Skip to document
Welcome to StudocuSign in to access the best study resources
Guest user
0followers
HomeMy LibraryAsk AI
  • You don't have any recent items yet.
My Library
  • You don't have any courses yet.
  • You don't have any books yet.
  • You don't have any Studylists yet.

Discharge Characteristics of Weir-Orifice and Weir-Gate Structures

okey
Course

Civil Engineering

32 Documents
Students shared 32 documents in this course
Academic year: 2022/2023
Uploaded by:
Anonymous Student
This document has been uploaded by a student, just like you, who decided to remain anonymous.
Universitas Brawijaya

Comments

Please sign in or register to post comments.

Preview text

Discharge Characteristics of Weir-Orifice

and Weir-Gate Structures

Saeed Salehi 1 and Amir H. Azimi, M 2

Abstract: The discharge characteristics of flow over and under different weir-gate structures were investigated using dimensional analysis

and multivariable regression techniques. Based on the shape and geometry of weir-gates, seven weir-gate structures were classified. The

interaction factor, defined as the ratio of the measured discharge over and under the weir-gate structure to the sum of the predicted weir and

gate discharges from the literature, was calculated for all types of weir-gate models. Six weir-gate models were experimentally tested to study

the discharge characteristics of flow over weirs of finite crest length and under gate. The interaction factors were correlated with the geometry

parameters for all weir-gate models with an average coefficient of determination of 0. A series of regime plots was developed to assist

designing the weir-gate structures as flow distributors for a sharp-crested weir-gate and a weir of finite crest length with an offset. The regime

plots show the contribution of weir and gate discharges for different weir-gate geometries. A critical normalized head was introduced as the

flow through the weir-gate structure is equally divided by the weir and gate. Based on the weir-gate geometry and discharge, general empirical

equations were developed to estimate the critical normalized head for practical engineering applications. DOI: 10/(ASCE)IR-

4774. © 2019 American Society of Civil Engineers.

Author keywords: Flow measurement; Weirs; Weir-gates; Sluice gates; Free flow; Weirs of finite crest length; Combined weir and gate.

Introduction

Weirs are commonly used as flow-measuring and water level

control structures in natural streams and irrigation channels. To

increase hydraulic performance and sediment removal capacity of

weirs, an opening (i., a sluice gate or orifice) is often included in

the design, and the resulting new weir structure is called a weir-gate

structure in the literature (Norouzi Banis 1992; Alhamid 1999;

Negm et al. 2002; Hayawi et al. 2008; Samani and Mazaheri 2009;

Severi et al. 2015). In weir-gate design, water passes simultane-

ously over and under the weir-gate structure. Therefore, for a con-

stant upstream head, the discharge passing through a weir-gate is

higher than the discharge over a weir of the same geometry. In ad-

dition, weir-gate structures experience more energy dissipation

due to interaction of the weir’s nappe with the wall jet coming off

from the gate. The high energy dissipation in weir-gate structures

significantly reduces scour formation downstream of irrigation

channels, and as a result, makes them a suitable choice for earthen

canals (Uyumaz 1998). It is also possible to employ weir-gate

structures as flow distributors, and the present study investigated

this possibility.

The schematic of the weir-gate models used in this study is

shown in Fig. 1. Table 1 lists the geometries and flow ranges of the

weir-gate models that were collected from the literature. One of

the early models of weir-gate structures was introduced by Norouzi

Banis ( 1992 ). In this simple weir-gate structure, a sharp-crested

weir is offset from the channel bed to form a fully suppressed gate

[Table 1 , Model 1 and Fig. 1(a)]. Samani and Mazaheri ( 2009 )

extended the study of Norouzi Banis ( 1992 ) by testing the fully

suppressed weir-gate structure in semisubmerged and fully sub-

merged flow conditions. The fully suppressed weir-gate structure

can be installed with an angle to form an oblique weir-gate struc-

ture [Table 1 , Model 2 and Fig. 1(b)]. Jalil and Abdulsatar ( 2013 )

proposed an empirical equation based on experimental data and

dimensional analysis to predict discharge through oblique weir-

gates. They reported that the major parameters affecting the head–

discharge relationship were the water head on the weir ho, the

ratio of the oblique length w to the channel width B, and the weir

height P. Uyumaz ( 1998 ) conducted laboratory experiments on the

erosion downstream of a fully suppressed, sharp-crested weir-gate

model. They found that the interaction of the wall jet from the gate

and the nappe flow reduced the scour depth.

Negm et al. ( 2002 ), Altan-Sakaraya et al. ( 2004 ), and Altan-

Sakaraya and Kokpinar ( 2013 ) experimentally studied the hy-

draulics of flow over a contracted rectangular weir and under a

rectangular gate (i., an H-weir) [Table 1 , Model 3 and Fig. 1(c)]

for a wide range of discharges and weir-gate widths. It was found

that weir-gate geometries such as gate height a, gate width bg, and

weir height P have major effects on the head–discharge relation-

ship. It was observed that the effect of viscosity can be assumed

negligible for Reynolds number R > 200,000 [i., R ¼ ρUðho þ

PÞ=μ] and the effect of surface tension can be considered negligible

for Weber number We > 40 [i., We ¼ ðρðho þ PÞU 2 Þ=σ] where

U is the averaged flow velocity in the upstream, ρ is the density, μ is

the dynamic viscosity, and σ is the surface tension of water. It was

found that the effects of viscosity and surface tension on H-weirs

were significant for very narrow openings bg=a < 1 and a=ðP −

aÞ > 2. An interaction factor IF, defined as the ratio of the measured

discharge over and under the weir-gate structure to the sum of the

predicted weir and gate discharges from the literature, was introduced

to show the effect of nappe–wall jet interaction on the discharge

capacity of H-weirs in both free and submerged flow conditions.

Different combinations of weir and gate geometries have also

been tested in the literature. Hayawi et al. ( 2008 ) combined a

1 Postdoctoral Fellow, Dept. of Civil Engineering, Lakehead Univ.,

Thunder Bay, ON, Canada P7B 5E1. Email: sseyedh@lakeheadu

2 Associate Professor, Dept. of Civil Engineering, Lakehead Univ.,

Thunder Bay, ON, Canada P7B 5E1 (corresponding author). ORCID:

orcid/0000-0003-0166-8830. Email: azimi@lakeheadu

Note. This manuscript was submitted on December 3, 2018; approved

on June 19, 2019; published online on August 28, 2019. Discussion period

open until January 28, 2020; separate discussions must be submitted

for individual papers. This paper is part of the Journal of Irrigation

and Drainage Engineering, © ASCE, ISSN 0733-9437.

© ASCE 04019025-1 J. Irrig. Drain. Eng.

Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.

rectangular sluice gate with a triangular weir (i., a V-notch)

[Table 1 , Model 4 and Fig. 1(d)]. The main objective of their study

was to propose a specific head–discharge relationship for a range

of weir apex angles (θ ¼ 30 °, 45°, and 60°) and weir heights

( 0. 09 m ≤ P ≤ 0. 32 m). It was found that the head–discharge rela-

tionship was correlated with the geometry parameters and the up-

stream head. Alhamid et al. ( 1996 ) and Alhamid ( 1999 ) conducted

laboratory experiments on the flow characteristics of a weir-gate

structure with a rectangular weir and triangular orifice [Table 1 ,

Model 5 and Fig. 1(e)].

A cylindrical weir-gate can be constructed by installing a pipe

perpendicular to flow direction with an offset from the channel bed

[Table 1 , Model 6 and Fig. 1(f)]. Masoudian et al. ( 2013 ) and Severi

et al. ( 2015 ) carried out extensive laboratory experiments to corre-

late weir-gate geometries with discharge coefficient. Ferro ( 2000 )

studied the hydraulics of flow over weirs of finite crest length and

under gates [Table 1 , Model 7 and Figs. 1(g and h)]. Based on the

classifications of weirs of finite crest length (Azimi and Rajaratnam

2009 ; Azimi et al. 2012, 2014 ) and the range of discharges, the weir

in Ferro’s study was classified as a narrow-crested weir.

The proposed head–discharge formulations for weir-gate struc-

tures in the literature were formulated based on discharge and

model geometry (Negm et al. 2002; Samani and Mazaheri 2009).

However, most data in the literature did not provide information on

the contribution of the weir and gate to explaining the effect of

nappe–wall jet interaction downstream of the weir-gate structures.

Therefore, the primary objective of the present research study was

to estimate the combined discharge through weir-gate structures

from available equations for weirs and gates in the literature. In an

ideal flow condition, with no nappe interaction nor excess energy

Fig. 1. Weir-gate models: (a) full-width sharp-crested weir; (b) oblique sharp-crested weir-gate; (c) rectangular sharp-crested weir (H-weir);

(d) triangular sharp-crested weir with rectangular gate; (e) rectangular sharp-crested weir with triangular gate; (f) cylindrical weir-gate;

(g) weir-gate with narrow crest length; and (h) weir-gate with broad crest length.

© ASCE 04019025-2 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.

loss due to interaction, the combined flow over weirs and under

gates can be simply predicted by adding the predicted flow using

the head–discharge formula for weirs and the sluice gate equa-

tion. In addition, limited data are available for prediction of

combined flow through weirs of finite crest length and gates. This

study provides new sets of data on flow over narrow-crested and

broad-crested weirs and under gates using detailed laboratory ex-

periments. The secondary objective of the present study was to pro-

vide a new head–discharge relationship for weir-gates with finite

crest length based on the head–discharge formulation for weirs of

finite crest length and sluice gate models. This research also inves-

tigated the possibility of using different designs of weir-gate struc-

tures as flow dividers.

Head–Discharge Relationship

Discharge Coefficient of Weirs

For free flow over a fully suppressed sharp-crested weir, the head–

discharge relationship can be formulated from energy considera-

tions and the discharge in free flow condition is described by

Qw ¼

2

3

BCd

ffiffiffiffiffi

2 g

p

h 3 o= 2 ð 1 Þ

where Qw = weir discharge; B = channel width; g = gravitational

acceleration; ho = elevation head over the weir, measured 3 ho– 4 ho

upstream of the weir (Ackers et al. 1978); and Cd = discharge

coefficient. The discharge coefficient of fully suppressed sharp-

crested weirs is well described by the Rehbock equation (Ackers

et al. 1978)

Cd ¼ 0. 611 þ 0. 075

ho

P

þ 0. 36



ho

ffiffiffiffiffiffiffiffiffiffiffiffiffi

ρg

σ

− 1

r − 1

ð 2 Þ

where P = weir height; and σ and ρ = surface tension and density

of water, respectively. Effects of the weir’s angle on the discharge

coefficient of inclined rectangular sharp-crested weirs were also

studied by Bijankhan and Ferro ( 2018 ). A commonly used dis-

charge equation for contracted rectangular weirs is (Swamee 1988)

Cd ¼

0. 611 þ 2. 23

 B

bw − 1

 0. 7

1 þ 3. 8

 B

bw − 1

 0. 7 þ

0. 075 − 0. 11

 B

bw − 1

 1. 46

1 þ 4. 8

 B

bw − 1

 1. 46



ho

P



ð 3 Þ

where bw = weir opening. Excluding the surface tension effect,

Eq. ( 3 ) becomes identical to the Rehbock equation for fully sup-

pressed sharp-crested weirs (i., bw ¼ B). Other discharge equa-

tions have been developed to improve the prediction of discharge

for rectangular weirs (Swamee et al. 2001; Aydin et al. 2002, 2006 ,

2011 ). Bijankhan et al. ( 2018 ) introduced a generalized equation

for prediction of discharge coefficient of rectangular weirs

Cd ¼ 0. 4178 ð 1. 416 Þ 3 bw = 2 B



bw

B

− 0. 1678

ð 4 Þ

The head–discharge formula for sharp-crested weirs with a tri-

angular section (i., a V-notch) can be described by (Bautista-

Capetillo et al. 2013)

Qw ¼ 8. 859 tan



θ

2



h 5 o= 2



Z 1



kZo þ Z 1 ln



Z 1

kZo þ Z 1



ð 5 Þ

where θ = apex angle; Zo ¼ 0. 682 ½tanðθ= 2 ފ 0. 044 ; Z 1 ¼ 0. 445

½tanðθ= 2 ފ− 0. 098 ; and k = correction coefficient of nonconcentricity

streamline (Bagheri and Heidarpour 2010).

The head–discharge relationship for weirs of finite crest length

can be developed using the concept of critical flow formation

within the crest length of the weir (Ackers et al. 1978). By equating

the specific energy upstream of the weir with the minimum energy

in the control section, the head–discharge equation can be formu-

lated as

Qw ¼



2

3

 3 = 2

CDB

ffiffiffi

g

p

h 3 o= 2 ð 6 Þ

where CD = discharge coefficient. Azimi and Rajaratnam ( 2009 )

provided empirical formulations to estimate the discharge coeffi-

cient of weirs of finite crest length. Four hydraulic regimes were

identified based on the ratio of the water head ho to the crest

length L: short-crested, narrow-crested, broad-crested, and long-

crested weirs. For broad-crested weirs (i., 0. 1 < ho=L < 0. 4 ) with

a square-edged entrance, the discharge coefficient can be de-

scribed as

CD ¼ 0. 95



ho

ho þ P

 2

− 0. 38



ho

ho þ P



þ 0. 89 ð 7 Þ

For narrow-crested weirs (i., 0. 4 < ho=L < 2 ) with a square-

edged entrance, the discharge coefficient is a linear function of

ho=L and can be described as

CD ¼ 0. 767 þ 0. 215



ho

L



ð 8 Þ

Chanson and Montes ( 1998 ) used the head–discharge formu-

lation for weirs of finite crest length to predict the discharge over

circular weirs. The total head (i., Ho ¼ ho þ Q 2 w=ð 2 gðBðho þ

PÞÞ 2 Þ) was used instead of ho in their head–discharge formulation.

An empirical correlation was proposed based on a wide range of

water head ho and the cylindrical radius r (i., 0. 45 < ho=r < 1. 9 )

CD ¼ 1. 185



ho

r

 0. 136

ð 9 Þ

Considering the effect of surface tension and streamflow curva-

ture in low flows, Sarginson ( 1972 ) proposed a prediction formula

for the discharge coefficient with a higher range of nondimensional

ho=r of 1. 9 ≤ ho=r ≤ 4

CD ¼ 0. 702 þ 0. 145

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

33 −



5. 5 −

ho

r

s  2

−

3. 146 σ

ρgho



1 −



1 þ

1. 2 ho

r

− 4. 9 

þ

0. 08 ho

r

ð 10 Þ

Bijankhan and Ferro ( 2017 ) also provided an overall review of

the head–discharge relationship for different weir models.

Discharge Coefficient of Gates

The flow through gates can be formulated using continuity and

energy equations. A discharge coefficient can be introduced to in-

corporate the effects of streamline curvature, energy losses in the

vicinity of the gate, and nonhydrostatic pressure as

Qg ¼ abgcD

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2 gðho þ PÞ

p

ð 11 Þ

© ASCE 04019025-4 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.

where a and bg = height and width of gate opening, respectively;

and cD = discharge coefficient of gate. A well-established discharge

coefficient based on a number of laboratory experiments was pro-

posed by Swamee ( 1992 )

cD ¼ 0. 611



ho − a

ho þ 15 a

 0. 072

ð 12 Þ

Belaud et al. ( 2009 ) and Habibzadeh et al. ( 2011 ) used theo-

retical approaches to estimate the contraction and discharge coef-

ficients of sluice gates by incorporating the conservation of

momentum and the effects of energy dissipation between the

upstream section of the gate and vena contracta. The discharge

coefficient for the free-flow condition in the study of Habibzadeh

et al. ( 2011 ) is expressed as

cD ¼ CC

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 − β 1

1 þ k − β 12

vu

u

t ð 13 Þ

where k = coefficient of minor head loss; CC = contraction coef-

ficient of gate; and β ¼ ðho þ PÞ=ðCCaÞ.

Bijankhan et al. ( 2012 ) used the Buckingham Π-theorem and

the incomplete self-similarity concept to develop a formula for

prediction of discharge through sluice gates in free, transition, and

submerged flow conditions. The free-flow discharge through sluice

gates can be estimated by



q 2 g

g

 1 = 3

¼ af



ho þ P

a

b

f

a ð 14 Þ

where qg = specific discharge (i., qg ¼ Qg=bg); and af and bf ¼

0. 784 and 0, respectively. Bijankhan et al. ( 2013 ) used Eq. ( 14 )

to predict the flow discharge for radial gates. The averaged values

of af and bf for the radial gates were 0 and 0, respectively.

Experimental Setup

Weirs of finite crest length are classified as short-, narrow-, broad-,

and long-crested weirs based on the value of ho=L. Limited data

are available in the literature to propose empirical formulations to

predict the interaction factors for offset weirs of finite crest length

in narrow-crested regimes and no data are available for broad-

crested regimes. Therefore, a series of laboratory experiments was

carried out in the hydraulic laboratory at Lakehead Univ., Thunder

Bay, Ontario to study the flow through weir-gates with finite crest

lengths using a glass-walled horizontal flume 12 m long, 0 m

wide, and 0 m deep.

The centerline water surface levels in the upstream were mea-

sured by mechanical point gauges with  0. 1 mm accuracy. The flow

in the flume was measured with an inline magnetic flow meter (FMG

600, Omega, Saint-Eustache, Canada) to  0. 01 L=s accuracy, and

flow measurements were checked by a V-notch sharp-crested weir.

The weir-gates with a finite crest length were installed around 7 m

upstream of the head tank to ensure uniform flow throughout the

flume, and screens were provided to produce a smooth flow.

Weir-gates with five different aspect ratios were fabricated using

two weir heights, 0 and 0 m, and three crest lengths, 0,

0, and 0 m, to cover both narrow-crested and broad-crested

regimes (Azimi and Rajaratnam 2009). The weirs were installed at

different distances from the flume bed to form four gate openings

a ¼. 01 , 0, 0, and 0 m (Table 2 ). To study the main flow

features, various discharges were tested to provide free-flow heads

ho ranging from 10 to 140 mm. The normalized upstream head

ho=P ranged from 0 to 1 and ho=L ranged from 0 to 1.

A total of 46 experiments were carried out with discharges ranging

from 7 to 27 L=s, and the discharge fluctuations for low and high

discharges varied between  0 .4% and  1 .2% of the average.

Model 7 in Table 1 gives the free-flow data for narrow-crested

[Fig. 1(g)] and broad-crested [Fig. 1(h)] weirs with various offsets

a from the channel bed ranging from 10 to 60 mm.

Results and Discussion

Interaction Factor

The interaction factor for a weir-gate with a weir height of P, gate

opening of a, crest length of L, and upstream water head of ho can

be expressed by the following functional relationship:

Table 2. Flow characteristics and geometry of combined weirs of finite

crest length and gate

Test

No.

Q

(L=s) a (m) P (m) L (m) ho (m) a=P ho=P ho=L

1 18 0 0 0 0 0 0 0.

2 23 0 0 0 0 0 0 0.

3 27 0 0 0 0 0 0 0.

4 18 0 0 0 0 0 0 0.

5 23 0 0 0 0 0 0 0.

6 27 0 0 0 0 0 0 0.

7 23 0 0 0 0 0 0 0.

8 27 0 0 0 0 0 0 0.

9 18 0 0 0 0 0 0 0.

10 23 0 0 0 0 0 0 0.

11 27 0 0 0 0 0 0 0.

12 18 0 0 0 0 0 0 0.

13 23 0 0 0 0 0 0 0.

14 27 0 0 0 0 0 0 0.

15 23 0 0 0 0 0 0 0.

16 27 0 0 0 0 0 0 0.

17 18 0 0 0 0 0 0 1.

18 27 0 0 0 0 0 0 1.

19 18 0 0 0 0 0 0 0.

20 23 0 0 0 0 0 0 0.

21 27 0 0 0 0 0 0 0.

22 23 0 0 0 0 0 0 0.

23 27 0 0 0 0 0 0 0.

24 7 0 0 0 0 0 0 0.

25 9 0 0 0 0 0 0 0.

26 18 0 0 0 0 0 0 0.

27 23 0 0 0 0 0 1 0.

28 27 0 0 0 0 0 1 0.

29 9 0 0 0 0 0 0 0.

30 18 0 0 0 0 0 0 0.

31 23 0 0 0 0 0 0 0.

32 27 0 0 0 0 0 0 0.

33 18 0 0 0 0 0 0 0.

34 23 0 0 0 0 0 0 0.

35 27 0 0 0 0 0 0 0.

36 27 0 0 0 0 0 0 0.

37 9 0 0 0 0 0 0 0.

38 18 0 0 0 0 0 0 0.

39 23 0 0 0 0 0 0 1.

40 27 0 0 0 0 0 1 1.

41 18 0 0 0 0 0 0 0.

42 23 0 0 0 0 0 0 0.

43 27 0 0 0 0 0 0 1.

44 23 0 0 0 0 0 0 0.

45 27 0 0 0 0 0 0 0.

46 27 0 0 0 0 0 0 0.

© ASCE 04019025-5 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.

0.

0.

0.

1.

0 0 0 0.

IF

ho /P

0.

0.

0.

1.

0 0 0 1.

IF

IFp

0.

0.

0.

0.

0.

0 0 0 0 0.

Qe (m 3 /s)

Q

####### m

(m

3 /s)

Norouzi Banis. (1992) [ ]=0.

Norouzi Banis. (1992) [ ]=0.

Norouzi Banis. (1992) [ ]=0.

Norouzi Banis. (1992) [ ]=0.

Norouzi Banis. (1992) [ ]=0.

a/(P-a)

a/(P-a)

a/(P-a)

a/(P-a)

a/(P-a)

(a)

(b)

(c)

Fig. 2. Flow over and under full-width sharp-crested weir-gate:

(a) variations of interaction factor with approach velocity; (b) proposed

versus obtained interaction factor; and (c) measured versus calculated

discharge.

0.
0.
1.
1.
0 1 2 3
IF
ho /P
0.
0.
0.
1.
1.
0 0 0 1 1.
IF
IFp
Jalil and Abdulsatar. (2013) ,[ ]=5.
Jalil and Abdulsatar. (2013) ,[ ]=2.
Jalil and Abdulsatar. (2013) ,[ ]=1.
Jalil and Abdulsatar. (2013) ,[ ]=0.
Jalil and Abdulsatar. (2013) ,[ ]=0.
Jalil and Abdulsatar. (2013) ,[ ]=0.
Jalil and Abdulsatar. (2013) ,[ ]=0.
Jalil and Abdulsatar. (2013) ,[ ]=0.
Jalil and Abdulsatar. (2013) ,[ ]=0.
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
0.
0.
0.
0.
0 0 0 0.
=30o
=30o
=30o
=45o
=45o
=45o
=60o
=60o
=60o
Qe (m 3 /s)
Q

####### m

(m
3 /s)

(a)

(b)

(c)

Fig. 3. Flow over and under oblique sharp-crested weir-gate:

(a) variations of interaction factor with approach velocity; (b) proposed

versus obtained interaction factor; and (c) measured versus calculated

discharge.

© ASCE 04019025-7 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.
ho / P
0.
1.
1.
1.
0 0 1 1.
IF
Negm et al. (2002) [ ]=2.
Negm et al. (2002) [ ]=1.
Negm et al. (2002) [ ]=0.
Negm et al. (2002) [ ]=0.
Negm et al. (2002) [ ]=0.
Negm et al. (2002) [ ]=0.
Altan Sakarya & Kokpinar (2013) [ ]=1.
Altan Sakarya & Kokpinar (2013) [ ]=1.
Altan Sakarya & Kokpinar (2013) [ ]=0.
Altan Sakarya & Kokpinar (2013) [ ]=0.
0.
0.
0.
0.
0.
0 0 0 0 0.
0.
1.
1.
1.
0 1 1 1.
IF
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
IFp

Qe (m 3 /s)

Q

####### m

(m

3 /s)

(a)

(b)

(c)

Fig. 4. Flow over and under rectangular sharp-crested weir-gate

(H-weir): (a) variations of interaction factor with approach velocity;

(b) proposed versus obtained interaction factor; and (c) measured

versus calculated discharge.

0.
0.
1.
1.
1.
0 0 0 1.
0.
0.
1.
1.
1.
0 0 1 1 1.
Hayawi et al. (2008) ,[ ]=1.
Hayawi et al. (2008) ,[ ]=1.
Hayawi et al. (2008) ,[ ]=1.
Hayawi et al. (2008) ,[ ]=0.
Hayawi et al. (2008) ,[ ]=0.
Hayawi et al. (2008) ,[ ]=0.
Hayawi et al. (2008) ,[ ]=0.
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
0.
0.
0.
0.
0.
0 0 0 0 0.
=30o
=30o
=30o
=30o
=30o
=45o
=60o
ho /P
IF
IF
IFp
Qe (m 3 /s)
Q

####### m

(m
3 /s)

(a)

(b)

(c)

Fig. 5. Flow over and under triangular sharp-crested weir with rectan-

gular gate: (a) variations of interaction factor with approach velocity;

(b) proposed versus obtained interaction factor; and (c) measured ver-

sus calculated discharge.

© ASCE 04019025-8 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.
0.
0.
0.
0.
1.
0 0 0 0 0.
0.
0.
0.
0.
1.
0 0 0 0 1.
0.
0.
0.
0.
0 0 0 0.
[ ]=0 ,[ ]=0.
[ ]=0 ,[ ]=0.
[ ]=0 ,[ ]=0.
[ ]=1 ,[ ]=0.
Ferro (2000) [ ]=1 ,[ ]=0.
Ferro (2000) [ ]=2 ,[ ]=0.
Ferro (2000) [ ]=2 ,[ ]=0.
Ferro (2000) [ ]=3 ,[ ]=0.
Ferro (2000) [ ]=3 ,[ ]=0.
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
a/(P-a)
ho /P
IF
IF
IFp
Qe (m 3 /s)
Q

####### m

(m
3 /s)

(a)

(b)

(c)

Fig. 8. Flow over and under narrow-crested weir-gate (NCW):

(a) variations of interaction factor with approach velocity; (b) proposed

versus obtained interaction factor; and (c) measured versus calculated

discharge.

0.
0.
0.
0.
1.
0 0 0 0 0 1.
0.
0.
0.
0.
1.
0 0 0 0 1.
0.
0.
0.
0.
0.
0 0 0 0 0.
[ ]=0 ,[ ]=0.
[ ]=0 ,[ ]=0.
[ ]=0 ,[ ]=0.
[ ]=1 ,[ ]=0.
[ ]=1 ,[ ]=0.
[ ]=1 ,[ ]=0.
[ ]=1 ,[ ]=0.
[ ]=2 ,[ ]=0.
[ ]=2 ,[ ]=0.
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
(P-a)/L
ho /P
IF
IF
IFp
Qe (m 3 /s)
Q

####### m

(m
3 /s)

(a)

(b)

(c)

Fig. 9. Flow over and under broad-crested weir-gate (BCW):

(a) variations of interaction factor with approach velocity; (b) proposed

versus obtained interaction factor; and (c) measured versus calculated

discharge.

© ASCE 04019025-10 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.

Finally, Figs. 2(c)–9(c) show the correlation of the measured dis-

charge Qm with the estimated discharge Qe using multivariable re-

gression analysis. The dashed lines in all subplots show the 10%

variations of prediction. These subplots also indicate the range

of discharges for each weir-gate model and the applicability of

Eqs. ( 19 ) and ( 20 ).

Fig. 2(a) shows the variation of interaction factor IF with ho=P

for fully suppressed sharp-crested weir-gates. The superposition of

weir and gate discharges provides a reasonable estimation of the

total flow but overestimates the discharge between 2% and 5%. The

superposition of weir and gate discharges predicted the total dis-

charge with reasonable accuracy for a=ðP–aÞ > 0. 2. The oblique

installation of the fully suppressed weir-gate structure increases the

complexity of the approaching flow, and a simple superposition

of discharges does not provide an accurate estimation of the total

discharge. A direct correlation was found between the interaction

factor IFp and the weir length:width ratio of w=B with a power of

0 (Table 3 ). Fig. 3(a) indicates that the superposition of weir and

gate discharges overestimates the overall discharge by 5% with

10% fluctuations. In addition, the interaction factor in oblique

sharp-crested weir-gates increases with increasing ho=P indicating

that the nappe–wall jet interaction has stronger effects in reducing

the overall flow.

By contracting the weir and gate openings to form a rectan-

gular weir-gate structure known as an H-weir (Altan-Sakaraya et al.

2004 ; Altan-Sakaraya and Kokpinar 2013), the effects of weir geom-

etry on predictions of interaction factor become more important.

Data scatter between interaction factor IF and ho=P in Fig. 4(a) in-

dicates that the simple superposition of weir and gate discharges does

not provide an accurate estimation of the total discharge. Negm et al.

( 2002 ) used a similar superposition approach to estimate the total

discharge of H-weirs and provided a linear correlation based on

Ho=a, where Ho is the total head upstream of the H-weirs. By

including other experimental data (Atlan Sakarya and Kokpinar

2013 ) and using multivariable regression analysis, the interaction

factor was found to be correlated with a=P, ho=P, and bw=B.

Among all parameters describing the variations of interaction factor,

a=P was found to have the highest influence, with a power of unity.

Using Eq. ( 19 ), the average prediction error of the total discharge

is  5 .8%.

Fig. 5(a) shows the correlation of the interaction factor IF with

the approach velocity indicator ho=P. The superposition of weir

and gate flow overestimates the total discharge for ho=P < 0. 4. The

multivariable regression analysis for this type of weir-gate model

indicates that the nondimensional products of a=P, ho=P, and

bw=B have almost the same influence in prediction of interaction

factor. The powers of the aforementioned nondimensional products

in Eq. ( 19 ) are – 0, 0, and 0 respectively. The influence of

ho=P in prediction of weir flow and interaction factor is shown in

Table 3. The coefficient associated with ho=P is C 4 , which is 0 for

triangular weirs and 0 for rectangular weirs. This indicates that

the approach velocity ho=P has less impact in weir flow with a

triangular cross section than with a rectangular weir section.

Variation of the interaction factor with ho=P for flow over a rec-

tangular sharp-crested weir and under a triangular orifice is shown

in Fig. 6(a). The superposition of rectangular weir flow and triangu-

lar orifice flow underestimates the total discharge by an average of

20%. It was found that the interaction factor increased as orifice

angle increased from θ ¼ 45 ° to 90°. The reason for underestima-

tion of the overall discharge may be due to the inaccuracy of dis-

charge prediction of triangular orifice.

The polynomial structure of the nondimensional products

[i., Eq. ( 19 )] was used to develop a formula for prediction of

interaction factor, and data were correlated with a low coefficient

of determination of R 2 ¼ 0. 35. The second form of multivariable

model [i., Eq. ( 20 )] provides better correlation between the non-

dimensional products and the interaction factor, with a coefficient

of determination of R 2 ¼ 0. 86. Fig. 6(c) compares the measured

discharge Qm and the estimated discharge Qe for this type of weir-

gate model. The proposed model underestimates the discharge in

low flows (Qm < 3. 6 L=s) and overestimates Qm for higher dis-

charges within 10% variations.

Flow over and under an offset cylindrical weir was experi-

mentally studied by Masoudian et al. ( 2013 ) and Severi et al.

( 2015 ). The multivariable regression analysis indicated that be-

tween two nondimensional products representing the weir-gate

geometry (a=P) and the approach velocity indicator (ho=P), the

weir-gate geometry has a higher impact on the magnitude of the

interaction factor, with a power of 0 (Table 3 ). The interaction

factor decreased as ho=P increased [Fig. 7(a)]. Eq. ( 9 ) was used

to predict the discharge coefficient of the weir flow, and any of

Eqs. ( 12 )–( 14 ) can be used to predict the discharge coefficient of

the gate flow. All three equations were tested for prediction of the

interaction factor, and Eq. ( 12 ) provided the highest correlation

coefficient.

Fig. 8(a) shows the correlation of the interaction factor

with ho=P for flow over narrow-crested weirs and under gates

(i., 0. 4 < ho=L < 2 ). Overall, the superposition of weir and gate

flow overestimated the total discharge by an average 21%. This

may be due to the nappe interaction with the wall jet that was de-

veloped in the downstream of the gate. Data correlation indicates

that ho=P has more influence than other nondimensional geometry

products in prediction of the interaction factor (Table 3 ). Fig. 9(a)

shows the correlation of the interaction factor IF with ho=P for the

combined flow through broad-crested weirs and gates. Similar to

broad-crested weirs with no offset, the effect of approach velocity is

negligible in discharge through broad-crested weirs and gates. The

excess friction losses in broad-crested weir-gate (BCW) models

reduce the overall discharge through this type of weir-gate. The

superposition of the weir and gate flows overestimated the overall

discharge by 20% with a fluctuation range of 8% [Fig. 9(a)].

Weir-Gate as Flow Distributor

Weir-gate structures with both sharp-crested weirs and weirs of fi-

nite crest length design can be used as a flow distributor (Fig. 10 ).

ho

a

Qw

Qg

ho

a

Qw

Qg

L

(a)

(b)

Fig. 10. Schematic of flow distributer using weir-gate structure:

(a) sharp-crested weir-gate; and (b) flow over weir of finite crest length

and under gate structure.

© ASCE 04019025-11 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.



ho

P



C

¼

9

4



a

ðP − aÞ

 0. 7

ð 22 Þ

Similar plots can be developed for design purposes if a specific

proportion between weir and gate discharges is desired.

The regime plots for the combined flow over weirs of finite

crest length and gates were developed, and the results are shown

for narrow-crested weir-gates (NCWs) and broad-crested weir-

gates in Figs. 13(a and b), respectively. Eq. ( 6 ) was used to es-

timate the weir discharge and Eq. ( 11 ) was used to predict the

gate flow. Because the discharge coefficient in broad-crested

weirs varies with P, variation of the normalized discharge differ-

ences were plotted with ho=P for this type of weir-gate models.

Fig. 13(a) shows the regime plot of broad-crested weir-gates

with ho=P. It was found that the regime plot is independent

of the crest length L, and the normalized critical head can be

estimated by



ho

P



C

¼ 3



a

ðP − aÞ

 2 = 3

ð 23 Þ

The discharge coefficient of narrow-crested weirs linearly in-

creases with ho=L [Eq. ( 8 )]. Therefore, discharge over narrow-

crested weirs and under gates is a function of the crest height P and

the crest length L. A family of regime plots was developed for a

wide range of P=L between 1 and 5. Fig. 13(b) shows the regime

plot of a narrow-crested weir-gate for P=L ¼ 1 and in the opera-

tional range for narrow-crested weirs (i., 0. 4 < ho=L < 2 ). The

normalized critical head increases as the normalized gate opening

increases. Fig. 14 shows the variations of the critical head ðho=PÞC

with the normalized gate opening a=ðP − aÞ for a wide range of

weir aspect ratios (i., 1 ≤ P=L ≤ 5 ). A formula is proposed to

predict the critical head for narrow-crested weir-gate structures



ho

P



C

¼



1. 80



P

L



þ 0. 90



a

ðP − aÞ

 3 = 5

ð 24 Þ

The solid curves in Fig. 14 show the performance of Eq. ( 24 )

in prediction of data points. The proposed equations for prediction

of the normalized critical head can be used to design flow

distributers.

Conclusions

This study presents a comprehensive analysis to estimate the

overall discharge through different types of weir-gate structures.

Empirical formulations for prediction of discharge coefficients of

different weirs, gates, and orifices were collected from the litera-

ture. The total discharge through weir-gates is different from the

superposition of weir and gate discharges due to interactions be-

tween the free nappe flow of the weir and the wall jet in the gate.

To quantify the influence of nappe and wall jet interaction, inter-

action factors were calculated based on the ratio of the measured

overall discharge to the superposition of the estimated weir and gate

a /(P−a)
0.
0.
1.
1.
2.
2.
0 0 0 0 0 0.

P/L = 1.

P/L = 3.

P/L = 1.

P/L = 5.

P/L = 2.

(h

/o

P)

####### C

Fig. 14. Effects of weir-gate geometry on variations of the critical

approach velocity for narrow-crested weir-gates.

0.
0.
1
10
0 0 0 0 1.
0.
0.
1
10
0 0 1 1 2.
0 0 0.
0 0 0.

Q

−w

Q

####### g

Q

####### w

Q

−w

Q

####### g

Q

####### w

ho /P

ho /L

(a)

(b)

Fig. 13. Regime plots of weirs of finite crest length for a wide

ranges of normalized weir-gate geometry 0. 01 ≤ a=ðP−aÞ ≤ 0. 20 :

(a) broad-crested weir ( 0. 1 ≤ ho=L ≤ 0. 4 ); and (b) narrow-crested

weir ( 0. 4 < ho=L ≤ 2 ). The minimum value in each curve indicates

Qw ¼ Qg.

© ASCE 04019025-13 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.

flow discharges. Multivariable regression analysis was used to cor-

relate the interaction factors with the nondimensional geometry

products and the hydraulic characteristics of the weir-gates. Two

general models were selected among several mathematical models

to predict the overall discharge through weir-gate structures. The

overall coefficient of determination for prediction of the interaction

factor was above 0.

Due to limited experimental data in the literature for a com-

bined weir of finite crest length and gate, a series of laboratory ex-

periments was carried out to obtain laboratory measurements and

calculate the interaction factor for both narrow-crested and broad-

crested regimes. It was also shown that weir-gates can be used as

flow distributors in irrigation channels. Variations of the weir and

gate discharges with weir-gate geometry and total discharge were

plotted for fully suppressed rectangular, narrow-crested, and broad-

crested weir-gates. In this study, the required upstream head to

equally divide the flow is called the critical head. Regime plots

and the normalized critical head ðho=PÞC were developed to

assist the design of flow distributors for practical engineering

and irrigational purposes. Empirical formulations were also devel-

oped to estimate the critical head based on the nondimensional

geometry products and the hydraulic characteristics of weir-gate

structures.

Data Availability Statement

Some or all data, models, or code generated or used during the

study are available from the corresponding author by request (head-

discharge data).

Notation

The following symbols are used in this paper:

a = gate opening (m);

B = channel width (m);

b = width (m);

CD = discharge coefficient of weir of finite crest length;

Cc = contraction coefficient of gate;

Cd = discharge coefficient of sharp-crested weir;

cD = discharge coefficient of gate;

C 1 – C 11 = coefficients;

g = gravitational acceleration (m=s 2 );

Ho = total head (m);

ho = upstream head (m);

IF = interaction factor;

IFp = proposed interaction factor;

k = correction coefficient of nonconcentricity streamline;

L = weir length (m);

m = number of independent variables;

n = number of basic physical dimension;

P = weir height (m);

Q = discharge (m 3 =s);

R = Reynolds number;

r = radius of cylindrical weir (m);

U = average flow velocity in upstream (m=s);

We = Weber number;

w = oblique length of weir (m);

β = dimensionless parameter (Ho=a);

θ = weir angle (degrees);

μ = dynamic viscosity (kg=ms);

ρ = density of water (kg=m 3 ); and

σ = surface tension (kg=s 2 ).

Subscripts

C = critical;

e = estimated;

f = flow;

g = gate;

m = measured;

p = predicted; and

w = weir.

References

Ackers, P., R. White, J. A. Perkins, and A. J. Harrison. 1978. Weirs and

flumes for flow measurement. Chichester, UK: Wiley.

Alhamid, A. A. 1999. “Analysis and formulation of flow through combined

V-notch-gate device.” J. Hydraul. Res. 37 (5): 697–705. doi

/10/00221689909498524.

Alhamid, A. A., D. Husain, and A. M. Negm. 1996. “Discharge equation

for combined flow rectangular weirs and below inverted triangular

gates.” J. Sci. Res. 14 (3): 595–607.

Altan-Sakarya, A., and M. A. Kokpinar. 2013. “Computation of discharge

for simultaneous flow over weirs and below gates (H-weirs).” Flow

Meas. Instrum. 29 (Mar): 32–38. doi/10.1016/j.flowmeasinst

.2012.09.

Altan-Sakarya, B., I. Aydin, and A. M. Ger. 2004. “Discussion of combined

free flow over weirs and below gates by Negm A. M., Al-Brahim A. M.,

Alhamid A. A.” J. Hydraul. Res. 42 (5): 557–560.

Aydin, I., A. Altan-Sakarya, and A. M. Ger. 2006. “Performance of slit

weir.” J. Hydraul. Eng. 132 (9): 987–989. doi/10.

/(ASCE)0733-9429(2006)132:9(987).

Aydin, I., A. B. Altan-Sakarya, and C. Sisman. 2011. “Discharge formula

for rectangular sharp-crested weir.” Flow Meas. Instrum. 22 (2):

144 – 151. doi/10.1016/j.flowmeasinst.2011.01.003.

Aydin, I., A. M. Ger, and O. Hincal. 2002. “Measurement of small

discharges in open channels by slit weir.” J. Hydraul. Eng. 128 (2):

234 – 237. doi/10.1061/(ASCE)0733-9429(2002)128:2(234).

Azimi, A. H., and N. Rajaratnam. 2009. “Discharge characteristics of weirs

of finite crest length.” J. Hydraul. Eng. 135 (12): 1081–1085. https://doi

.org/10/(ASCE)HY.1943-7900.

Azimi, A. H., N. Rajaratnam, and D. Z. Zhu. 2012. “A note on sharp-

crested weirs and weirs of finite crest length.” Can. J. Civ. Eng. 39 (11):

1234 – 1237. doi/10.1139/l2012-106.

Azimi, A. H., N. Rajaratnam, and D. Z. Zhu. 2014. “Submerged flows over

rectangular weirs of finite crest length.” J. Irrig. Drain. Eng. 140 (5):

06014001. doi/10.1061/(ASCE)IR.1943-4774.

Bagheri, S., and M. Heidarpour. 2010. “Flow over rectangular sharp crested

weirs.” Irrig. Sci. 28 (2): 173–179. doi/10.1007/s00271-

-0172-1.

Bautista-Capetillo, C. F., O. Robles, H. Junez-Ferreira, and E. Playan.

2013. “Discharge coefficient analysis for triangular sharp-crested weirs

using low-speed photographic technique.” J. Irrig. Drain Eng. 140 (3):

060130051. doi/10.1061/%28ASCE%29IR.1943-4774.0000683.

Belaud, G., L. Cassan, and J. P. Baume. 2009. “Calculation of contraction

coefficient under sluice gate and application to discharge measure-

ment.” J. Irrig. Drain. Eng. 135 (12): 1086 – 1091. https://doi/

.1061/%28ASCE%29HY.1943-7900.

Bijankhan, M., C. Di Stefano, and V. Ferro. 2018. “Generalized stage-

discharge relationship for rectangular weirs.” Water Manage. 171 (3):

125 – 133. doi/10.1680/jwama.16.00102.

Bijankhan, M., and V. Ferro. 2017. “Dimensional analysis and stage-

discharge relationship for weirs: a review.” J. Agric. Eng. 48 (1): 1–11.

doi/10.1080/09715010.2014.939503.

Bijankhan, M., and V. Ferro. 2018. “Experimental study and numerical

simulation of inclined rectangular weirs.” J. Irrig. Drain. Eng. 144 (7):

04018012. doi/10.1061/(ASCE)IR.1943-4774.

© ASCE 04019025-14 J. Irrig. Drain. Eng.
Downloaded from ascelibrary by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.
Was this document helpful?

Discharge Characteristics of Weir-Orifice and Weir-Gate Structures

Course: Civil Engineering

32 Documents
Students shared 32 documents in this course

University: Universitas Brawijaya

Was this document helpful?
Discharge Characteristics of Weir-Orifice
and Weir-Gate Structures
Saeed Salehi1and Amir H. Azimi, M.ASCE2
Abstract: The discharge characteristics of flow over and under different weir-gate structures were investigated using dimensional analysis
and multivariable regression techniques. Based on the shape and geometry of weir-gates, seven weir-gate structures were classified. The
interaction factor, defined as the ratio of the measured discharge over and under the weir-gate structure to the sum of the predicted weir and
gate discharges from the literature, was calculated for all types of weir-gate models. Six weir-gate models were experimentally tested to study
the discharge characteristics of flow over weirs of finite crest length and under gate. The interaction factors were correlated with the geometry
parameters for all weir-gate models with an average coefficient of determination of 0.85. A series of regime plots was developed to assist
designing the weir-gate structures as flow distributors for a sharp-crested weir-gate and a weir of finite crest length with an offset. The regime
plots show the contribution of weir and gate discharges for different weir-gate geometries. A critical normalized head was introduced as the
flow through the weir-gate structure is equally divided by the weir and gate. Based on the weir-gate geometry and discharge, general empirical
equations were developed to estimate the critical normalized head for practical engineering applications. DOI: 10.1061/(ASCE)IR.1943-
4774.0001421.© 2019 American Society of Civil Engineers.
Author keywords: Flow measurement; Weirs; Weir-gates; Sluice gates; Free flow; Weirs of finite crest length; Combined weir and gate.
Introduction
Weirs are commonly used as flow-measuring and water level
control structures in natural streams and irrigation channels. To
increase hydraulic performance and sediment removal capacity of
weirs, an opening (i.e., a sluice gate or orifice) is often included in
the design, and the resulting new weir structure is called a weir-gate
structure in the literature (Norouzi Banis 1992;Alhamid 1999;
Negm et al. 2002;Hayawi et al. 2008;Samani and Mazaheri 2009;
Severi et al. 2015). In weir-gate design, water passes simultane-
ously over and under the weir-gate structure. Therefore, for a con-
stant upstream head, the discharge passing through a weir-gate is
higher than the discharge over a weir of the same geometry. In ad-
dition, weir-gate structures experience more energy dissipation
due to interaction of the weir’s nappe with the wall jet coming off
from the gate. The high energy dissipation in weir-gate structures
significantly reduces scour formation downstream of irrigation
channels, and as a result, makes them a suitable choice for earthen
canals (Uyumaz 1998). It is also possible to employ weir-gate
structures as flow distributors, and the present study investigated
this possibility.
The schematic of the weir-gate models used in this study is
shown in Fig. 1. Table 1lists the geometries and flow ranges of the
weir-gate models that were collected from the literature. One of
the early models of weir-gate structures was introduced by Norouzi
Banis (1992). In this simple weir-gate structure, a sharp-crested
weir is offset from the channel bed to form a fully suppressed gate
[Table 1, Model 1 and Fig. 1(a)]. Samani and Mazaheri (2009)
extended the study of Norouzi Banis (1992) by testing the fully
suppressed weir-gate structure in semisubmerged and fully sub-
merged flow conditions. The fully suppressed weir-gate structure
can be installed with an angle to form an oblique weir-gate struc-
ture [Table 1, Model 2 and Fig. 1(b)]. Jalil and Abdulsatar (2013)
proposed an empirical equation based on experimental data and
dimensional analysis to predict discharge through oblique weir-
gates. They reported that the major parameters affecting the head–
discharge relationship were the water head on the weir ho, the
ratio of the oblique length wto the channel width B, and the weir
height P. Uyumaz (1998) conducted laboratory experiments on the
erosion downstream of a fully suppressed, sharp-crested weir-gate
model. They found that the interaction of the wall jet from the gate
and the nappe flow reduced the scour depth.
Negm et al. (2002), Altan-Sakaraya et al. (2004), and Altan-
Sakaraya and Kokpinar (2013) experimentally studied the hy-
draulics of flow over a contracted rectangular weir and under a
rectangular gate (i.e., an H-weir) [Table 1, Model 3 and Fig. 1(c)]
for a wide range of discharges and weir-gate widths. It was found
that weir-gate geometries such as gate height a, gate width bg, and
weir height Phave major effects on the head–discharge relation-
ship. It was observed that the effect of viscosity can be assumed
negligible for Reynolds number R >200,000 [i.e., R¼ρUðhoþ
PÞ=μ] and the effect of surface tension can be considered negligible
for Weber number We >40 [i.e., We ¼ ðρðhoþPÞU2Þ=σ] where
Uis the averaged flow velocity in the upstream, ρis the density, μis
the dynamic viscosity, and σis the surface tension of water. It was
found that the effects of viscosity and surface tension on H-weirs
were significant for very narrow openings bg=a<1and a=ðP−
aÞ>2. An interaction factor IF, defined as the ratio of the measured
discharge over and under the weir-gate structure to the sum of the
predicted weir and gate discharges from the literature, was introduced
to show the effect of nappe–wall jet interaction on the discharge
capacity of H-weirs in both free and submerged flow conditions.
Different combinations of weir and gate geometries have also
been tested in the literature. Hayawi et al. (2008) combined a
1Postdoctoral Fellow, Dept. of Civil Engineering, Lakehead Univ.,
Thunder Bay, ON, Canada P7B 5E1. Email: sseyedh@lakeheadu.ca
2Associate Professor, Dept. of Civil Engineering, Lakehead Univ.,
Thunder Bay, ON, Canada P7B 5E1 (corresponding author). ORCID:
https://orcid.org/0000-0003-0166-8830. Email: azimi@lakeheadu.ca
Note. This manuscript was submitted on December 3, 2018; approved
on June 19, 2019; published online on August 28, 2019. Discussion period
open until January 28, 2020; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Irrigation
and Drainage Engineering, © ASCE, ISSN 0733-9437.
© ASCE 04019025-1 J. Irrig. Drain. Eng.
J. Irrig. Drain Eng., 2019, 145(11): 04019025
Downloaded from ascelibrary.org by Nottingham Trent University on 08/28/19. Copyright ASCE. For personal use only; all rights reserved.