paper2 WRM2005 - CiteSeerX

Comparative study of methodologies determine inlet efficiency from test data. HEC-12 methodology vs UPC method.

to

M. Gómez1 , B. Russo1 1

Department of Hydraulic, Maritime and Environmental Engineering Technical University of Catalonia, Barcelona, Spain

Abstract The hydraulic capacity of a storm drainage inlet depends upon its geometry as well as the characteristics of the gutter flow. Inlet capacity governs both the rate of water removal from the gutter and the amount of water that can enter into the storm drainage system. Inadequate inlet capacity or poor inlet location may cause flooding on the roadway resulting in a hazard to pedestrians. Actually the most important reference that allows estimating inlet hydraulic capacities is the known HEC -12 procedure but it was elaborated for some different type of grate and its use is limited to these ones. In recent years the Department of Hydraulic, Maritime and Environmental Engineering (DEHMA) of the Technical University of Catalonia (UPC) has carried out a new methodology always usable for each type of grate and each type of street geometry, even that could be applied to inlets not previously tested but similar to those used in the experimental campaign A comparative study between these methodologies was carried out and it was demonstrated the similarity of the results in terms of captured flow according to the roadway flow. Particularly the hydraulic efficiency of a specific grate (P50*100) was studied according to the two methodologies and the results showed that for the same roadway flow the two functions are similar up to 120 l/s approximately and then the UPC methodology gives values of efficiency smaller. Keywords: Inlet interception capacity, gutter flow.

1 Introduction Storm sewer systems are typically designed as conveyance systems to prevent the nuisance and the flow damages that could be created during heavy storms. Stormwater is conveyed into the sewer system through inlets in roadway gutters, parking lots, and other locations. Normally surface runoff is not conveyed entirely by storm sewer; rather, it flows over the land surface in roadways according to efficiency of the inlets present. Actually the reference procedure for estimating inlet hydraulic capacities is the known “HEC -12 methodology” but this procedure was elaborated for some different types of grate and its use is limited to these ones. Particularly in march 1984, the U.S. Department of Transportation published the Hydraulic Engineering Circular No. 12, entitled “Drainage of Highway Pavements” that is widely known as HEC-12 and describes a semi-theoretical method for estimating inlet hydraulic capacities, [1]. HEC -22 has incorporated the same information, but actually the most important texts concerning to urban drainage still refer to HEC -12 as a reference-procedure in this field. In the 1997, the Department of Hydraulic, Maritime and Environmental Engineering (DEHMA) of the Technical University of Catalonia (UPC) started a new research line in the field of inlet hydraulics and one of the goals was the finding of a formula that could be applied for each type of grate and each type of street geometry, even that could be applied to inlets not previously tested but similar to those used in the experimental campaign.

2 Flow in gutter section In a uniform gutter section (Fig. 1), the depth flow is related to the spread and the pavement cross slope as: d = TS x . (1) The cross -sectional area of the flow is:

A=

Td T 2 S x . = 2 2

(2)

and the wetted perimeter is

P = T (1 + S x ) ≈ T . where: d = flow depth (m) T = spread (m) Sx = pavement cross slope (m/m) A = cross-sectional flow area (m2 )

(3)

Figure 1: Uniform gutter cross section Substitution of these expressions into the Manning equation yields

Q=

C f 53 83 12 S T S0 . n x

(4)

where: Q = flow in gutter section (m 3/s) C f = 0.376 n = Manning’s roughness coef ficient S0 = Gutter longitudinal slope (m/m) Equation (4) is a modified form of the Manning equation. The modification is necessary because the hydraulic radius does not adequately describe the gutter section, [2,3].

3 Inlet interception capacity The hy draulic capture efficiency is a function of grating type, gutter flow, and geometric conditions of the road. The efficiency of an inlet is defined as the ratio of the discharge intercepted by the inlet to the total discharge approaching the inlet: E =

Q int . Q

(5)

where: E = efficiency of the inlet Q int = discharge intercepted by the inlet (m 3/s) Q = total discharge approaching the inlet (m 3/s) Bypass flow is the term given to any discharge not intercepted by an inlet. 3.1 HEC-12 methodology to calculate the efficiency “E” Federal Highway Administration (FHWA) has developed a number of standardized grates designs, which are described in t he Table 1, [1].

Grate type

Description

Reticuline P-50

“Honeycomb” pattern of lateral and longitudinal bearing bars Parallel bar grate with bar spacing 48 mm on center Parallel bar grate with bar spacing 48 mm on center, and with 10-mm diameter lateral rods spaced at 102 mm on center Parallel bar grate with bar spacing 29 mm on center Curved vane grate with longitudinal bar spacing 82 mm on center and transverse bar spacing 114 mm on center 45º tilt-bar grate with longitudinal bar spacing 57 mm on center and transverse bar spacing 102 mm on center 45º tilt-bar grate with longitudinal bar spacing 83 mm on center and transverse bar spacing 102 mm on center 30º tilt-bar grate with longitudinal bar spacing 82 mm on center and transverse bar spacing 102 mm on center

P-50x100 P-30 Curved Vane 45º-60 tilt bar 45º-85 tilt bar 30º-tilt bar

Table 1: FHWA standard grate type The procedure considers that the analysis of the interception capacity of a grate inlet requires the determination of a frontal flow (Qw) that is the discharge in the gutter over the width W of the grate, and the side flow (Q s) that is the discharge in the gutter above the grate width. If the gutter section is uniform, the ratio E0 of frontal flow to total flow is given by: E 0 = 1 − (1 −

W 2 .67 . ) T

(6)

where: E0 = ratio of frontal flow to total gutter flow (Q w/Q) W = grate width (m) Once E0 is known, the gutter flow and side flow approaching the grate are given by the equations:

Q w = E 0Q .

(7)

and

Q s = (1 − E 0 )Q .

(8)

The frontal flow intercepted by the inlet, denoted by (Q w)int is: ( Q w ) int = R f Q w .

where: R f = 1-Kc(V-V0 ) ⇒ V ≥ V0 = 1 ⇒ V ≤ V0

(9)

K c = 0.295 V = Q/A, the flow velocity in the gutter (m/s) V0 = the velocity at which splash-over occurs (m/s) R f cannot be greater than one nor less than zero. Generally V0 is named splash-over velocity (the minimum velocity at which some of frontal flow passes over the top of the grate without being intercepted). Vo (and R f) depends on the grate type and its length in the direction of flow and can be determined from an apposite graph for the grates analyzed, Fig.1. It is evident that it is possible to know the different values of the splash over velocity V 0 only by experimental data. For this reason this methodology is useful only for the standard grates analyzed in this study or for grates that should be tested in laboratory previously in the same conditions. The side flow intercepted denoted by (Q s)int is:

(Q s ) int = R sQ s .

(10)

where R s depends on some factors and is given by:  K sV 1 .8 R s =  1 + S x L 2 .3 

  

−1

.

where: K s = 0.0828 Sx = roadway cross slope (m/m) L = grate length (m)

Figure 1: Graphs for determining Vo and R f for standard grate types

(11)

Combining the above equations gives the total discharge intercepted by an inlet:

Q int = (Q w ) int + ( Qs ) int = R f Q w + RsQ s = Q [R f E 0 + Rs (1 − E 0 ) ] .

(12)

The efficiency of the inlet is, therefore: E = R f E 0 + R s (1 − E 0 ) .

(13)

3.2 UPC methodology to calculate the efficiency “E” In the 1997 the Hydraulic and Hydrological Engineering Section of the Technical University of Catalonia (UPC) promoted a new research line in the field of the road grates efficiency, [4,5]. The most common grates were tested in a modern laboratory by a platform that can simulate the hydraulic behaviour of a roadway. Particularly, the platform can simulate roadway with transversal slope up to 4 and longitudinal slop up to 14% and it is possible to test drainage grates with a large range of flow (0–200 l/s). The UPC results jointed the efficiency of a grate to same parameters as such as empty area, gradient, form of chink, number and type of the bars. On the basis of these tests and the studies of the HR Wallingford (1998) a potential law expression was achieved, [6]: E = A(

Q −B . ) y

(14)

where: E = efficiency of the inlet Q = total discharge approaching the inlet (m 3/s) y = the flow depth (m) A and B = characteristic coefficients of the grate and specifically: A=

0.39 ⋅ (nt + 1)0.01 ⋅ (nl + 1) 0.11 ⋅ (nd + 1)0.03 . − 0. 13 ⋅p L .

− 0. 35

Ag

B = 0 . 36 ⋅

(15) (16)

W

where: A g = area that includes the empty area of the grate inlet (A H) p = ratio of the A g to the AH nt, n l, n d = number of transversal, longitudinal and diagonal bars L = length of the grate inlet W = width of the grate inlet Other grates were used to confirm this methodology and the results confirmed that it can be applied theoretically for each type of grate without previous experimental tests.

Equation (12) was achieved by a roadway with a widt h of 6 m corresponding to two driveways. By the hypothesis on uniform distribution of velocity it is possible to use this methodology for each type of roadways, Table 2, Fig.2, [7]. Width of half roadway x = 3 m For each y

E = E '= A (

Q

E = E '= A(

Q

roadway

y

)

− B

Width of half roadway x < 3 m y ≤ x·Ix

x·Ix ≤ y ≤ 3·Ix m

 Q E ' = A·    Q E ' = A ·   

y = 3·Ix m

roadway

y

roadway

y

⋅

)−

B

1 1 − (1 −

x ⋅ I y

3⋅ I y ⋅ x ⋅I 1 − (1 − y 1 − (1 −

roadway

y

x

x

x

   )2  

− B

 )2   ) 2  

− B

Width of half roadway x > 3 m Q

− B

y ≤ 3·Ix m

E = E '= A (

3·Ix m ≤ y ≤ x·Ix m

 Q roadway 3⋅ Ix 2  E'= A ⋅  ⋅ (1 − ( 1 − ) ) y y  

y = x·Ix m

 Q E ' = A ·   

roadway

y

)

3⋅ I y ⋅ x ⋅ I 1 − (1 − y 1 − (1 −

roadway

y

x

x

 )2   2 )  

−B

−B

where: y = flow depth Qroadway = approaching flow circulating on the road (m3 /s) Ix = transversal slope of the gutter (m/m) E’= efficiency of the inlet related to a width of roadway = 3 m Q int = E’Q Q = flow related to a width of roadway = 3 m (m3 /s) E = Q int/Q roadway Qint = total discharge intercepted by the inlet (m 3/s) E = efficiency of the inlet

Table 2: Efficient equations for different roadway types

Figure 2: Roadway cross section in the condition x > 3 m and 3Ix m ≤ y ≤ xIx m

4 Comparative study between the two methodologies The “P-50x100” is one of the grates presented in the study of the HEC -12 and among the other ones is the most similar to the grates produced in Europe, Fig.3. Its geometric characteristics are: Type of grate inlet: P50x100 Length: 0.818 m Width: 0.412 m Total Area: 0.3370 m2 Empty Area: 0.2734 m 2 Including Empty Area: 0.3224 m2 Number of longitudinal bars: 8 Number of transversal bars: 7 According to the two methodologies explained, its hydraulic behavior was analyzed for different street geometries and every time the efficiency was estimated. Specifically the study was elaborated for many flow depths as well roadway flows. Every time the intercepted flows, related to the same roadway flow, were calculated according to HEC -12 methodology and UPC method. For this reason it is possible to compare efficiency function in each case of geometric condition.

Figure 3: Grate inlet “P-50x100”

In the graphs below two cases with two specific geometric conditions are presented. The graphs consider the roadway flow circulating on a driveway of 3 meters and the intercepted flows by an inlet according to the analyzed methodology, Fig. 3,4.

Comparative graphic Q-Qint 1.2E-01

Qint (m3/s)

1.0E-01

Graphic UPC

8.0E-02

Graphic HEC12

6.0E-02 4.0E-02 2.0E-02

3.6E-01

2.8E-01

2.1E-01

1.5E-01

1.1E-01

7.3E-02

4.5E-02

2.5E-02

1.2E-02

4.3E-03

7.7E-04

1.7E-06

0.0E+00

Q (m3/s)

Figure 3: First case (Longitudinal Slope = 2%; Transversal Slope = 2%)

Comparative graphic Q-Qint 1.4E-01

Qint (m3/s)

1.2E-01

Graphic UPC

1.0E-01 8.0E-02

Graphic HEC12

6.0E-02 4.0E-02 2.0E-02

5.1E-01

3.9E-01

3.0E-01

2.2E-01

1.5E-01

1.0E-01

6.4E-02

3.6E-02

1.7E-02

6.0E-03

1.1E-03

2.4E-06

0.0E+00

Q (m3/s)

Figure 4: First case (Longitudinal Slope = 4%; Transversal Slope = 2%)

5 Conclusions A new methodology to determine inlet efficiency has been developed in the Technical University of Catalonia. This methodology allows calculating inlet efficiency for each type of great and each type of street according to characteristic parameters and it does not need previous experimental tests contrary to all methodologies actually used. A comparative study was carried out to compare UPC Methodology with HEC12 method universally considered the most important reference in this field. The results showed that, for the same roadway flow, the intercepted flows coincide up to 120 l/s approximately and then the UPC methodology gives values of efficiency (E) smaller. If we consider the range of the roadway flows (Q < 200 l/s) used in the tests to find experimental equations about efficiency we can mainly estimate the nearness of the results.

References [1]

[2] [3] [4] [5] [6] [7]

Brown, S. A., Stein, S. M. & Warner, J. C., Urban Drainage Design Manual, Hydraulic Engineering Circular No. 22. Federal Highway Administration, US Department of Transportation, Washington DC, 1996. Izzard, C. F., Hydraulics of Runoff from developed Surfaces, Proc. Highway Research Board, vol. 26. Highway Research Board, Washington DC, 1946. American Society of Civil Engineering (ASCE), Design and Construction of Urban Storm Water Management System. New York, 1992. Department of Hydraulic, Maritime and Environmental Engineering of the Technical University of Catalonia. Course o f Urban Hydrology, 2004. Martínez P., Gómez, M. V., Estudio de Eficiencia de la Captación de rejas. XIX Congreso Latinoamericano de Hidráulica, Córdoba, Argentina 2000. Spaliviero, F. Way, R. W. P., Spacing of Road Gullies. Hydraulic performance of BS EN 124 gully gratings. HR WALLINGFORD, 1998. Gómez, M. V., Russo, B. Metodología para el diseño de un nuevo sistema de captación en un tramo de calle en Barcelona. XXI Congreso Latinoamericano de Hidráulica, Sao Pedro, Brasil, 2004.