Subido por cazapuentes

Eficiencia Hidraulica de Sumideros. En ingles

Anuncio
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
Proceedings of the Institution of Civil Engineers
Water Management 164 February 2011 Issue WM2
Pages 81–90 doi: 10.1680/wama.900070
Paper 900070
Received 29/09/2009
Accepted 02/08/2010
Published online 06/12/2010
Keywords: drainage & irrigation/hydrology & water resources/
sewers & drains
ICE Publishing: All rights reserved
Methodology to estimate
hydraulic efficiency of drain
inlets
1
j
Manuel Gómez PhD
2
j
Beniamino Russo PhD
Full professor and civil engineer, Research Group FLUMEN, School of
Civil Engineering of the Technical University of Catalonia, Barcelona,
Spain
1
j
Associate professor and civil engineer, Group of Hydraulic and
Environmental Engineering of the Technical School of La Almunia
(University of Zaragoza), Zaragoza, Spain
2
j
Effective drainage of roadway pavements is essential to the maintenance of street service level and traffic safety.
Storm drainage inlets are used to collect urban runoff and discharge it to an underground sewer system. Inlet
efficiency governs both the rate of water removal from the gutter and the amount of water that can enter into the
storm sewer system and it depends upon inlet and road geometry as well as the hydraulics of the approaching flow.
In the present study a methodology to assess inlet efficiency from experimental tests is presented. An empirical
relationship is proposed to obtain the hydraulic efficiency as a function of inlet and street flow characteristics.
According to this procedure inlet efficiency could be estimated on the basis of grate geometry and the hydraulics of
the approaching flow. The procedure was compared with other methodologies proposed in recent years in the field
of urban hydrology.
Notation
A
Ag
AH
B
C
E
E9
g
Ix
Iy
K
K1
k
L
nd
nl
nt
p
Q
Qb
specific parameter of the inlet grate
minimum area including AH
inlet void area
specific parameter of the inlet grate
discharge coefficient of the grate
hydraulic inlet efficiency related to the real geometry
of the street
hydraulic inlet efficiency related to a width of
roadway x ¼ 3 m
acceleration of gravity
transversal slope
longitudinal slope
NFCO experimental coefficient
characteristic parameter of the inlet grate
proportional factor between flows
length of the inlet
number of diagonal bars
number of longitudinal bars
number of transversal bars
AH /Ag
flow discharge approaching the inlet circulating
through the models
carryover discharge
Qint
intercepted discharge by the inlet
Qroadway flow discharge approaching the inlet related to half
roadway
Qs
side discharge in the gutter over the width of the grate
(Qs )int side discharge intercepted by the inlet
Qw
frontal discharge in the gutter over the width of the
grate
(Qw )int frontal discharge intercepted by the inlet
T
water spread
v
flow velocity
vo
splash-over velocity
W
width of the inlet
x
half roadway width
y
hydraulic depth
ª
specific weight of water
r
density of water
1.
Introduction
Storm sewer systems are designed to reduce the risks and damage
produced by heavy storm events and are typically designed on the
assumption of near full-flowing pipes, often with little regard for
how surface runoff is delivered to the system (Schmitt et al.
2004; Smith, 2006). Furthermore, the surface runoff is almost
never fully conveyed by a storm sewer in cases of medium or
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
81
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
heavy rainfall owing to the lack of an efficient system of drainage
inlets. An inadequate surface drainage may be due to poor inlet
locations or to an inefficient individual inlet capacity.
2:
Q b ¼ Qroadway Q int
where Qb is the bypass discharge (m3 /s).
Inlet efficiency governs, at the same time, both the rate of water
removal from the gutter and the amount of water that can enter
the storm drainage system. In this frame, it is obvious that the
general problem of the urban drainage cannot consider these two
distinct components separately: (1) the surface (or ‘major’)
system composed of streets, ditches, and various natural and
artificial channels and (2) a subsurface storm sewer network or
‘minor’ system (Smith, 2006). Prior to the 1980s, Kidd and
Helliwell (1977) described the urban runoff process as a twophase phenomenon, incorporating a surface phase with an underground phase. They recognized the complexity of the interactions
between these two phases by stating: ‘Unfortunately, there is no
clear-cut interface between the two phases’. Surface collecting
systems represent this interface and nowadays the lack of knowledge about the hydraulic behaviour of these types of structures
(inlets, macro-inlets, continuous grates, etc.) has not been fully
overcome.
Poor knowledge of the hydraulic behaviour of surface drainage
structures could produce unreliable simulations from storm water
management models (Russo et al., 2005) and suggest a considerable amount of surface runoff that can interrupt traffic, reduce
skid resistance and increase the potential of hydroplaning (Guo,
1997). Generally a proper surface drainage of roadway pavements
is an essential condition to maintain a good street service level
and a good traffic safety level. Pavement drainage requires
consideration of the hydrological condition and rainfall pattern,
hydraulics of the gutter flow, hydraulic inlet capacity and risk
criteria related to urban runoff in the case of storm. All these
factors affect the design of an inlet drainage system.
2.
Inlet efficiency: state of the art
The hydraulic capacity of a storm drainage inlet is a function of
grate type, gutter flow, geometric road conditions and clogging
phenomena related to the void area of the grate. The efficiency of
an inlet is defined as the ratio of the discharge intercepted by the
inlet to the total discharge approaching the inlet
1:
E¼
In the field of analytical procedures, flow over a grate represents
a typical example of spatially varied flow with decreasing
discharge. Several authors, using trough semi-theoretical studies,
have proposed equations for the spatially varied flow profile
relating the intercepted flow to the specific energy or the flow
depth and a discharge coefficient C depending on the grate
geometry (Mostkow, 1957; Noseda, 1956; Subramanya and
Sengupta, 1981). These studies were carried out making the
assumptions of rectangular (transversal slope Ix ¼ 0%) and prismatic channels considering only frontal one-dimensional flow
(without side flow).
Moreover a relevant problem concerning inlet efficiency is that
the available published data on the hydraulic capacity of inlets
are specific to the particular typologies that were tested and have
not been generalized. As a consequence, the use of the methodologies carried out and the results obtained are only applicable to
a limited number of inlet types. For instance, these are the cases
of the Hydraulic Engineering Circular No. 22 (following HEC22) procedure (ASCE, 1992) or Neenah Foundry Company
(following NFCO) procedure (NFCO, 1998).
The HEC-22 procedure considers that the analysis of the
interception capacity of a grate inlet requires the determination of
a frontal flow (Qw ) which is the discharge in the gutter over the
grate width, and the side flow (Qs ) which is the discharge along
the side of the grate. Once Qw and Qs are known, the frontal flow
intercepted by the inlet (Qw )int and the side flow intercepted
(Qs )int can be determined from graphs and relationships obtained
experimentally. Specifically, efficiency E is related to a parameter
named splash-over velocity (vo ) (the minimum velocity at which
some of the frontal flow passes over the grate without being
intercepted). As with other parameters involved in this procedure,
vo , depends on the grate type and the grate length in the flow
direction and can be determined only for the grates tested during
the experimental campaign. Using the HEC-22 nomenclature,
hydraulic efficiency E (defined as a decimal between 0 and 1)
becomes
Q int
Qroadway
3:
where E is the hydraulic inlet efficiency (defined as a decimal
between 0 and 1), Qint is the discharge intercepted by the inlet
(m3 /s), and Qroadway is the total discharge approaching the inlet
related to half roadway (m3 /s).
The flow that is not intercepted by an inlet, carryover (ASCE
1992; Guo, 1997) or bypass flow (Nicklow and Hellman, 2004) is
defined as follows:
82
E¼
(Qw )int þ (Qs )int
Qroadway
In the context of the inlet manufacturers, a North American
foundry tested its grates to calculate their hydraulic capacity. The
results were plotted logarithmically for given longitudinal and
transverse slopes. Based on these results, the following relationship between the flow intercepted by the inlet Qint (expressed in
cubic feet per second) and the water depth (expressed in feet) at
the kerb immediately upstream from the inlet (y) was proposed
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
Water Management
Volume 164 Issue WM2
4:
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
Qint ¼ K y 5=3
The specific parameter K varies depending on longitudinal (I y )
and transversal street slopes (Ix ). Evidently the methodology can
be used only for the tested grates (NFCO, 1998).
A few generalised design methods for predicting the flow
capacity of inlets have been identified (Argue, 1986; Li, 1956;
Spaliviero and May, 1998). The first method was developed by Li
at John Hopkins University (Li, 1956). This method requires the
knowledge of three non-dimensional coefficients, and only very
limited testing has been carried out to determine their values for
the types of grates used in Europe. It appears to be fairly
generally accepted that hydraulic testing of gratings can be
carried out satisfactorily using scale models (Spaliviero and May,
1998). This implies that correct application of Froude similarity
should enable results from this phase of the study to be generalized to inlets of different sizes. In order to evaluate its suitability,
Li’s method was analysed in a study of the Hydraulic Research
Wallingford Limited (following HR Wallingford) (Spaliviero and
May, 1998) in the UK because it was the normal procedure
indicated by the British Standard Code of Practice (BS 6367)
(BSI, 1983) to design the drainage systems for roofs, roads and
other paved areas. In particular it was demonstrated that nondimensional parameters used in Li’s procedure are not constant
but depend on the flow condition upstream from the inlet.
The study concerned typical grates used in the UK (these grates
present a poor hydraulic efficiency and dimensions smaller than
the common grates used in the rest of Europe and in the USA)
and, according to the experimental protocol, maximum circulating
flows were rather limited (Q/y ratio reached the maximum value
of 1.5) (Martı́nez, 2000). The results proposed in this paper
improve the procedure demonstrating the ineffectiveness of
Equation 5 for a large spectrum of circulating flow (Q/y ratio up
to 15–20) and for the typical grates used in other countries.
3.
Experimental campaign
3.1 Test facilities
The most common inlets used in Barcelona were tested in the
hydraulic laboratory of the Technical University of Catalonia
(following UPC) by a platform that can simulate the hydraulic
behaviour of a roadway (Figure 1). Tests were made in a 1 : 1 scale
model of a roadway measuring 3 m wide and 5.5 m long. The
platform is able to simulate lanes with a transversal slope up to 4%
and longitudinal slope up to 14%. According to the system
capacity, it is possible to test drain inlets and study their hydraulic
capacity for a large set of flows (0–0.2 m3 /s) (Gómez et al., 2002).
The second method (Spaliviero and May, 1998) constitutes the
basis of the methodology that will be explained in this paper. In
1996 the Highways Agency of the UK commissioned HR Wallingford, in association with the Transport Research Laboratory, to
carry out a study on the hydraulic performance of inlets used to
collect surface runoff from roads. The study consisted of experimental tests on several inlet grates used in the UK and the
objective was to develop a consolidated design method to define
inlet spacing depending on the road geometry and the grate type.
Tests were carried out using a 1 : 1 hydraulic model. Through the
analysis of the results, it was demonstrated that inlet efficiency E
and the ratio Q/y can be related, where Q is the discharge
circulating through Spaliviero and May’s model and y is the flow
depth upstream from the inlet measured at the kerb. In this case
all the efficiency values from different flow widths and crossslopes have been collapsed into a single curve which can be
approximated as a straight line. In this way, the analysis of the
experimental data showed that, except at low efficiency values,
the results for an individual inlet could be described satisfactorily
by a linear equation E against Q/y (Spaliviero and May, 1998)
5:
E ¼ 102:7 K 1
(a)
Q
y
(b)
where E is the inlet efficiency (expressed in %) and K1 is a
characteristic parameter related to the grate geometry.
Figure 1. UPC platform and testing area
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
83
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
Pumps supply the flow up to a tank placed approximately 15 m
above the platform. A motorised slide valve regulates the flow
discharged to the model. Discharge measurement is done by an
electromagnetic flow meter with an accuracy of 1 l/s. The flow
circulates through the model, first through a tank located upstream
of the platform. This tank dissipates the flow energy and provides
a horizontal profile to the surface water level. In this way the
surface water elevation is the same for the entire platform width
and the model reproduces the runoff through a roadway in a more
realistic way. In this frame the flow may more easily reach the
steady and normal depth conditions. The discharge intercepted by
the inlet is conveyed to a V-notch triangular weir and the flow
measurement is carried out through a limnimeter with an accuracy
of 0.1 mm. Flow depth measurements on the platform are obtained
directly with a thin graduated invar scale.
The first results of the experimental campaign showed that inlet
efficiency decreased for high longitudinal slopes and circulating
flows and increased for high transversal slopes. For the maximum
circulating flow of testing (0.2 m3 /s) and high longitudinal slopes
(from 4 to 10%) the inlets tested presented a hydraulic efficiency
between 10 and 20% depending on the transversal slopes (Figure
4). Experimental data were used to create summary tables about
hydraulic efficiency for each type of grate inlet depending on the
geometric conditions of the street. For cases not included in the
testing protocol, interpolation and extrapolation were required.
For all these reasons a new and more general expression was
developed.
3.2 Testing protocol and UPC methodology
As a first step in the experimental campaign, 11 different inlets
(Table 1) were tested to determine their hydraulic capacity for a
large range of geometric conditions and approaching discharges.
The results for the first nine inlets (Figure 2) were used to
develop a methodology to determine inlet efficiency, while the
data concerning the latest two inlets were used to validate the
procedure (Figure 3).
The testing protocol established the following geometric conditions for different circulating flows:
(a) Q (total discharge approaching to the inlet through the
model): 0.02, 0.05, 0.1, 0.15 and 0.2 m3 /s
4.
Hydraulic approach
From the dimensional analysis it can be established that the
discharge flow captured by any particular grate depends basically
on the grate size and shape, water depth and velocity of the flow
upstream of the inlet, and the specific weight and density of the
water. This relationship can be expressed as
Qint ¼ f ð L, y, v, ª, rÞ
in which Qint is the discharge intercepted by the inlet, L is a
characteristic length of the problem, y and v are the water depth
and velocity in the gutter and street upstream of the inlet, and ª
and r are the specific weight and density of water. Dimensional
analysis leads to the relationship
6:
Qc
y
v
pffiffiffiffiffiffiffiffiffi ¼ f
, pffiffiffiffiffiffiffi
T
gT
gT 5
(b) Ix (transversal slope): 0, 1, 2, 3 and 4%
(c) I y (longitudinal slope): 0, 0.5, 1, 2, 4, 6, 8 and 10%.
As can be expected, one of the dimensionless numbers is the
Froude number, because the flow along the street is basically
Grate
Length (L):
cm
Width (W):
cm
Area including
void area (Ag ):
m2
Void area
(AH ): m2
Number of
longitudinal bars
(nl )
Number of
transversal bars
(nt )
Number of
diagonal bars
(nd )
Type
Type
Type
Type
Type
Type
Type
Type
Type
Type
Type
78
78
64
77.6
97.5
80
60.2
74.5
100
60.2
99.9
36.4
34.1
30
34.5
47.5
30
31.5
26
50
31.5
50
0.2114
0.1850
0.1647
0.2250
0.3431
0.1622
0.1807
0.1540
0.5000
0.1807
0.4940
0.1214
0.0873
0.0693
0.1050
0.1400
0.0736
0.0881
0.0852
0.2012
0.0865
0.1760
5
1
1
2
3
0
2
1
1
2
1
1
17
0
13
7
15
1
0
3
0
3
0
0
12
0
0
0
10
11
21
8
28
1
2
3
4
5
6
7
8
9
10
11
Table 1. Geometric characteristics of the tested grates
84
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
1
4
7
Figure 2. Some of the grates tested during the experimental
campaign (grate types 1, 2, 3, 4, 5, 6, 7, 8, 9)
2
3
8
6
9
5
Figure 3. The two grates used to validate the methodology
carried out (grate types 10 and 11)
governed by gravity forces. The other two numbers are related
one to the cross-section (y/T, invert aspect ratio if y is water depth
and T is water spread), and the other to the approaching flow. So
the first term can be expressed with another dimensionless
number, E ¼ Qint /Q, inlet/grate efficiency. Any data obtained
from laboratory testing could be expressed in terms of these
dimensionless numbers.
Different tests were carried out with the dimensionless numbers
proposed, but finally the same ratio Q/y was used, presented in
Spaliviero and May (1998), the parameter that showed the best
results for the whole data set for every inlet. On the basis of the
analysed data, it was shown that the function efficiency plotted
against Q/y is not exactly linear as supposed by Spaliviero and
May. In fact for a large spectrum of flow conditions (up to
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
85
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
1·0
E
Grate Type 8
Q ⫽ 0·2 m3/s
0·8
Ix ⫽ 4%
0·6
Ix ⫽ 2%
0·4
Ix ⫽ 0%
0·2
0·0
0
0·5
1
4
2
6
Longitudinal slope: %
8
10
Figure 4. Test results related to the grate 3 and different
geometric conditions for an approaching flow of 0.2 m3 /s and
different transversal slopes (Ix )
1·0
0·9
0·8
0·7
0·6
E 0·5
0·4
0·3
0·2
0·1
0·0
Experimental values
Experimental trendline
E ⫽ 0·3551(Q/y)⫺0·85
R2 ⫽ 0·9323
4
2
0
6
8
Q/y: m2/s
10
14
12
Figure 5. Experimental data and proposed power trendline
0.2 m3 /s) and consequently, with a range of hydraulic efficiencies
as low as 10%, a power law expression was proposed
7:
E9 ¼ A
the grate (such as void area, number and type of the bars, etc.)
through two parameters A and B
B
Q
y
:
A¼
8:
where E9 is the hydraulic efficiency of the inlet for a 3 m wide
lane (defined as a decimal between 0 and 1), Q is the discharge
approaching the inlet circulating through the model (m3 /s), y is
the flow depth measured at the curb immediately upstream from
the inlet (m), A is the empirical coefficient of the inlet grate, and
B is the empirical coefficient of the inlet grate.
High correlation coefficients (from 81% up to 93%) between
experimental data and potential trendlines were obtained for all
the inlet grates (Table 2; Figure 5). As the background and the
state of the art in this field demonstrate, one of the most
important problems related to inlet efficiency assessment is that
the procedures developed can be used only for the grates tested
during previous experimental campaigns. In order to estimate
inlet efficiency without inlet-specific laboratory data, based on
the experience of Spaliviero and May (1998), the second phase of
this study consisted of relating the characteristic parameters A
and B and the geometry of the inlet grates.
The important goal obtained was that these coefficients, which
should properly be determined by experimental tests, could be
estimated from some geometric characteristics too. Experimental
results linked inlet efficiency to some geometric parameters of
Grate type
Correlation coefficient: %
1:988 A0g 403
:
:
L0179
B ¼ 1:346 0394
W
9:
where Ag is the area of the smallest rectangle having sides
parallel to the kerb containing all the void of the grate (including
bars area) (m2 ), p is the ratio between the void area (AH ) and Ag
(in %), nt is the number of transversal bars, nl is the number of
longitudinal bars, nd is the number of diagonal bars, L is the
length of the inlet (cm) and W is the width of the inlet (cm).
In comparison with the Spaliviero and May (1998) expression,
coefficients A and K1 present a relevant similarity, while the new
coefficient B considers the main dimensions of the grate. In the
previous studies, grates with small dimensions (only one reached
a length of 50 cm) were tested. This type of grate is typical of
countries with low rainfall intensity. On the contrary a large
spectrum of grate dimensions was used in this study (width: from
33 to 63 cm; length: from 47.5 to 100 cm).
Experimental results related to other inlets (types 10 and 11) were
1
2
3
4
5
6
7
8
9
10
11
81.04
91.20
92.13
85.08
88.39
88.05
90.34
93.23
82.53
88.73
81.97
Table 2. Correlation coefficient between experimental data and potential law achieved
86
:
p0:190 (nt þ 1)0 088 (nl þ 1)0 012 (nd þ 1)0 082
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
Grate type 10
1·0
0·9
0·8
0·7
0·6
E 0·5
0·4
0·3
0·2
0·1
0·0
Sidewalk
Platform lane of 3 m width
Experimental values
Q
Experimental trendline
y
Ix
Calculated trendline
E ⫽ 0·3522(Q/y)⫺0·718
R2 ⫽ 0·8873
0
5
10
15
Q/y: m2/s
20
Qroadway
Figure 7. Roadway cross-section for the condition x . 3 (m) and
3Ix < y < xIx
25
Figure 6. Validation phase of the procedure by two other grates
(grate type 10)
platform). A specific case is shown in Figure 7, and the values of
coefficient k for each street geometric condition and each flow
depth y are shown in Table 3. Once E9 was calculated, the
intercepted flow (Qint ) could be determined by the equation
11:
used to validate the procedure carried out (Figure 6). The great
similarity between the potential curves plotted from experimental
data and the curve plotted by the calculation of parameters A and
B on the basis of grates geometry can be seen in Figure 6. So,
through Equations 7, 8 and 9, it is possible to approach the
hydraulic efficiency of any inlet in a similar way to the tested ones,
in cases where there have been no experimental tests.
The procedure for inlet efficiency estimation was carried out from
experimental tests on a 3 m wide platform, so it should be used
for a roadway with two lanes of 3 m width (one lane for each
traffic direction). In order to extend the methodology to any
roadway width with uniform gutter, assuming the hypothesis of
uniform velocity distribution in the hydraulic cross-section, other
equations were determined. For streets with several lanes presenting a half roadway width x that is different to 3 m, it is possible
to generalise Equation 7 according to the flow depth (y)
10:
x: width of half roadway
Qroadway B
E9 ¼ A k
y
where y is the flow depth immediately upstream from the inlet
(m), Qroadway is the flow approaching an inlet related to half
roadway (m3 /s), E9 is the inlet efficiency related to a width of
half roadway x ¼ 3 m (defined as a decimal between 0 and 1) and
k is the coefficient related to the street geometric conditions and
to the flow depth (y).
Qroadway is the circulating flow associated with the real geometry
of the street, whereas Q was the circulating flow through the
model. Flow hydraulic section, and consequently the flow depths,
may vary depending on the street geometry. Qroadway and Q
generate the same flow depth at the kerb y. The product k Qroadway
represents the discharge Q approaching the inlet for a roadway
width x ¼ 3 m (or the discharge circulating through the UPC
Qint ¼ E9 Q ¼ E9 k Qroadway
The most common hydrological softwares (such as HEC-HMS)
or storm sewer model (SWMM5.0, Mike Urban, Infoworks CS,
Half roadway width x ¼ 3 m
Any y
k¼1
Half roadway width x , 3 m
y < xIx
k¼1
xIx < y < 3Ix
k¼
1
1 1
y > 3Ix
x Ix
y
2
3 Ix 2
1 1
y
k¼
x Ix 2
1 1
y
Half roadway width x . 3 m
y < 3Ix
k¼1
3 Ix 2
3Ix < y < xIx
k ¼1 1
y
y > xIx
3 Ix 2
1 1
y
k¼
x Ix 2
1 1
y
Note: k is the coefficient related to the street geometric conditions
and to the flow depth y; Ix is the transversal slope of the gutter (m/m);
k is the correlation coefficient (m/m); x is the half roadway width (m);
y is the flow depth upstream of the inlet (m).
Table 3. Coefficient k for each type of street geometric conditions
and each flow depth
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
87
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
etc.) allow the characterisation of diversion elements (inlets,
weirs, etc.) through inflow/outflow tables. From Equations 10 and
11 it is possible to obtain a very useful expression that relates the
approaching discharge to the inlet and the intercepted one
and to compare these results with the experimental values
obtained during the tests. In Table 4 the result for the longitudinal
slope I y ¼ 1% and transversal slope Ix ¼ 0% are shown. In this
table it is possible to observe that discharge coefficients C and
intercepted flow values Qint are generally lower than experimental
data. These differences are due to the intercepted flow coming
from side flow and seem to justify the need for empirical
approaches for the study of inlet efficiency in order to take into
account the two-dimensional behaviour of the flow. Moreover, it
was demonstrated that, in the case of gutter flow, the coefficient
of discharge was strongly influenced by the non-zero transversal
slope (Martı́nez, 2000).
12:
Qroadway B
Qint ¼ k Qroadway A k
y
Owing to the laboratory conditions described in the previous
section, the kinematic wave model and normal depth conditions
could be assumed as a first approach for the inlets system design.
It is clear that for the particular geometric conditions of the street
(for example low longitudinal slopes) this approach may cause
significant deviations. So assuming normal depth upstream of the
inlet (in m), Qroadway (in m3 /s) can be estimated by Izzard’s
equation
13:
Qroadway ¼
Cf 8=3 1=2
y Iy
n Ix
where Cf is the constant (¼ 0.376 m1=3 /s for SI units), n is the
Manning’s roughness coefficient, Ix is the gutter transversal slope
(m/m), and I y is the gutter longitudinal slope (m/m).
Equation 13 is a modified form of the Manning equation. Izzard
modified Manning’s equation because the hydraulic radius does
not adequately describe the gutter cross-section, particularly
where the water spread may be more than 40 times the curb depth
(Izzard, 1946).
5.
Comparative analysis of the UPC method
and other procedures
First several analyses were carried out to calculate the discharge
coefficients C and intercepted flow Qint by the Subramanya and
Sengupta (1981) and Noseda (1956) approach for the grate type 2
Concerning the comparison with experimental methodologies,
the UPC procedure was compared to the HEC-22 (US Department of Transportation, 1996) and NFCO (1998) methods.
Some drain inlets were analysed through these different
methodologies and the similarity of the results in terms of
efficiency was demonstrated (Gómez and Russo, 2005). In
particular Figure 8 shows the captured flows, calculated by the
UPC and HEC-22 methodologies, plotted against the circulating
flows for a specific grate analysed in the HEC-22 circular (P50*100). In this graph, which is related to a specific geometric
configuration, it is possible to observe that the captured flow
values are very similar for the circulating flow range 0–
0.12 m3 /s. For higher flows, HEC-22 proposes a higher efficiency than the UPC method. The same behaviour was observed for other geometric conditions. The maximum
circulating flow considered in the HEC-22 was 0.14 m3 /s, for
higher values extrapolation is required, while during the UPC
experimental campaign the value of the maximum flow reached
was 0.2 m3 /s. So the HEC-22 procedure seemed to overestimate
hydraulic efficiency for high circulating flows. The UPC
procedure was also compared with the NFCO (1998) method.
In this case the grate R-3246-E-F type C was analysed and
chosen for its similarity to the grates tested during the UPC
0·12
Comparative graph Q–Qint
Analytical data
Experimental data
Q: m3 /s
y: m
C
Qint : m3 /s
C
Qint
0.050
0.100
0.150
0.215
0.014
0.024
0.032
0.040
0.08
0.09
0.09
0.09
0.005
0.008
0.009
0.010
0.05
0.10
0.14
0.16
0.004
0.008
0.014
0.018
Table 4. Comparative analysis between numerical and
experimental approaches in terms of discharge coefficients and
intercepted flows for the grate type 2 and a longitudinal slope
I y ¼ 1%
88
Qint: m3/s
0·10
0·08
UPC
HEC-22
0·06
0·04
0·02
0·00
0·00 0·01 0·02 0·03 0·05 0·08 0·12 0·17 0·23 0·30
Q: m3/s
Figure 8. Intercepted flow plotted against circulating flow for the
grate P-50*100 of the HEC-22 procedure and a specific grate
geometry (transversal slope ¼ 2%, longitudinal slope ¼ 2%).
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
Comparative graph (Iy ⫽ 1%)
30
20
K
10
NFCO
UPC
0
0
1
2
3
Ix: %
4
5
6
Figure 9. Comparative graph about ‘K’ data between UPC and
NFCO methodologies for the grate R-3246-E-F Type C and the
longitudinal slope Iy ¼ 1%
experimental campaign. As in the other comparative study, the
hydraulic capture efficiency of this grate was analysed for
different geometric conditions according to the two methodologies. The results showed a great convergence of the data,
above all for low longitudinal slopes (Figure 9). In this case
the comparative study concerned circulating flows up to
0.12 m3 /s.
6.
Conclusions
Considering a 1 : 1 scale hydraulic structure, a series of experimental studies on inlet grates were carried out considering higher
discharges than the values used in previous experimental studies.
A new methodology for inlet efficiency estimation has been
developed and it can be used for a large spectrum of inlet
dimensions. A potential equation to relate hydraulic inlet capacity
to street flow conditions and two inlet-specific parameters is
proposed. The specific parameters can be obtained from test data
or can be approached from the inlet geometry, so the procedure
can be applied to any non-tested inlet similar to those presented.
The procedure has been generalised for each geometric condition
of streets with uniform triangular gutter section including a
coefficient k, as a function of the road geometry. Comparative
studies were carried out among some methodologies. The results
confirm the usefulness of the UPC procedures and a great
convergence in terms of results. Moreover, the proposed methodology could be applied to characterise, through inflow/outflow
tables, the hydraulic surface drainage structures in the codes
normally used for the approach of sewer system and dual
drainage modelling.
REFERENCES
Argue JR (1986) Storm Drainage Design in Small Urban
Catchments, a Handbook for Australian Practice. Australian
Road Research Board, South Vermont, Victoria, Australia,
Special Report No. 34.
ASCE (American Society of Civil Engineering) (1992) Design and
Construction of Urban Stormwater Management System.
ASCE Manuals and Reports on Engineering Practice No. 77,
ASCE, New York, USA.
BSI (British Standards Institution) (1983) BS 6367: Drainage of
Roofs and Paved Area. BSI, London, UK.
Gómez M and Russo B (2005) Comparative study of
methodologies to determine inlet efficiency from test data.
HEC-12 methodology vs UPC method. Proceedings of the
Conference Water Resources Management III, Wessex
Institute of Technology. WIT Press Southampton, Boston,
UK, pp. 633–642.
Gómez M, Sánchez H, Malgrat P, et al. (2002) Inlet spacing
considering the risk associated to runoff: application to
streets and critical points of the City of Barcelona.
Global Solutions for Urban Drainage, 9th International
Conference on Urban Drainage, (9ICUD) (Strecker EW
and Huber WC (eds)). ASCE/IWA/EWRI/IAHR,
Reston, VA.
Guo JCY (1997) Street Hydraulics and Inlet Sizing. Using the
Computer Model UDINLET. Water Resources Publications,
LCC, Colorado, USA.
Izzard CF (1946) Hydraulics of runoff from developed surfaces.
Proceedings of the Highway Research Board, vol. 26, pp.
129–150, Highway Research Board, Washington DC,
USA.
Kidd CHR and Helliwell PR (1977) Simulation of the inlet
hydrograph for urban catchments. Journal of Hydrology,
35(1–2): 159–172.
Li WH (1956) The Design of Stormwater Inlets. John Hopkins
University, Baltimore, MD, USA, internal report.
Martı́nez P (2000) Estudio de eficiencia de la captación de rejas
y criterios de ubicación en viales urbanos. Thesis for the
Civil Engineer Degree, Technical University of Catalonia,
Barcelona, Spain.
Mostkow MA (1957) A theoretical study of bottom type water
intakes. La Houille Blanche 12(4): 570–580.
NFCO (Neenah Foundry Company) (1998) Inlet grate capacity.
In Construction castings, Catalog – R, 12th edn.
Engineering Laboratory Design, Inc., Neenah, Wisconsin,
USA.
Nicklow JW and Hellman PA (2004) Optimal design of storm
water inlets for highway drainage. Journal of
Hydroinformatics 06(4): 245–257.
Noseda G (1956) Correnti permanenti con portata
progressivamente decrescente, defluenti su griglie di fondo.
L’Energia Elettrica 33(6): 565–584.
Russo B, Gómez M, Martı́nez P and Sánchez H (2005)
Methodology to study the surface runoff in urban streets and
the design inlets systems. Application in a real case study.
Proceedings of the 10th International Conference on Urban
Drainage, Copenhagen, Denmark.
Schmitt TG, Thomas M and Ettrich N (2004) Analysis and
modeling of flooding in urban drainage systems. Journal of
Hydrology 299(3–4): 300–311.
Smith MB (2006) Comment on ‘Analysis and modeling of
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
89
Water Management
Volume 164 Issue WM2
Methodology to estimate hydraulic
efficiency of drain inlets
Gómez and Russo
flooding in urban drainage systems’. Journal of Hydrology,
317(1–2): 355–363.
Spaliviero F and May RWP (1998) Spacing of Road Gullies.
Hydraulic Performance of BS EN 124 Gully Gratings. HR
Wallingford, UK, internal report.
Subramanya K and Sengupta D (1981) Flow through bottom
racks. Indian Journal of Technology 19(2): 64–67.
US Department of Transportation (1996) Urban Drainage Design
Manual. US Department of Transportation, Washington DC,
USA, Hydraulic Engineering Circular No. 22.
WHAT DO YOU THINK?
To discuss this paper, please email up to 500 words to the
editor at [email protected] Your contribution will be
forwarded to the author(s) for a reply and, if considered
appropriate by the editorial panel, will be published as a
discussion in a future issue of the journal.
Proceedings journals rely entirely on contributions sent in
by civil engineering professionals, academics and students.
Papers should be 2000–5000 words long (briefing papers
should be 1000–2000 words long), with adequate illustrations and references. You can submit your paper online via
www.icevirtuallibrary.com/content/journals, where you
will also find detailed author guidelines.
90
Downloaded by [ Mr Luis Miguel Millan Galante] on [17/08/19]. Copyright © ICE Publishing, all rights reserved.
Descargar