agacci_d78aa3782ed9778805199355440ad7b1

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

1/12

Flow Measurement and Instrumentation 22 (2011) 319330

Contents lists available at ScienceDirect

Flow Measurement and Instrumentation

journal homepage: www.elsevier.com/locate/flowmeasinst

Discharging capacity of rectangular side weirs in straight open channels

M. Emin Emiroglu a,, Hayrullah Agaccioglu b, Nihat Kaya aa Firat University, Engineering Faculty, Department of Civil Engineering, 23119, Elazig, Turkeyb Yildiz Technical University, Faculty of Civil Engineering, 34210, Esenler, Istanbul, Turkey

a r t i c l e i n f o

Article history:

Received 28 December 2009

Received in revised form6 December 2010

Accepted 5 April 2011

Keywords:

Side weir

Water discharge

Discharge coefficient

Intake

Channel flow

Flow measurement

Hydraulic structure

a b s t r a c t

A side weir is a hydraulic control structure used in irrigation and drainage systems and combined sewersystems. A comprehensive laboratory study, including 843 tests for the discharge coefficient of a sharp-

crested rectangular side weir in a straight channel, was conducted in a large physical model undersubcritical flow conditions. The discharge coefficient is a function of the upstream Froude number, the

ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth. Anequation was developed considering all dimensional parameters for discharge coefficient of the sharp-

crested rectangular side weir. Theaverage error of theproposed equation is 4.54%.The present study datawere compared with ten different discharge coefficient equations developed by several researchers. Thestudy also presents water surface profile and surface velocity streamlines.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

Side weirs have been extensively used in hydraulic andenvironmental engineering applications. They are substantial partsof distribution channels of irrigation systems and water andwastewater treatment plants. Side weirs are also used as anemergency structure in many hydraulic structures. The side weir isnormally installed at one side of a channel to divert flow laterally.

Nandesamoorthy et al. [1], Subramanya et al. [2], Yu-tech [3],Ranga Raju et al. [4], Hager [5], Cheong [6], Singh et al. [7], Jaliliet al. [8], and Borghei et al. [9] gave equations for dischargecoefficients for rectangular, sharp-crested side weirs based onexperimental results. Swamee et al. [10] used an elementaryanalysis approach to estimate the discharge coefficient in smoothside weirs through an elementary strip along the side weirs.Ghodsian [11] studied behavior in the rectangular side weir underconditions of supercritical flow. Khorchani et al. [12] studied theflow over side weirs with a full-scale experiment using digitalcameras. Muslu [13], Yksel [14] and Muslu et al. [15] usednumericalanalysisto analyze the flow over a rectangular side weir.

Considering the discharge dQ through an elementary strip oflengthds along theside weir in a rectangular main channel in termsof De Marchis [16] equation, one gets

q = dQds

= 23

Cd

2g(h p)3/2 (1)

Corresponding author. Tel.: +90 4242370000x5441; fax: +90 4242415526.E-mail addresses: [email protected](M.E. Emiroglu), [email protected]

(H. Agaccioglu), [email protected](N. Kaya).

where Q is the discharge in the main channel, s is the distancefrom the beginning of the side weir, dQ/ds (or q) is the discharge

overflow per unit length of the side weir, g is the accelerationdue to gravity, p the is height of the side weir, h is the depthof flow at the section s (at s = 0 : h = h1 and Q = Q1), (h p) isthe pressure head on the weir and Cd is the discharge coefficientof the rectangular side weir. Thus, Qs = q.L, in which Qs is theflow rate over theside weir and L is the length ofthe side weir. Thedischarge coefficient (Cd) depends on the following dimensionlessparameters [2,7,9,17,18].

Cd = f1

F1 =V1gh1

,L

b,

L

h1,

p

h1, , S0

(2)

where F1 is the upstream Froude number at the beginning of theside weir in the main channel, V1 is the mean velocity of flow atthe upstream section of the side weir in the main channel, L is the

width of the side weir, b is the width of the main channel, h1 isthe depth of flow on the upstream end of the side weir in the mainchannel centerline, is the deviation angle of flow, and S0 is thechannel slope. Notations and a definition sketch of subcritical flowover a rectangular side weir can be seen in Fig. 1.

The water nape deviationor thedeflection angle , isdefinedasthe deflection of the side weir nape from the water surface towardthe weir side which is formulated as follows [2]:

sin =

1

V1

Vs

2(3)

in which, Vs is velocity of flow dQs over the brink. Accordingto Eq. (3), takes different values for each fluid particle and

0955-5986/$ see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2011.04.003
http://dx.doi.org/10.1016/j.flowmeasinst.2011.04.003http://www.elsevier.com/locate/flowmeasinsthttp://www.elsevier.com/locate/flowmeasinstmailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.flowmeasinst.2011.04.003http://dx.doi.org/10.1016/j.flowmeasinst.2011.04.003mailto:[email protected]:[email protected]:[email protected]://www.elsevier.com/locate/flowmeasinsthttp://www.elsevier.com/locate/flowmeasinsthttp://dx.doi.org/10.1016/j.flowmeasinst.2011.04.003

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

2/12

320 M.E. Emiroglu et al. / Flow Measurement and Instrumentation 22 (2011) 319330

Nomenclature

b Width of channel, m

Cd Side weir discharge coefficient,E Specific energy, mF1 Froude number at upstream end of side weir,

g Acceleration due to gravity, m/s2

h Main channel depth, mh1 Flow depth at upstream end of side weir at main

channel centerline, mh2 Flow depth at downstream end of side weir at

channel centerline, mL Length (width) of side weir, m

p Height of weir crest, mQ Discharge in the main channel, m3/sQ0 Discharge at upstream of side weir at main channel

centerline, m3/sQ1 Discharge at upstream end of side weir at main

channel centerline, m3/sQ2 Discharge at downstream end of side weir at main

channel centerline, m3/s

Qs Total flow rate over the side weir, m3

/sq Discharge per unit length over side weir, m2/sdQ/ds = dQs Discharge per unit length of side weir, m2/sR Correlation coefficient,S0 Channel slope,

s Distance along side weir measured from upstreamend of side weir, m

V Mean velocity in any section of channel, m/sV1 Mean velocity of flow at upstream end of side weir,

m/sV2 Mean velocity of flow at downstream end of side

weir, m/sVs Velocity of flow dQs over the brink, m/s Deviation angle of flow,

varies with the Froude number, which changes along the side weir

due to spilling over the side weir. The deviation angle increases

toward theweirsidewhenthe Froude number in themainchannel

decreases toward the downstream direction. El-Khashab [17]

also mentioned that the dimensionless length of the side weir

(L/b) includes the effect of the deviation angle on the discharge

coefficient. Therefore, the deviation angle is not specified in

the side weir discharge coefficient equations in the literature.

Therefore, the effect of on Cd is not considered separately in

the present study. In addition, Borghei et al. [9] reported that

a

b

c

Fig. 1. Definition sketch of subcritical flow over a rectangular side weir.

the channel slope can be ignored in conditions of subcriticalflow. Thus, dimensionless parameters for rectangular side weirdischarge coefficient can be formulated as shown in Eq. (4).

Cd = f2

F1 =V1gh1

,L

b,

L

h1,

p

h1

. (4)

The flowovera side weir is a typical case of spatially varied flowwith decreasing discharge. Like normal weirs, side weirs may be

sharp or broad-crested. The flow in the main channel along a sideweir may be subcritical or supercritical. In side weir applications,the most common form is a sharp-crested rectangular design. Inaddition, the most common flow type is subcritical. Therefore, thisweir type and flow regime are considered in the present study.Table 1 shows equations presented in the literature, relating Cdfor rectangular side weir located on straight channels. As seenin Table 1, Froude number is taken into account in all of theequations. However, the dimensionless parameter L/h1 is not seenin any of the equations previously presented in the literature. Itwas mentioned by Subramanya et al. [2], El-Khashab [17], Singhet al. [7], and Durga Rao et al. [18] that the L/h1 dimensionless

Table 1

Side weir discharge coefficient equations presented in the literature for straight channels.

No. Discharge coefficient equations for rectangular side weirs Source

1 Cd = 0.432

2F21

1+2F21

0.5Nandesamoorthy et al. [1]

2 Cd = 0.611

1

3F21

F21+2

= 0.864

1F2

1

2+F21

0.5Subramanya et al. [2]

3 Cd = 0.623 0.222F1 Yu-Tech [3]4 Cd = 0.81 0.6 F1 Ranga Raju et al. [4]5 Cd = 0.485

2+F2

1

2+3 F21

0.5Hager [5]

6 Cd = 0.45 0.221F21 Cheong [6]7 Cd = 0.33 0.18F1 + 0.49

p

h1

Singh et al. [7]

8 Cd = 0.71 0.41F1 0.22

p

h1

Jalili et al. [8]

9 Cd = 0.7 0.48F1 0.3

p

h1

+ 0.06 L

bBorghei et al. [9]

10 Cd = 1.06[ 14.14p8.15p+h1 10

+ h1h1+p15]0.1

Swamee et al. [10]

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

3/12

M.E. Emiroglu et al. / Flow Measurement and Instrumentation 22 (2011) 319330 321

Table 2

Range of variables for present study and several studies.

Variable Source

Present study Borghei

et al. [9]

Singh

et al. [7]

Cheong [6] Subramanya

et al. [2]

Agaccioglu et al. [21]

Channel width (m) 0.50 0.30 0.25 0.350.67 0.2480.61 0.40

Discharge (L/s) 10150 35100 1014 3.575 7.9568.8

Weir length (m) 0.151.50 0.200.70 0.100.20 0.280.97 0.250.75

Weir height (m) 0.120.20 0.010.19 0.060.12 0.080.51 0.120.16Froude number 0.080.92 0.10.9 0.400.90 0.240.99 0.024.3 0.0770.869

L/b ratio (max.) 0.303.00 2.30 0.50 1.45 0.21.0 0.6251.875

p/h1 ratio 0.340.91 0.420.85 0.20.96 0.5420.877

Dimensionless parameters in

equation

F1, L/b, L/h1 and,

p/h1

F1, L/b, and

p/h1

F1 and p/h1 F1 F1 F1, L/b

Number of runs 843 253 78 200 320 (for straight channel)

Fig. 2. Experimental arrangement.

parameter is among the parameters that affect the discharge

coefficient. Therefore, L/h1 and L/b dimensionless parametershave

been tested together with p/h1 parameter for the experimental

data. The range of test variables used in the present study is given

Table 2.

The purpose of this study is to systematically investigate

the effect of side weir length in relation to the dischargecoefficient under subcritical flow conditions, using a broad range

of experiments, and considered together with the other effective

dimensionless parameters. Additionally, water surface profiles and

surface velocity streamlines were investigated in the weir region.

2. Experimental set-up and experiments

Experiments were carried out in the Hydraulic Laboratory of

Firat University, Elazig, Turkey. A schematic representation of the

experimental set-up is shown in Fig. 2. The experimental set-upconsists of a main channel and a discharge collection channel. The

main channel is 12 m long and the bed has a rectangular cross

section. The main channel is 0.5 m wide, 0.5 m deep and has a0.001 bed slope. The channel consists of a smooth horizontal well-

painted steel bed with a vertical glass sidewall. A sluice gate is

fitted at the end of themainchannel in orderto control flow depth.The collection channel is 0.5 m wide and 0.7 m deep, and situated

parallel to the main channel. The width of the collection channel

acrossthe side weiris 1.3 m and it isconstructedas a circularshape

to provide free overflow conditions over the side weirs. A Mitutoyo

brand digital point gauge with0.01 mm sensitivity is fitted 0.4 mfrom the weir. The side weirs were fabricated from steel plates,

which are sharp edged and fully aerated and installed flush with

the main channel bank.

Water for the main channel was supplied through a supply

pipe from a sump and the flow was controlled by a gate valve.

In previous studies, experiments to determine the dischargecoefficient were generally conducted within a narrower range

Fig. 3. Locations where water level was measured.

of discharges than those examined in the present study. In thisstudy, the flow rate was between 0.010 and 0.150 m3/s and wasmeasured by means of a Siemensbrandelectromagnetic flowmeter(0.01 L/s sensitivity) installed on the supply line. Additionally,the results were compared by a calibrated 90 V-notched weir atthe beginning of the system (Q1). The overflow rate at thesideweirwas obtained by calibrated standard rectangular weir, located atthe downstream end of the collection channel (Qs).

Water depth was measured using the point gauge at the sideweir region, along the channel centerline (C2, D2 and E2) and the

weir side of the main channel (C1, D1 and E1), as seen in Fig. 5.Water surface measurements were made using a special type of

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

4/12


0.00 0.20 0.40 0.60 0.80 1.000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Rectangular side weir

p=0.12 m, L=0.75 m

Depthofflowinm

Longitudinal section in m

F1=0.28, Surface profile along the centerline

0.00 0.20 0.40 0.60 0.80 1.000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50


p=0.12 m, L=0.75 m

Depthofflowin

m


F1=0.28, Surface profile along the weir-side

0.00 0.20 0.40 0.60 0.80 1.000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50


p=0.16 m, L=0.75 m

Depthofflowinm



0.00 0.20 0.40 0.60 0.80 1.000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50


p=0.16 m, L=0.75 m

Depthofflowinm



0.00 0.20 0.40 0.60 0.80 1.00

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

o.50


p=0.20 m, L=0.75 m

Depthofflowinm



0.00 0.20 0.40 0.60 0.80 1.000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50


p=0.20 m, L=0.75 m

Depthofflowinm



Fig. 4. Water surface profiles along the weir side and centerline at straight channel.

measurement car which can move in both x and y directions on a

rail (see Fig. 3). Velocities were measured using a Nortek Acoustic

Doppler velocity meter with high sensitivity.

Experiments were conducted for subcritical flow, stable flow

and free overflow conditions. Coleman et al. [19] stated that

minimum nape height should not be less than 0.019 m because of

the surface tension over the weir crest. Therefore, minimum nape

height was taken into account as 0.020 m. The experiments were

conducted for five different lengths of the weir (0.15, 0.25, 0.50,

0.75, and 1.50 m) and three different heights of the weir (0.12,0.16, and 0.20 m). As seen in Table 2, the length of side weir, L was

between 0.20 and 0.70 m to achieve the discharge coefficient of

rectangular side weir. Thelengthof theside weir (L) is an important

parameter for discharge coefficient of the side weir. Therefore, the

dimensionless parameters, L/b and L/h1, were studied in detail in

the present study. The length of the side weir (L) was considered

between 0.15 and 1.50 m in the present study, permitting the

dimensionless L/b parameter to be tested across a wide range (i.e.,

L/b = 0.3 to 3.0).After the completion of a good physical description of the

rectangular side weir flow at the straight rectangular channel, sideweir flow rates were tested for different Froude numbers, different

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

5/12


a

b

Fig. 5. Definition sketch: velocity streamlines for L/b = 1.50: (a) F1 < 0.28; (b) F1 > 0.42.

p/h1 ratios, different L/b ratios, and different L/h1 ratios in orderto determine the variation of the discharge coefficient (Table 2).A total of 910 test runs for discharge coefficient and water level

measurements were performed in the present study.

3. Experimental results and analysis

3.1. Water level profile

Water surface levels were measured both along the channelcenterline (C2, D2 and E2) and the weir side of the main channel(C1, D1 and E1) to describe the flow structure in the main channel.As shown in Fig. 4, the water depth at the upstream end of the

side weir is lower than that at the downstream end of the sideweir. This same situation is observed in all previous experimentalruns. Water surface profiles along side weirs drop slightly at theupstream end of the weir crest. As El-Khashab [17] and Emirogluet al. [20] reported in previous studies, this is due to the side weir

entrance effect at the upstream end. The water level then quicklyrises toward the downstream end of theweir. The rate of rise at thewater level decreases substantially after the midspan of the sideweir crest. The change in water level is not noticeable in almost

the last third of the weir length, where the water surface is almosthorizontal. This behavior of the water surface is due to the effectof secondary flow created by lateral flow. Fig. 4 also indicates thatthe water surface level along the main channel centerline is almosthorizontal. This shows that the side weir entrance effect does notspread as for as the centerline of themain channel, but occurs only

near the weir crest.Fig. 5(a) and (b) show surface velocity streamlines for F1 0.42, respectively. The effect of lateral flow issignificant, especially for high overflow conditions. The effect of

the breakdown in flow near the end of the weir at the channelside is obvious near the channel bed. Since the low velocity layerstarts to exist, the path of maximum velocity gradually movesfrom a position toward the side weir toward the centerline of the

main channel passing through the separation zone. The separationzone occurs due to decreasing momentum in the direction of the

main channel flow overflowing the collection channel. The areaoccupied by this zone is always near the bed, from 0.2 to 0.4 times

the mean depth of flow at that section along the weir length, andvaries with this area occupied by the low velocity layer. A reverseflow at the downstream end of the side weir was also observed

when the Froude number is small. When F1 > 0.42, the reserveflow area diminishes and weak standing waves are formed. WhenF1 > 0.85, a surface jump occurs earlier at the end of side weirs,

because lateral flow reduces the potential energy and increasesthe kinetic energy of the flow in the downstream direction withinthe main channel. The existence of a stagnation zone is due to thediversion that occurs from the path of maximum velocity thread.

The location of the stagnation zone and the reverse flow areadepend especially on the Froude number F1 at the upstream sideof the weir in the main channel in addition to the length of the

side weir and thenapethickness over the side weir. When theflowintensity or momentum toward the downstream direction in themain channel increases, then the reverse flow area moves towardthe downstream end of the side weir.

3.2. Cd coefficient

A series of 843 experimental runs were conducted to determine

the discharge coefficient of sharp-crested rectangular side weirs.The discharge coefficient was computed using De Marchisequation (Eq. (2)). In other words, h1 and Qw were measured for

each side weir configuration in the laboratory. Thus, the dischargecoefficient was computed with Eq. (5) (i.e., De Marchis equation).

Cd =(3/2)Qw

2g(h1 p)3/2L. (5)

To study the effect of parameter p/h1 on discharge coefficients,Cd values were plotted againstp/h1 together with the different L/bratios, as shown in Fig. 6((a)(c)). Experiments were performed for

constantp, b and L with varying depth of flow (h1). In otherwords,the crest heightis 0.12m in Fig. 6(a), 0.16 m in Fig. 6(b), and 0.20m

in Fig. 6(c). As is seen in Fig. 6((a)(c)), Cd values correspondingto the same p/h1 values, especially for high L/b ratios, are very

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

6/12


a b

c

Fig. 6. Cd vs. different p/h1 values for L/b = 0.3; L/b = 1.5, and L/b = 3.0 (a) p/b = 0.24; (b) p/b = 0.32; and (c) p/b = 0.24.

Fig. 7. Side weir coefficient (Cd) vs. F1 together with different dimensionless weir

heights (p/h1).

different from each other.The scatterof thedata is attributed to theeffect of the other parameters, such as F1 and L/h1 parameters. Thevariation ofCd with p/h1 shows a decreasing tendency for L/b =0.3. This decreasingtendency forL/b < 1 is similar to that reportedin previous studies [8,9,21,22]. The variation of Cd with p/h1 for

L/b = 1 to 1.5 shows a slightly increasing tendency. However,for L/b = 3.0, this increasing tendency is very high. The intensity

of secondary flow due to lateral flow is more dominant whena side weir is relatively long. Therefore, the deviation angle andthe kinetic energy caused by the secondary flow toward the sideweir increases when the relative side weir length (or the overflowlength) increases. Thus, it can be conclusively stated that p/h1 isan important parameter for the discharge coefficient. Therefore,

the effect of p/h1 on Cd has been investigated in detail for allrectangular side weirs.

Fig. 7 shows Cd plotted against F1 together with differentdimensionless weir heights (p/h1) and weir lengths (L/b). The

p/h1 and L/b values were kept constant, and several series of

experiments with different Froude numbers were performed.Although the variation in Cd value does not change greatly with

increasing p/h1 value for L/b = 0.3, the values of Cd increasesignificantly with increasing p/h1 for L/b = 3.0. Fig. 7 clearlyshows the effect of both p/h1 and L/b on Cd . The effect of p/h1on Cd can be explained with reference to the discontinuity region.This discontinuityregion hasa strongsecondary motionnext to theboundary of the weir side: the intensity of the secondary motion

next to the boundary depends on the crest height of the side weirand decreases with increasing crest height of the side weir, dueto the friction of the weir surface. The intensity of secondary flowcreated by lateral flow is defined as the ratio of the mean kineticenergyof the lateral motionto the total kinetic energyof main flowat a given cross section.

The variation of Cd with F1 while L/b, p/h1, and L/h1 areconstant is shown in Fig. 8((a)(e)). Moreover, Fig. 8((a)(e)) also

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

7/12


ab

cd

e

Fig. 8. Cd for different F1 values: (a) p = 0.12 m; (b) p = 0.16 m; (c) p = 0.20 m.

show the effect of L/b parameter on Cd . For L/b = 0.3 and0.5, when the Froude number increases, Cd values decrease. The

results indicate that the discharge coefficient increases when the

Froude number increases for L/b > 1. Agaccioglu et al. [21] and

Kaya et al. [22] also found a similar tendency. The values of Cdhave a tendency to increase with increasing values of L/b. The

variation ofCd with F1 shows an increasing tendency when L/b =3, as shown in Fig. 8(e). The primary reason for this may be the

intensity of secondary flow created by lateral flow turbulence

and velocity streamlines that is oriented toward the side weir. By

the orientation of the velocity streamlines toward side weir, the

occurrence of the stagnation zone plays an important role in flow

interactions. As mentioned above, the strength of the secondary

flow created by the lateral flow was affected by the length of the

side weir crest height of the side weir and the Froude number. Anincrease in the secondary flow causes the growth of the deviation

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

8/12


a b

c

Fig. 9. Cd for different L/h1 values (a) L/b = 0.3; (b) L/b = 1.5; (c) L/b = 3.0.

angle and kinetic energy toward the side weir when the relative

length of the side weir increases. A review of the literature shows

that previous experiments generally used narrower main channel

widths, smaller weir lengths, and lower flow rates. Most previous

researchers ignored the effect of L/b, L/h1, and p/h1 ratios on the

discharge coefficient. However, Jalili et al. [8] and Borghei et al. [9]

considered the effect ofL/b and p/h1.

Fig. 9 shows theeffect ofL/h1 on Cd, wherep/b is kept constant.

In other words, the crest height is 0.12 m in Fig. 9(a), 0.16 m in

Fig. 9(b), and 0.20 m in Fig. 9(c). However, it was not possible

to take p/h1 and F1 as constants, due to the variation of L/h1ratio. Although many researchers (e.g., El-Khashab [17]; Durga

Rao [18]) stated that the dimensionless parameter L/h1 is effective

on discharge coefficient, the effect of thisdimensionless parameter

was not studied adequately in previous studies. As shown in Fig. 9,

the variation in Cd tends to increase with increasing values of

L/h1. The scatter of the data is attributed to the effect of the other

parameters, such as the Froude number and p/h1 parameters. This

could be observed in almost all of the experiments. For the higher

values ofL/b, the effect ofL/h1 can be seen more clearly. The fact

that the literature studied low L/b ratios more commonly led to

researchers overlooking the real effect of L/h1. The results of the

present study demonstrate conclusively that L/h1 should not be

ignored.

Empirical correlations to predict discharge coefficient Cd weredeveloped for rectangular side weirs according to the results of the

dimensionless analysis. The resulting correlation is given in Eq. (6).

Cd =

0.836 +0.035 + 0.39

p

h1

12.69+ 0.158

L

b

0.59

+ 0.049

L

h1

0.42+ 0.244F2.1251

3.0185.36

(6)

where the weir width L, the channel width b, the height of weir

crestp, and the flow depth h1 are in meters and theFroudenumber

F1 is dimensionless.To evaluate the accuracy of the estimated nonlinear equation,

the root mean square errors (RMSE), the mean absolute error

(MAE), the average percent error (APE) and the correlation

coefficient (R) criteria were used. The value ofR shows the degree

to which two variables are linearly related. Different types of

information about the predictive capabilities of the estimated

nonlinear equation are measured through RMSE and MAE. The

RMSE indicates the goodness of the fit related to high discharge

coefficient values, whereas the MAE provides a more balanced

perspective of the goodness of the fit at moderate discharge

coefficients [23]. The RMSE, MAE and APE are defined as

RMSE = 1NN

i=1(Cd(observed) Cd(estimated))

2

(7)

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

9/12


Table 3

Comparison of present results with those of researchers in the literature when L/b = 0.3.F1 p/h1 L/b L/h1 Subramanya

et al. [2]

Ranga

Raju

et al. [4]

Hager [5] Singh

et al. [7]

Jalili

et al. [8]

Borghei

et al. [9]

Swamee

etal. [10]

Cheong[6] Nandesamoorthy

et al. [1]

Yu-

Tech [3]

Present

study

0.099 0.74 0.3 0.923 0.426 0.750 0.483 0.674 0.507 0.449 0.712 0.448 0.603 0.601 0.378

0.118 0.84 0.3 1.044 0.423 0.739 0.482 0.718 0.478 0.411 0.701 0.447 0.600 0.597 0.345

0.219 .79 0.3 0.989 0.402 0.678 0.474 0.678 0.446 0.375 0.706 0.439 0.576 0.574 0.318

0.313 0.77 0.3 0.963 0.372 0.622 0.464 0.651 0.412 0.337 0.708 0.428 0.545 0.554 0.3650.153 0.34 0.3 0.426 0.417 0.718 0.480 0.469 0.572 0.542 0.831 0.445 0.594 0.589 0.406

0.198 0.34 0.3 0.424 0.407 0.691 0.476 0.460 0.554 0.521 0.832 0.441 0.583 0.579 0.404

0.228 0.37 0.3 0.466 0.399 0.673 0.473 0.472 0.535 0.497 0.812 0.439 0.574 0.572 0.401

0.267 0.41 0.3 0.518 0.387 0.650 0.469 0.485 0.509 0.465 0.792 0.434 0.561 0.564 0.397

0.294 0.40 0.3 0.505 0.378 0.633 0.466 0.475 0.500 0.456 0.797 0.431 0.552 0.558 0.397

0.226 0.34 0.3 0.422 0.400 0.674 0.473 0.455 0.543 0.508 0.833 0.439 0.574 0.573 0.402

0.257 0.34 0.3 0.422 0.391 0.656 0.470 0.449 0.530 0.493 0.833 0.435 0.565 0.566 0.408

0.634 0.62 0.3 0.772 0.215 0.430 0.420 0.518 0.314 0.229 0.732 0.361 0.407 0.482 0.320

0.650 0.58 0.3 0.728 0.206 0.420 0.418 0.498 0.316 0.231 0.740 0.357 0.400 0.479 0.318

0.088 0.72 0.3 0.541 0.427 0.757 0.483 0.668 0.515 0.459 0.715 0.448 0.605 0.603 0.402

0.119 0.88 0.3 0.661 0.423 0.739 0.482 0.741 0.467 0.396 0.696 0.447 0.600 0.597 0.365

0.143 0.63 0.3 0.473 0.419 0.724 0.480 0.613 0.513 0.460 0.730 0.445 0.596 0.591 0.400

0.123 0.46 0.3 0.347 0.422 0.736 0.481 0.534 0.558 0.520 0.773 0.447 0.600 0.596 0.410

0.167 0.51 0.3 0.379 0.414 0.710 0.478 0.547 0.530 0.486 0.759 0.444 0.590 0.586 0.407

0.172 0.47 0.3 0.353 0.413 0.707 0.478 0.530 0.536 0.494 0.770 0.443 0.589 0.585 0.404

0.515 0.90 0.3 0.674 0.280 0.501 0.437 0.678 0.301 0.201 0.694 0.391 0.460 0.509 0.318

0.590 0.91 0.3 0.681 0.240 0.456 0.426 0.669 0.268 0.162 0.693 0.373 0.426 0.492 0.3270.550 0.87 0.3 0.650 0.262 0.480 0.432 0.656 0.294 0.194 0.697 0.383 0.444 0.501 0.281

0.567 0.83 0.3 0.621 0.253 0.470 0.429 0.634 0.295 0.197 0.701 0.379 0.437 0.497 0.338

0.606 0.87 0.3 0.649 0.231 0.447 0.424 0.645 0.271 0.168 0.698 0.369 0.419 0.489 0.285

0.615 0.82 0.3 0.617 0.226 0.441 0.423 0.623 0.277 0.176 0.702 0.367 0.415 0.487 0.314

0.184 0.86 0.3 1.071 0.410 0.700 0.477 0.717 0.446 0.373 0.698 0.443 0.586 0.582 0.376

0.366 0.86 0.3 1.071 0.351 0.591 0.457 0.684 0.371 0.285 0.698 0.420 0.524 0.542 0.366

0.424 0.86 0.3 1.071 0.325 0.555 0.449 0.674 0.348 0.257 0.698 0.410 0.500 0.529 0.346

0.127 0.89 0.3 0.833 0.422 0.734 0.481 0.743 0.462 0.390 0.695 0.446 0.599 0.595 0.434

0.210 0.89 0.3 0.833 0.404 0.684 0.475 0.728 0.428 0.351 0.695 0.440 0.579 0.576 0.412

0.294 0.89 0.3 0.833 0.378 0.633 0.466 0.713 0.394 0.310 0.695 0.431 0.552 0.558 0.412

0.405 0.91 0.3 0.682 0.334 0.567 0.452 0.703 0.344 0.251 0.693 0.414 0.508 0.533 0.403

0.466 0.91 0.3 0.682 0.305 0.530 0.444 0.692 0.319 0.222 0.693 0.402 0.482 0.520 0.394

0.549 0.75 0.3 0.938 0.262 0.481 0.432 0.599 0.320 0.230 0.711 0.383 0.445 0.501 0.335

0.600 0.75 0.3 0.938 0.235 0.450 0.425 0.590 0.299 0.205 0.711 0.371 0.422 0.490 0.356

0.178 0.80 0.3 0.750 0.412 0.703 0.478 0.690 0.461 0.393 0.705 0.443 0.588 0.584 0.424

0.251 0.80 0.3 0.750 0.392 0.659 0.471 0.677 0.431 0.357 0.705 0.436 0.567 0.567 0.410

0.409 0.83 0.3 0.625 0.332 0.565 0.451 0.665 0.359 0.272 0.701 0.413 0.506 0.532 0.3830.463 0.83 0.3 0.625 0.306 0.532 0.444 0.655 0.337 0.246 0.701 0.403 0.483 0.520 0.375

0.293 0.67 0.3 0.833 0.379 0.634 0.466 0.604 0.443 0.378 0.723 0.431 0.552 0.558 0.391

0.417 0.67 0.3 0.833 0.328 0.560 0.450 0.582 0.392 0.318 0.723 0.412 0.503 0.530 0.382

0.494 0.73 0.3 0.682 0.291 0.513 0.439 0.597 0.347 0.262 0.714 0.396 0.469 0.513 0.388

0.621 0.73 0.3 0.682 0.222 0.437 0.422 0.575 0.295 0.202 0.714 0.365 0.412 0.485 0.342

0.168 0.77 0.3 0.577 0.414 0.709 0.478 0.677 0.472 0.407 0.708 0.444 0.590 0.586 0.414

0.241 0.77 0.3 0.577 0.395 0.666 0.472 0.664 0.442 0.372 0.708 0.437 0.570 0.570 0.409

MAE = 1N

Ni=1

|Cd(observed) Cd(estimated)| (8)

APE = 100N

N

i=1

Cd(observed) Cd(estimated)Cd(observed)

(9)

in which N is the number of data set.

The root mean square error (RMSE), the mean absolute error

(MAE), the average percent error (APE) and correlation coefficient

(R) values for Eq. (6) are 0.0401%, 0.0281%, 4.527% and 0.955%

(i.e., deterministic coefficient R2 = 0.912), respectively. Very goodagreements are obtained between the values observed experi-

mentally and the values computed from the predictive equation

(i.e., Eq. (6)). Thus, the present study introduces an accurate equa-

tion for the coefficient of discharge of the rectangular side weirs in

subcritical flow conditions.

The results of the present study, shown in Tables 35 were

compared with ten previous studies from the literature. As seen

from the relevant tables and also Fig. 10, at lower L/b values, the

results of the present studies are generally compatible with theliterature. The same is nottrue at high L/b ratios. Table 5 and Fig. 11

show that small F1 numbers are compatible with the literaturebut that, at high F1 numbers, the present results differ from thosereported in the literature. This can be explained as follows: at highL/b ratios, the intensity of secondary flow increases even more. Asmentioned above, the present study examined higher L/b ratios.The values obtained using equations produced in other studies are

not very compatible within themselves. This situation can be seenin Tables 35.

4. Conclusions

The present study provides an experimental examination ofthe variation in the discharge coefficient of a rectangular, sharp-crested side weir located on a straight, rectangular main channel.As a result of dimensional analysis, the results indicate that thedimensionless parameters of L/b and L/h1 should not be ignoredin equations determining the discharge coefficient of the sideweir. In this study, the ranges of experimental conditions werebetween 0.08 and 0.92 for F1, 0.34 and 0.91 for p/h1, 0.30 and3.00 for L/b, and 0.347 and 10.71 for L/h1. For L/b = 0.3and 0.5, when the Froude number increases, Cd values decrease.However, the variation ofCd with F1 shows an increasing tendency

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

10/12


Table 4

Comparison of present results with those in the literature when L/b = 1.5.F1 p/h1 L/b L/h1 Subramanya

et al. [2]

Ranga

Raju

et al. [4]

Hager [5] Singh

et al. [7]

Jalili

et al. [8]

Borghei

et al. [9]

Swamee

etal.[10]

Cheong[6] Nandesamoorthy

et al. [1]

Yu-

Tech[3]

Present

study

0.161 0.78 1.5 4.925 0.415 0.713 0.479 0.687 0.471 0.476 0.706 0.444 0.592 0.587 0.390

0.169 0.82 1.5 5.095 0.414 0.708 0.478 0.699 0.461 0.464 0.703 0.444 0.590 0.585 0.361

0.226 0.70 1.5 4.378 0.400 0.674 0.473 0.633 0.463 0.471 0.718 0.439 0.574 0.573 0.422

0.236 0.72 1.5 4.514 0.397 0.668 0.472 0.641 0.454 0.460 0.715 0.438 0.571 0.570 0.4160.737 0.63 1.5 3.965 0.155 0.368 0.406 0.508 0.268 0.246 0.729 0.330 0.361 0.459 0.501

0.631 0.54 1.5 3.344 0.217 0.431 0.420 0.479 0.333 0.326 0.751 0.362 0.408 0.483 0.485

0.728 0.59 1.5 3.677 0.161 0.373 0.407 0.487 0.282 0.264 0.738 0.333 0.365 0.461 0.525

0.692 0.54 1.5 3.347 0.182 0.395 0.412 0.468 0.309 0.297 0.751 0.344 0.381 0.469 0.506

0.804 0.56 1.5 3.495 0.116 0.328 0.398 0.459 0.257 0.237 0.745 0.307 0.332 0.445 0.562

0.454 0.88 1.5 4.135 0.311 0.537 0.445 0.680 0.330 0.307 0.696 0.404 0.487 0.522 0.390

0.310 0.61 1.5 2.860 0.373 0.624 0.464 0.573 0.449 0.458 0.734 0.429 0.546 0.554 0.426

0.352 0.67 1.5 3.119 0.356 0.599 0.459 0.593 0.419 0.421 0.724 0.423 0.530 0.545 0.448

0.435 0.77 1.5 3.589 0.320 0.549 0.448 0.627 0.363 0.351 0.709 0.408 0.495 0.526 0.466

0.506 0.85 1.5 3.973 0.285 0.506 0.438 0.654 0.316 0.293 0.699 0.393 0.464 0.511 0.451

0.345 0.60 1.5 2.797 0.359 0.603 0.460 0.560 0.437 0.445 0.737 0.424 0.533 0.546 0.428

0.394 0.65 1.5 3.056 0.339 0.574 0.453 0.579 0.405 0.405 0.726 0.416 0.513 0.536 0.440

0.475 0.74 1.5 3.461 0.301 0.525 0.442 0.606 0.353 0.341 0.712 0.400 0.478 0.518 0.483

0.089 0.88 1.5 3.294 0.427 0.757 0.483 0.744 0.480 0.484 0.696 0.448 0.605 0.603 0.447

0.134 0.83 1.5 3.105 0.420 0.729 0.481 0.711 0.473 0.477 0.702 0.446 0.597 0.593 0.440

0.153 0.90 1.5 3.381 0.417 0.718 0.479 0.744 0.449 0.446 0.694 0.445 0.594 0.589 0.401

0.175 0.79 1.5 2.947 0.413 0.705 0.478 0.684 0.465 0.470 0.706 0.443 0.589 0.584 0.444

0.402 0.83 1.5 3.097 0.335 0.569 0.452 0.662 0.364 0.349 0.702 0.414 0.509 0.534 0.497

0.453 0.89 1.5 3.356 0.312 0.538 0.445 0.687 0.327 0.304 0.695 0.405 0.487 0.522 0.527

0.304 0.63 1.5 2.367 0.375 0.628 0.465 0.585 0.447 0.455 0.730 0.430 0.548 0.556 0.437

0.360 0.71 1.5 2.647 0.353 0.594 0.458 0.611 0.407 0.406 0.717 0.421 0.527 0.543 0.469

0.425 0.79 1.5 2.956 0.325 0.555 0.449 0.640 0.362 0.349 0.706 0.410 0.499 0.529 0.489

0.494 0.87 1.5 3.267 0.291 0.514 0.440 0.668 0.316 0.291 0.697 0.396 0.469 0.513 0.504

0.334 0.62 1.5 2.338 0.363 0.610 0.461 0.575 0.436 0.443 0.731 0.425 0.537 0.549 0.436

0.408 0.71 1.5 2.672 0.332 0.565 0.452 0.606 0.386 0.380 0.716 0.413 0.507 0.532 0.478

0.494 0.81 1.5 3.033 0.291 0.513 0.440 0.637 0.329 0.310 0.704 0.396 0.469 0.513 0.508

0.558 0.88 1.5 3.288 0.257 0.475 0.430 0.659 0.288 0.259 0.696 0.381 0.441 0.499 0.532

0.389 0.65 1.5 2.421 0.341 0.576 0.454 0.576 0.408 0.409 0.727 0.417 0.515 0.537 0.453

0.466 0.73 1.5 2.730 0.305 0.531 0.444 0.603 0.359 0.348 0.714 0.402 0.482 0.520 0.502

0.541 0.80 1.5 3.015 0.267 0.486 0.433 0.627 0.311 0.289 0.704 0.385 0.448 0.503 0.501

0.632 0.89 1.5 3.344 0.216 0.431 0.420 0.653 0.255 0.219 0.695 0.362 0.408 0.483 0.545

0.608 0.86 1.5 5.357 0.230 0.445 0.423 0.641 0.272 0.241 0.698 0.368 0.418 0.488 0.689

0.684 0.86 1.5 5.357 0.186 0.400 0.413 0.627 0.241 0.205 0.698 0.347 0.384 0.471 0.6060.334 0.89 1.5 4.167 0.363 0.609 0.461 0.705 0.377 0.363 0.695 0.425 0.537 0.549 0.504

0.376 0.89 1.5 4.167 0.346 0.584 0.456 0.698 0.360 0.343 0.695 0.419 0.520 0.539 0.511

0.100 0.91 1.5 3.409 0.426 0.750 0.483 0.758 0.469 0.469 0.693 0.448 0.603 0.601 0.537

0.126 0.91 1.5 3.409 0.422 0.735 0.481 0.753 0.458 0.457 0.693 0.447 0.599 0.595 0.538

0.156 0.91 1.5 3.409 0.416 0.716 0.479 0.747 0.446 0.442 0.693 0.445 0.593 0.588 0.546

0.217 0.91 1.5 3.409 0.402 0.680 0.474 0.736 0.421 0.413 0.693 0.440 0.577 0.575 0.564

0.280 0.91 1.5 3.409 0.383 0.642 0.468 0.725 0.395 0.383 0.693 0.433 0.557 0.561 0.583

0.342 0.91 1.5 3.409 0.360 0.605 0.460 0.714 0.370 0.353 0.693 0.424 0.534 0.547 0.582

Fig. 10. Comparison of present results with those of Singh et al. [7] and Borghei

et al. [9] when L/b = 0.50.Fig. 11. Comparison of recent results with those of Singh et al. [7] and Borghei

et al. [9] when L/b = 3.00.

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

11/12


Table 5

Comparison of present results with those in the literature when L/b = 3.0.F1 p/h1 L/b L/h1 Subramanya

and

Awasty [2]

Ranga

Raju

et al. [4]

Hager [5] Singh

et al. [7]

Jalili

and

Borghei[8]

Borghei

et al. [9]

Swamee

etal. [10]

Cheong [6] Nandesamoorthy

and

Thomson [1]

Yu-

Tech [3]

Present

study

0.282 0.82 3.0 10.266 0.382 0.641 0.467 0.682 0.414 0.498 0.702 0.432 0.556 0.560 0.608

0.328 0.79 3.0 9.824 0.366 0.614 0.462 0.656 0.403 0.487 0.706 0.426 0.539 0.550 0.585

0.369 0.78 3.0 9.720 0.350 0.589 0.457 0.645 0.388 0.470 0.707 0.420 0.523 0.541 0.602

0.405 0.83 3.0 10.356 0.334 0.567 0.452 0.663 0.361 0.437 0.701 0.414 0.508 0.533 0.6760.473 0.84 3.0 10.492 0.302 0.527 0.443 0.656 0.332 0.401 0.700 0.401 0.479 0.518 0.932

0.495 0.80 3.0 9.974 0.291 0.513 0.439 0.632 0.332 0.403 0.705 0.396 0.469 0.513 0.672

0.507 0.81 3.0 10.184 0.284 0.506 0.438 0.638 0.323 0.392 0.703 0.393 0.463 0.510 0.7010.637 0.80 3.0 7.487 0.213 0.428 0.419 0.607 0.273 0.334 0.705 0.360 0.405 0.482 0.834

0.786 0.79 3.0 7.448 0.126 0.339 0.400 0.578 0.213 0.265 0.705 0.314 0.340 0.449 1.0660.826 0.79 3.0 7.361 0.102 0.314 0.395 0.566 0.199 0.248 0.706 0.299 0.322 0.440 1.116

0.807 0.80 3.0 7.509 0.114 0.326 0.397 0.577 0.203 0.252 0.705 0.306 0.331 0.444 1.148

0.652 0.79 3.0 7.445 0.205 0.419 0.417 0.602 0.268 0.329 0.705 0.356 0.398 0.478 0.841

0.485 0.72 3.0 6.730 0.296 0.519 0.441 0.594 0.353 0.432 0.715 0.398 0.473 0.515 0.618

0.440 0.73 3.0 6.821 0.318 0.546 0.447 0.607 0.369 0.450 0.714 0.407 0.493 0.525 0.609

0.389 0.75 3.0 7.031 0.341 0.577 0.454 0.627 0.386 0.468 0.711 0.417 0.515 0.537 0.600

0.343 0.78 3.0 7.335 0.360 0.605 0.460 0.652 0.397 0.481 0.707 0.424 0.533 0.547 0.628

0.284 0.81 3.0 7.619 0.382 0.640 0.467 0.677 0.415 0.500 0.703 0.432 0.556 0.560 0.6390.236 0.85 3.0 7.980 0.397 0.668 0.472 0.705 0.426 0.511 0.699 0.438 0.571 0.571 0.697

0.181 0.90 3.0 6.713 0.411 0.701 0.477 0.736 0.439 0.524 0.695 0.443 0.587 0.583 0.6820.221 0.84 3.0 6.305 0.401 0.678 0.474 0.702 0.435 0.522 0.700 0.439 0.576 0.574 0.592

0.263 0.81 3.0 6.092 0.389 0.652 0.470 0.681 0.423 0.510 0.703 0.435 0.562 0.565 0.576

0.307 0.90 3.0 6.761 0.374 0.626 0.465 0.716 0.386 0.462 0.694 0.429 0.547 0.555 0.770

0.411 0.84 3.0 6.267 0.331 0.564 0.451 0.666 0.358 0.432 0.701 0.413 0.506 0.532 0.690

0.435 0.72 3.0 5.379 0.320 0.549 0.448 0.603 0.374 0.456 0.715 0.408 0.495 0.526 0.544

0.615 0.90 3.0 6.774 0.226 0.441 0.422 0.662 0.259 0.314 0.694 0.367 0.415 0.487 1.020

0.679 0.90 3.0 6.784 0.189 0.403 0.414 0.651 0.233 0.283 0.694 0.348 0.387 0.472 1.160

0.651 0.88 3.0 6.604 0.205 0.419 0.417 0.644 0.249 0.303 0.696 0.356 0.399 0.478 1.009

0.703 0.88 3.0 6.575 0.175 0.388 0.410 0.633 0.229 0.279 0.696 0.341 0.376 0.467 1.020

0.735 0.90 3.0 6.773 0.156 0.369 0.406 0.640 0.210 0.256 0.694 0.331 0.362 0.460 1.3470.808 0.91 3.0 6.813 0.113 0.325 0.397 0.630 0.179 0.220 0.693 0.306 0.330 0.444 1.746

0.769 0.88 3.0 6.591 0.136 0.348 0.402 0.622 0.201 0.247 0.696 0.319 0.347 0.452 1.2880.244 0.86 3.0 10.714 0.395 0.664 0.472 0.706 0.421 0.506 0.698 0.437 0.569 0.569 0.677

0.367 0.86 3.0 10.714 0.350 0.590 0.457 0.684 0.371 0.447 0.698 0.420 0.524 0.542 0.722

0.797 0.86 3.0 10.714 0.294 0.517 0.440 0.662 0.322 0.389 0.698 0.397 0.472 0.515 0.792

0.715 0.89 3.0 8.333 0.168 0.381 0.409 0.637 0.221 0.270 0.695 0.337 0.371 0.464 1.347

0.750 0.89 3.0 8.333 0.147 0.360 0.404 0.631 0.207 0.253 0.695 0.326 0.355 0.456 1.556

0.165 0.91 3.0 6.818 0.415 0.711 0.479 0.746 0.443 0.528 0.693 0.444 0.591 0.586 0.731

0.277 0.91 3.0 6.818 0.384 0.644 0.468 0.726 0.397 0.474 0.693 0.433 0.558 0.562 0.785

0.397 0.75 3.0 9.375 0.337 0.572 0.453 0.626 0.382 0.464 0.711 0.415 0.511 0.535 0.5830.550 0.75 3.0 9.375 0.262 0.480 0.432 0.599 0.320 0.391 0.711 0.383 0.444 0.501 0.682

0.610 0.80 3.0 7.500 0.228 0.444 0.423 0.612 0.284 0.347 0.705 0.368 0.417 0.487 0.8570.679 0.80 3.0 7.500 0.189 0.403 0.414 0.600 0.256 0.314 0.705 0.348 0.387 0.472 0.914

0.246 0.83 3.0 6.250 0.394 0.663 0.471 0.694 0.426 0.512 0.701 0.437 0.568 0.569 0.6000.328 0.83 3.0 6.250 0.366 0.614 0.462 0.679 0.392 0.473 0.701 0.426 0.539 0.550 0.656

0.434 0.83 3.0 6.250 0.320 0.550 0.448 0.660 0.349 0.422 0.701 0.408 0.496 0.527 0.674

when L/b = 3. An equation predicting the discharge coefficientof rectangular sharp-crested side weirs was developed. The

presented equation for Cd, De Marchis coefficient is reliable in

subcritical flow conditions. Thus, the discharge coefficient derived

from the equation can be used with confidence.

Acknowledgments

The authors are grateful for the constructive comments of

various anonymous reviewers, which strengthened and further

focused the manuscript. The authors acknowledge the financial

support of the Scientific and Technological Research Council of

Turkey (TUBITAK) under Project No. MAG 104M394.

References

[1] Nandesamoorthy T, Thomson A. Discussion of spatially varied flow over sideweir. ASCE Journal of the Hydraulics Division 1972;98(12):22345.

[2] SubramanyaK, AwasthySC. Spatiallyvariedflow overside weirs. ASCEJournalof the Hydraulics Division 1972;98(1):110.

[3] Yu-Tech L. Discussion of spatially varied flow over side weir. ASCE Journal ofthe Hydraulics Division 1972;98(11):20468.

[4] Ranga Raju KG, Prasad B, Grupta SK. Side weir in rectangular channel. ASCEJournal of the Hydraulics Division 1979;105(5):54754.

[5] Hager WH. Lateral outflow over side weirs. ASCE Journal of HydraulicEngineering 1987;113(4):491504.

[6] Cheong HF. Discharge coefficient of lateraldiversion fromtrapezoidalchannel.ASCE Journal of Irrigation and Drainage Engineering 1991;117(4):32133.

[7] Singh R, Manivannan D, Satyanarayana T. Discharge coefficient of rectangularside weirs. ASCE Journal of Irrigation and Drainage Engineering 1994;120(4):

8149.[8] Jalili MR, Borghei SM. Discussion of Discharge coefficient of rectangular side

weir, by R. Singh, D. Manivannan and T. Satyanarayana. ASCE Journal ofIrrigation and Drainage Engineering 1996;122(2):132.

[9] Borghei M, Jalili MR, Ghodsian M. Discharge coefficient for sharp-crested sideweir in subcritical flow. ASCE Journal of Hydraulic Engineering 1999;125(10):10516.

[10] Swamee PK, Santosh KP, Masoud SA. Side weir analysis using elementarydischarge coefficient. ASCE Journal of Irrigation and Drainage Engineering1994;120(4):74255.

[11] Ghodsian M. Supercritical flowover rectangular side weir. CanadianJournalofCivil Engineering 2003;30(3):596600.

[12] Khorchani M, Blanpain O. Free surface measurement of flow over side weirsthe videomonitoring concept. FlowMeasurement and Instrumentation 2004;15(2):1117.

[13] Muslu Y. Lateral weir flow model using a curve fitting analysis. ASCE Journalof Hydraulic Engineering 2002;128(7):7125.

[14] Yksel E. Effect of specific variation on lateral overflows. Flow Measurementand Instrumentation 2004;15(56):25969.

7/27/2019 agacci_d78aa3782ed9778805199355440ad7b1

12/12


[15] Muslu Y, Yksel E, Tozluk H. Transition effects in flow over side weirs. ASCEJournal of Irrigation and Drainage Engineering 2004;130(1):925.

[16] De Marchi G. Essay on the performance of lateral weirs. L Energia Electtrica,Milan 1934;11(11):84960 [in Italian].

[17] El-Khashab AMM. Hydraulics of flow over side weirs. Ph.D. thesis. England:University of Southampton; 1975.

[18] Durga Rao KHV, Pillai CRS. Study of flow over side weirs under subcriticalconditions. Water Resources Management 2008;22:13143.

[19] Coleman GS, Smith D. The discharging capacity of side weirs. Proceedings ofthe Institution of Civil Engineers (London) 1923;6:288304.

[20] Emiroglu ME, Kaya N, Agaccioglu H. Discharge capacity of labyrinth side-weir located on a straight channel. ASCE Journal of Irrigation and DrainageEngineering 2010;136(1):3746.

[21] Agaccioglu H, Yksel Y. Side-weir flow in curved channels. ASCE Journal ofIrrigation and Drainage Engineering 1998;124(3):16375.

[22] Kaya N, Emiroglu ME, Agaccioglu H. Discharge coefficient of semi-ellipticalside weir in subcritical flow. Flow Measurement and Instrumentation. 2010[in press]. doi:10.1016/j.flowmeasinst.2010.11.002 .

[23] KarunanithiN, GrenneyWJ, Whitley D, Bovee K. Neural networksfor river flowprediction. ASCEJournal of Computingin Civil Engineering 1994;8(2):20120.
http://dx.doi.org/doi:10.1016/j.flowmeasinst.2010.11.002http://dx.doi.org/doi:10.1016/j.flowmeasinst.2010.11.002http://dx.doi.org/doi:10.1016/j.flowmeasinst.2010.11.002

agacci_d78aa3782ed9778805199355440ad7b1

Documents