a perfect gas, 57 parameters that affect, 53, 57 theoretical,53 Regenerated gas exchanger design of, 148- 153 vibration check, 153- 154 Reinforcing pads (external loadings) pad width, maximum, 170 disadvantage of pads, 170 Reynolds number, 9, 66-67, 7 4, 89 -91, 93, 95 -96, t25-127, 140, 141, l5l-152, 156-157, 1U non-Newtonian fluid, Metzner-Reed, 162-163 versus drag coefficients for long circular cylinders, r42 Rotating equipment APr 611,61 APr 612, 61 API 617, 61 API 618, 61 API criteria, 61-62 NEMA. See Nozzle Loadings. nozzle loadings on, 61-62 allowable, defined, 61-62 NEMA,61_62 applications for, 61 options to, basic, 62 steam turbines, ideal expansion joint, 64 turbo-expanders, reasonable values for, 63 typical for in-line pumPs, 61 piping systems for, 60-65 pulsation bottles. Se? Pulsation response spectra. steam turbines, piping to, 62 surge drums. 'gee Pulsation response spectra Rotary pumps, types of, 37 Screw pumps, 40-41 Shell-and-tube heat exchangers advantages of, 99 ASME Section VIII Division I Code, 99, 101 ASME tube joint load criteria, 1 13- 1 15 joint reliability factor. I l3-l14 maximum tube joint force, 113 tube joint load, 113 baffle cuts, 111 baffle details, 111 baffle lanes, channel and head, 128 baffle plates, 99 baffle windows, 139 various schemes, 139 baffles annular orifices, 110 doughnut and disc tYPes, 110 flow direction, used for, 107 horizontally cut, 107, 109 longitudinal, 109 structural supports, as, 107 verticaliy cut, 107 vibration dampers, as, 107 baffle windows, Ill basic components of, 107 -112 caloric temperature, 117 , 122-123, 158 Kern relationships for, I22 caloric versus arithmetic rnean, 122 chlorine superheater design, 154- 160 chiller, 101 condenser, 101 deflexion or ligament efficiency, 158 design classifications of, 101 final condenser, 101 fixed tubesheet, 102-1O4 fixed tubesheet design, 100 floating heat exchangers 211 242 Mechanical Design of Process Systems internal floating head design, 103-104 advantages of, 104 outside-packed floating head design, 103-104 operating range, 104 packed latern ring design, 103-1M operating range, 1M pull-through bundle design, 103- 104 limitations of, 104 types of, regenerated gas exchanger design, 148-153 sensible heat, 116- 117 shell-side, defined, 99 shell-side equivalent, tube diameter, 129, 152, 156, 164 shell-side pressure drop, \39, 152-153,157, 164-165 103- 104 forced circulation reboiler, 101 fouling resistances, recommended minimum, 125 friction factors for, shell-side surfaces, 140 heat transfer bulk temperature of fluid, 125 continuity equation, 128 convection, basic expressions for, 115 factor jH, 129,138, 152, 157 film coefficients, shell-side, 128 Kern correlation, 128 fouling factors, 124 bare tubes versus finned tubes, 124 definition of, 124 versus thermal conductance, 124 fouling resistance, 124 Fourier's law of heat conduction, 116 Grimson equation, for film coefficient, 126 inside film coefficient, 122, 151 laminar, 125 turbuient, 125 laminar boundary layer. 125 modes reboiler, 99, l0l kettle type, 99 of, 115 McAdams correlation, 125 film coefficient, lZZ, 126, 1,29 overall heat transfer coefficient, 152 caloric, 117, 122, 152, 157, 158 parameter jH, 129, 138 effective diameters for, 129 versus Reynolds number, 138 shell-side film coefficient, 151-152, 156, 163-t64 tube-side film coefficient, 151, i54-156 tube wall resistance, 124 turbulent boundary layer, 125 impingement baffles, i28 latent heat, I 16- 117 ligament or deflexion efficiency, 158 outside LMTD correction factor R 117- 121 multipass exchangers, variance in, 117 variance of, 117 overall heat transfer coefficient, 122 caloric, 117, 122, 152 partial condenser, 101 process evaluation of, 115-140 expression for, 139, 152 shell-side mass density, 151 shell-side mass flow rate, G,, 139, 152-154, 156, I O-l Sieder-Thte correlation, laminar flow, for, 125, 162 turbulent flow, for, 125 steam generator, 101 TEMA class B exchanger, 99, lO4 class C exchanger, 99, 104 class R exchanger, 99, 104 comparisons of types, 105 mode constants for tubes, 112 natural frequencies of straight tubes, I 12- I l3 natural frequencies of U-tubes, 113 nomenclature of, 102 TEMA specification sheet, 150, i55 tubes, stress, allowable compressive, l12 tubesheets, compressive stress induced OD, lll thermosyphon reboiler, 101 tie rods TEMA recommendations for, 110 uses of, 110 tube arrangements, pros and cons tube bundle, 99, 126, 128 flow area of, of, 152 Keys and London constants foq 129 tube bundle cross-flow arca, 128 staggered inline, for, 128 triangular layouts, for, 128 tube count tables, 130- 137 tube geometry angtlar pitch, 126-127 diamond-square pitch, 126 - 127 inJine square pitch, 126-127 inJine triangular pitch, 126-127 tubes bare, 107 bend radii, minimum, 109 boundary layer, 125 laminar, 125 turbulent, 125 buckling of 129 { 2rl:t Euler columl formula, 114 exchanger tubes, 113 Johnson short column equation, 1i4 finned, 107 foreign deposits, 124 inside film coefficient, 122 outside film coefficient, 122 pitch, nominal, 114 stress factors for, 159- 160 tabulated properties of, 108 tubesheets, 99 double tubesheets, 110 uses of, 110 maximum radial stresses in, 159 single tubesheets, 110 tubesheet-tube connections, typical, I 1 1 tubesheet layouts staggered in{ine, for, 128 triangular layouts, for, 128 typical, 128 tube-side defined, 99 tube-side mass flow rate, 151, 162 tube vibrations. See Tube vibrations. tube wall temperature, 117,122, 124 U-tube exchangers kettle type reboiler, 100 tubesheet vaporizer, fot 103 101 vapor-liquid equilibrium calculations, I 17 vertical gas-gas exchanger, 151 Silos. See Bins. Specific diameter, 48 versus specific speed, 49 Specific speed, 48 versus specific diameter, 49 Stack design anchor bolt torque, 26-27 base support detail for, 27 carbon precipitation in, 8 buckling stress allowable, 22 deflection, dynamic, 26 deflection, static, 26 excitation, flexural, 9 flexural frequency, 9 lining of, 8 effect of, 8 gunite,8 modulus of elasticity of, 8 Michell and Love equation, 9, 28 ovaling,8-9 flexural modes of, 9 in-plane, 9 out-of-plane,9 modes of, 9 ovaling frequency. See Flexural frequencl ovaling rings, 9, 26 natural frequency of, 9, 26 reasons for, 9 section modulus of, required, 9 pressure vessels, vertical differences bef$'een. 8 seismic response spectra, 8 vibration, cantilev er, 25 -26 vortex shedding frequency, 9, 26 vortex strakes, 9-11, 27 -28 clearances for, 11 critical wind velocities for, 10 fabrication detail of, 11 fabrication, method of, 11 helix angle of, 10 length of, 10 Morgan equation, 10, 28 radius of curvature of, l0 strake height, 10 range for, 10 wind design anchor bolt design for, 23 bearing pressure for, 23 base plate, Brownell and Young method, 24 chair design, Brownell and Young method, 24-25 compression rings, gusset plate thickness, required,25 effective diameters for, 20 weld, skirt-to-base ring, 25 wind load, 2l-22 wind moment, 21-22 wind pressure, 21 wind response spectra, 8 Steam turbines piping of, 62 Strouhal number, 9 Suction lift, IOr WAIe\ +5, I I TEMA class B exchanger, 99, 104 class C exchanger, 99, 104 class R exchanger, 99, 104 heat exchanger specification sheet, 150-161 mode constants for tubes, 112 natural frequencies of, straight tubes, 112- 113 U-tubes, 113 nomenclature for shell-and+ube heat exchangers. 102 standard, TEMA, 99, 104 TEMA types, composition of, 105 tie rods, 244 Mechanical Design of Process Systems recommendations uses of, for, 1 10 110 tube joint load formulations, 113 tubes, minimum bend radii, 109 stress, allowable compressive, I 12 tubesheets, compressive stress induced on, 111 Tube vibration baffle damage, modified damage number, 143, 153 baffle plate, illustrated, 143 displacements, inducing excessive, 143-144, t53-154 drag coefficients versus Reynolds number, 142 flow-induced vibration, 144 fluid vortices, force exerted on tubes, l4i jetting, or jet switching, 144 compared to turbulence, 146 cornpared to vortex shedding, 146 shear force on tube, l4l, 143, 153 shell-side fluid, velocity of, 141 maximum recommended, 148 Thorngren, John T., maximum velocity method, 139 tubes boundary conditions of continuous beams, 142 circle of contact, diameter of, 143 colliding of, 139 deflection oI, 141, 154 effective tube wall, 141 fatiguing of, 139 fluid force causing baffle impingement, 143 force coefficient, 146 fundamental natural frequency of, 146 natural frequency of, (Blevins formulation), 146, 154 shear of against baffles, 143 turbulence deflection, root-mean-square, 145 joint efficiency, 145 pressure distribution for, 144- 145 response spectra, 145 Wambsganss and Chen relation, 146 Venturi effect, 144 von Karman equation, 141 vortex shedding, 139, 144 compared to turbulence, 146 compared to whirling, 146 resonant frequency of, 141 vortex street, limits of, 141 vortices, breaking-up of, 141 whirling, 144 compared to turbulence, 146 compared to vortex shedding, 146 critical velocity, cxiteria of, 147 whirling parameter, for tube arrays, 148 Tubular Exchanger Manufacturing Association. TEMA. Vane pumps, 37 Velocity heads (K-values), 66-68, See 7 4, 88-89, 90-9 Vibration ovaling. Se€ Stack design. Rayleigh method for, 8. Also see Volume l. Viscosity absolute viscosity, 68 conversion to kinematic, 68 centrifugal pumps, effect on, 68, 70-72 converting centipose to SSU units, 74 kinematic,68 Vortex shedding, 8-9, 139, l4l,144, 146 Welding Research Council. See WRC. WRC 107 Standard, 169 WRC 297 Standard, 169 1