This article was downloaded by: [Florida International University] On: 29 December 2014, At: 12:31 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK ISH Journal of Hydraulic Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tish20 GENERALIZED GEOMETRIC ELEMENTS OF ARTIFICIAL CHANNELS: A NOTE Subhasish Dey M.ISH a a Department of Applied Mechanics , Regional Engineering College , Durgapur , West Bengal Published online: 07 Jun 2012. To cite this article: Subhasish Dey M.ISH (1998) GENERALIZED GEOMETRIC ELEMENTS OF ARTIFICIAL CHANNELS: A NOTE, ISH Journal of Hydraulic Engineering, 4:1, 1-4, DOI: 10.1080/09715010.1998.10514615 To link to this article: http://dx.doi.org/10.1080/09715010.1998.10514615 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. 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Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions VOL. 4, (I) GENERALIZED GEOMETRIC ELEMENTS OF ARTIFICIAL CHANNELS (1) THE INDIAN SOCIETY FOR HYDRAULICS JOURNAL OF HYDRAULIC ENGINEERING Downloaded by [Florida International University] at 12:31 29 December 2014 GENERALIZED GEOMETRIC ELEMENTS OF ARTIFICIAL CHANNELS : A NOTE by Subhasish Dey, M.ISH ABSTRACT The generalized equations for geometric elements of commonly used artificial irrigation channels are presented. The use of the proposed equations eliminates the need of separate computations for different channel sections. KEY WORDS : Open channel, Geometric elements, Irrigation channel. INTRODUCTION The effective and economic water transport techniques through artificial irrigation channels have been of immense importance in hydraulic engineering. Artificial channels are found to be of different types (Chow, 1959) depending on the purpose for which they are used. Discharge in an open channel is a function of its geometric elements. The geometric elements are the physical properties of a channel section which can be defined by the flow depth and other dimensions of the channel section. The estimation of flow that involves the use of geometric elements is a common and regular job of engineers. As the separate computation is needed for each channel section, the work becomes tedious. In this note, an attempt is made to formulate the generalized geometric elements of commonly used artificial open channels. The use of these formulae can reduce the volume of computational work. FORMULATION OF GENERALIZED GEOMETRIC ELEMENTS The most commonly used artificial irrigation channels as given in Chow ( 1959) are rectangular, trapezoidal, triangular, exponential, round cornered rectangular and round bottomed triangular (Figure I). The different geometric elements of these channels are generalized as follows: (I) Senior Lecturer, Department of Applied Mechanics, Regional Engineering College, Durgapur (West Bengal). Note : Written discussion of this paper will be open until 30th June, 1998. ISH JOURNAL OF HYDRAULIC ENGINEERING, VOL. 4. I 998, NO. I (2) GENERALIZED GEOMETRIC ELEMENTS OF ARTIFICIAL CHANNELS VOL. 4, (I) where A= flow area, y = flow depth, B = bottom width made by the tangent of side slopes, k 1 = coefficient for side slope, k2 = coefficient for curvature, n = exponent, and r = radius. (2) Downloaded by [Florida International University] at 12:31 29 December 2014 (3) (4) (5) (6) where T = top width, P = wetted perimeter, R = hydraulic radius, D = hydraulic mean depth, and Z = section factor. The value·s of coefficients and exponents, used in the developed equations, for different channel sections are given in Table 1. APPLICATION The use of the developed equations is demonstrated considering the case of best channel section. The condition for a best section is obtained differentiating Eqs (1) and (2) with respect to y and solving simultaneously for a minimum wetted perimeter condition, that is dP/dy =0. Therefore, one obtains the generalized equation for the condition for a best channel section as: (7) The above equation is applicable to all the channel sections given in Fig. I. The appropriate values of coefficients and exponents given in Table I are to be incorporated into Eq. (7) to obtain the condition for best channel section for a particular channel. Similar treatment can be made to obtain the generalized equations for other hydraulic problems involving geometric elements of the channels. CONCLUSION The generalized equation for geometric elements of commonly used artificial irrigation channels have been developed which eliminates the need of separate computations for different channel sections. ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 4. 1998, NO. I VOL. 4, (I) GENERALIZED GEOMETRIC ELEMENTS OF ARTIFICIAL CHANNELS ACKNOWLEDGEMENT The author appreciates the assistance provided by Mr. Bimalendu Dey. REFERENCES Chow, V. T. (1959). Open Channel Hydraulics. McGraw-Hill Book Co., New York, p. 20. Downloaded by [Florida International University] at 12:31 29 December 2014 APPENDIX : NOTATION A Flow area B Bottom width made by the tangent of side slopes b Bottom width of trapezoidal channel C Coefficient for exponential channel D Hydraulic mean depth k1 Coefficient for side slope Is Coefficient for curvature n Exponent P Wetted perimeter p Exponent for exponential channel R Hydraulic radius r Radius of curvature T Top width x Abscissa for exponential channel profile y Flow depth or ordinate for exponential channel profile Z Section factor z Side slope ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 4, 1998. NO. I (3) (4) VOL. 4, (I) GENERALIZED GEOMETRIC ELEMENTS OF ARTIFICIAL CHANNELS TABLE ·1 COEFFICIENTS AND EXPONENTS FOR DIFFERENT CHANNEL SECTIONS Section Downloaded by [Florida International University] at 12:31 29 December 2014 B n (2) (3) Rectangular Trapezoidal Triangular b b 0 0 2 2 Exponential* p-1 + 1 0 2C"(l+p)/(1+2p) Round cornered rectangular I b + 2r 0 Round bottomed triangular 2 2r( .JT+Z- z) z (1) k, (4) k2 (5) 0 0 0 z z 2[ 0 0.57t-2 z-( 1+ z2 f 5 ]+cot-l z * The equation for the profile of exponential channel is given by y = Cx P; where C = coefficient, and p = exponent. T b T \: }\ ~'} ~ It 1 0 T \:}} ~, b ~ T VI lliJ 0 T T y} .. ~ L @] if b VI 0 OJ FIG. 1 (a) RECTANGULAR, (b) TRAPEZOIDAL, (C) TRIANGULAR, (d) EXPONENTIAL, (e) ROUND CORNERED RECTANGULAR, (f) ROUND BOTTOMED TRIANGULAR ISH JOURNAL OF HYDRAULIC ENGINEERING, VOL. 4, 1998, NO. I