Flow Measurement and Instrumentation 21 (2010) 418–424

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Flow Measurement and Instrumentation

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

Discharge characteristics of sharp-crested circular side orifices in open channelsA. Hussain, Z. Ahmad ∗, G.L. AsawaDepartment of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee-247 667, Uttarakhand, India

a r t i c l e i n f o

Article history:Received 29 April 2010Received in revised form18 June 2010Accepted 26 June 2010

Keywords:Open channelCircular side orificeFlow diversionCoefficient of dischargeFroude number

a b s t r a c t

A side orifice is a flow diversion structure provided in one or both side walls of a channel to spill/divertwater from the main channel. It is widely used in irrigation and environmental engineering. Analyticaland experimental studies related to the discharge characteristics of sharp-crested circular side orifices inopen channels under free flow conditions have been presented in this paper. Considering the side orificeas large, the discharge equation for the side orifice is derived analytically. Experiments were performedto estimate the coefficient of discharge which depends on the approach flow Froude number and ratio ofthe diameter of the orifice and bed width of the channel. Relationships for the coefficient of discharge,considering the orifice as large and small were developed. Such relationships were used to compute thedischarge through the orifice for data not used for proposing such relationships for the coefficient ofdischarge. The computed discharges werewithin±5% of the observed ones. The average percentage errorin computation of discharge through the orifice considering it as large and small are, respectively, 1.59%and 1.66% which are practically the same. Therefore, it is recommended that the discharge through theside orifice can be computed considering it as a small orifice within the range of data used in the presentstudy.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

A side orifice, commonly used in irrigation engineering, is a flowdiversion structure provided in the side of a channel to spill waterfrom the main channel. It is also used in water and wastewatertreatment plants to distribute the incoming flow to parallel processunits such as flocculation basins, sedimentation tanks, and aerationbasins [1]. Besides the side orifice, the sluice gate and side weir areother structures used for diverting the flow from themain channel.Such structures are special cases of a rectangular orifice and havebeen extensively studied in the literature [2–6]. Ghodsian [2] andSwamee et al. [4] obtained the relationship for discharge througha side sluice through the concept of elementary coefficient ofdischarge for an elementary strip along the gate length. Swameeet al. [4] related the elementary discharge coefficient with depth offlow in themain channel and gate opening for free flow conditions.However, Ghodsian [2] found that it also depends on the approachflow Froude number. A review of literature related to flow throughsharp-crested side weirs indicates that the coefficient of dischargeis mainly dependent on the approach flow Froude number, ratio of

∗ Corresponding author.E-mail addresses: ajmalamin.iitr@gmail.com (A. Hussain), zulfifce@iitr.ernet.in

(Z. Ahmad), asawafce@iitr.ernet.in (G.L. Asawa).

0955-5986/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2010.06.005

the depth of flow in themain channel and crest height, and ratio ofthe length of weir and width of channel [3].Gill [7] studied relatively short rectangular side orifices (as in

sewers) as a special case of spatially varied flow in the open chan-nel and pressure flow. Ramamurthy et al. [1] derived a dischargeequation for rectangular side orifices by taking the velocity of jetequal to the resultant of velocity in the main channel and veloc-ity due to differential pressure across the orifice. They found thatthe coefficient of discharge is a function of the length of the ori-fice, width of channel and ratio of velocity in themain channel andthe resultant jet velocity. Considering the flow in the main chan-nel provided with a side orifice as spatially varied flow, Ojha andSubbaiah [8] proposed a discharge equation using an elementarycoefficient of discharge which is mainly dependent on the orificegeometry and crest height. Their equation predicts the dischargethrough the orifice within an error band ±10%. Recently, Bryantet al. [9] investigated the flowpattern behind a normal orifice usingpotential theory and through experimentation. Emiroglu et al. [10]and Bilhan et al. [11] studied the hydraulics of side weirs using softcomputing techniques.Discharge capacity of a sharp-crested circular orifice in an

open channel under free flow conditions has been investigatedanalytically and through experimentation in this paper. Tothe knowledge of the authors, this has not been investigatedpreviously.

A. Hussain et al. / Flow Measurement and Instrumentation 21 (2010) 418–424 419

Nomenclature

B Width of the main channel, (m)Cd Coefficient of dischargeD Diameter of the orifice, (m)Fr Froude numberg Acceleration due to gravity, (m/s2)H Headofwater above the centerline of the orifice, (m)Q Discharge through the orifice, (m3/s)Qm Discharge in the main channel, (m3/s)Re Reynolds numberT Length of the elemental strip, (m)V Velocity in the main channel, (m/s)W Crest height, (m)Ym Depth of flow in the main channel, (m)z Head over the elemental strip, (m)ζ Height of the elemental strip from the base of the

orifice, (m)α Inclination of left nappe of water jet, (degree)β Inclination of right nappe of water jet, (degree)ρ Mass density, (kg/m3)µ Viscosity, (N s/m2)ε Average percentage errorξ ζ/D

2. Analytical considerations

2.1. Discharge equation

Consider a large orifice of diameter D fitted in the side of thewall of an open channel at crest heightW as shown in Fig. 1. Depthof flow in the channel is Ym and head of water above the centre ofthe orifice isH . Considering ideal flowwithout any contraction andvarying pressure head over the flow area of the orifice, dischargethrough an elemental section of width dζ and length T is [12,13]

dQ =√2gz · Tdζ . (1)

From geometry z = H + D2 − ζ and T = 2D

(ζ

D

)1/2 (1− ζ

D

)1/2.

Substituting these equations for z and T into Eq. (1), one obtains

dQ =√2g(H +

D2− ζ

)1/2· 2D

(ζ

D

)1/2 (1−

ζ

D

)1/2dζ . (2)

Total discharge flowing through the orifice is given by

Q = 2√2gD3/2

∫ D

0

(HD+12−ζ

D

)1/2 (ζ

D

)1/2 (1−

ζ

D

)1/2dζ .

(3)

Taking K = H/D+ 0.5, Eq. (3) may be simplified as

Q = 2√2gD3/2

∫ D

0

(Kζ

D− (K + 1)

ζ 2

D2+ζ 3

D3

)1/2dζ . (4)

Introducing the coefficient of discharge Cd to account for contrac-tion of the water jet issuing out from the orifice, energy loss, ap-proach velocity head, boundary effects etc., the actual dischargethrough the orifice is expressed as [14]

Q = 2Cd√2gD3/2

∫ D

0

(Kζ

D− (K + 1)

ζ 2

D2+ζ 3

D3

)1/2dζ . (5)

For evaluating the above integral, consider ζ/D = ξ , thus

Q = 2Cd√2gD5/2

∫ 1

0

(Kξ − (K + 1) ξ 2 + ξ 3

)1/2dξ . (6)

Fig. 1. Circular side orifice in an open channel.

For a known value of Cd,D and H , discharge Q flowing through theorifice can be computed by integrating Eq. (6) numerically. For asmall orificewith constant pressure distribution over the flowarea,the discharge equation is

Q = Cd√2gH ·

π

4D2. (7)

2.2. Dimensional analysis for Cd

Side sluice gate and side weir in an open channel are specialcases of side orifice. For zero crest height, the rectangular orificebehaves like a sluice gate and once the upper edge of therectangular orifice is above the free surface, it corresponds to a sideweir. Therefore, it is likely that variables affecting the coefficientof discharge of a side sluice gate and side weir would also affectthe coefficient of discharge of a side circular orifice. Thus, froma review of the literature, it is found that probable variablesaffecting the coefficient of discharge Cd for a circular side orifice areD, B,W , upstreamvelocity in themain channelV , Ym,mass densityρ, viscosity µ, and acceleration due to gravity g . The functionalrelationship for Cd may, thus, be written as

Cd = f1 (D, B,W , V , Ym, ρ, µ, g) . (8)

Taking ρ, V and D as the repeating variables, the functionalrelationship for Cd in terms of non-dimensional parameters may,thus, be written as

Cd = f2

(BD,WD,YmD,ρVDµ,V√gD

). (9a)

This equation can, alternatively, be written as

Cd = f2

(BD,WD,YmD,ρVDµ,V√gYm

). (9b)

So that Fr = V/√gYm represents the approach flow Froude

number, Fr. Influence of the Reynolds number, Re = ρVD/µ isrelatively insignificant in open channel flows and, hence, may bedropped from Eq. (9b). The final functional relationship for Cdmay,therefore, be expressed as

Cd = f2

(BD,WD,YmD, Fr). (10)

An experimental study was carried out to investigate the effect ofthe identified non-dimensional parameters on Cd.

420 A. Hussain et al. / Flow Measurement and Instrumentation 21 (2010) 418–424

Fig. 2. Layout of the experimental set-up.

Table 1Ranges of data collected in the present study.

Parameter Unit Range of dataMinimum Maximum

Qm m3/s 0.01654 0.15647Q m3/s 0.00144 0.02942D m 0.05 0.15Ym m 0.1716 0.5938V m/s 0.0771 0.8901W m 0.05 0.25Fr Dimensionless 0.036 0.521

3. Experimental work

The experimentswere carried out in a rectangularmain channelof 9.15 m length, 0.50 m width and 0.60 m depth (Fig. 2). A sluicegate was provided at the end of the main channel to regulate thedepth of the flow. Water was supplied to the main channel fromtwo 0.20 m diameter supply pipes. A circular orifice was providedin the left side of the main channel at a distance of 5.18 m from theupstream end of the channel. Discharge through the orifice waspassed into a diversion channel of 3.80 m length, 0.26 m widthand 0.41 m depth and, then, to a return channel. A rectangularsharp crested weir-A, calibrated using an ultrasonic flow meter,was provided at the end of the diversion channel to measure thedischarge flowing through the orifice. The discharges from themain and the diversion channels were passed into a return channelof 15.0 m length, 0.65 m width and 0.45 m depth and, then, toa sump. A rectangular sharp-crested weir-B, calibrated with anultrasonic flow meter, was provided at the end of this channel tomeasure the total discharge. Splitter plates and flow suppressorswere provided at the upstream of each channel to break large sizeeddies and to dissipate the surface disturbances, respectively.Experiments were performed for orifice sizes D = 5, 10, and

15 cm and crest heights of orifice W = 0.5, 0.10, 0.15, 0.20 and

0.25 m and for each set of D and W for three to four dischargesin the main channel Qm. For each Qm, different depths of flowweremaintained in themain channel by regulating the sluice gate.For each run, water levels in the main channel in the vicinityof the orifice and head over the crests of weir-A and weir-Bwere measured by digital point gauges of accuracy 0.01 mm.Experiments were performed under free flow through the orificeand also under no-formation-of-vortex conditions in the mainchannel in the vicinity of the orifice. The ranges of data collectedin the present study are given in Table 1 and complete sets of dataare given in Table 2.

4. Analysis of data

4.1. Observations during experiments

Measured water surface level in the main channel indicates asmall decrease in water level in the main channel downstream ofthe orifice. Such a decrease was more for the 15 cm size orificethan for the 5 cm orifice. Specific energy in the main channel wasobserved to be constant as were the findings of Mostkow [15]and Ghodsian [2] for flow over the bottom rack and sluice gate,respectively. Thewater jet issuing out from the circular orifice, wasnot truly circular downstream of the orifice. The centreline of thewater jet was inclined and not in the direction of normal to flow inthe main channel. Such an inclination increased with the increasein the velocity of the channel. Further, inclination of the left nappeof water jet αwasmore than the inclination of the right nappe β asshown in Figs. 1 and 3. Under the same conditions, increase in thevelocity in themain channel resulted in a decrease in the dischargethrough the orifice. A vortex was noticed in the main channel inthe vicinity of the orifice during the experiments when the headof water above the orifice was relatively less. However, no run fordischarge through the orifice was taken under this condition.

A. Hussain et al. / Flow Measurement and Instrumentation 21 (2010) 418–424 421

Table 2Data collected in the present study.

Runno.

D(m)

Q(m3/s)

Qm(m3/s)

Ym(m)

W(m)

Runno.

D(m)

Q(m3/s)

Qm(m3/s)

Ym(m)

W(m)

1 0.05 0.00167 0.03183 0.1716 0.05 54 0.05 0.00279 0.05161 0.4740 0.152 0.05 0.00207 0.03183 0.2222 0.05 55 0.05 0.00315 0.05161 0.5375 0.153 0.05 0.00234 0.03183 0.2583 0.05 56 0.05 0.00155 0.08894 0.3114 0.154 0.05 0.00320 0.03183 0.3855 0.05 57 0.05 0.00173 0.08894 0.3291 0.155 0.05 0.00356 0.03183 0.4511 0.05 58 0.05 0.00215 0.08894 0.3800 0.156 0.05 0.00226 0.07728 0.2465 0.05 59 0.05 0.00261 0.08894 0.4470 0.157 0.05 0.00254 0.07728 0.2811 0.05 60 0.05 0.00285 0.08894 0.4873 0.158 0.05 0.00281 0.07728 0.3221 0.05 61 0.05 0.00340 0.08894 0.5870 0.159 0.05 0.00329 0.07728 0.4060 0.05 62 0.05 0.00215 0.12112 0.3806 0.1510 0.05 0.00354 0.07728 0.4678 0.05 63 0.05 0.00231 0.12112 0.4112 0.1511 0.05 0.00282 0.11113 0.3306 0.05 64 0.05 0.00257 0.12112 0.4553 0.1512 0.05 0.00294 0.11113 0.3505 0.05 65 0.05 0.00304 0.12112 0.5160 0.1513 0.05 0.00309 0.11113 0.3780 0.05 66 0.05 0.00337 0.12112 0.5892 0.1514 0.05 0.00341 0.11113 0.4395 0.05 67 0.10 0.01359 0.12142 0.4788 0.0515 0.05 0.00275 0.11898 0.3623 0.10 68 0.10 0.01323 0.12142 0.4586 0.0516 0.05 0.00294 0.11898 0.3984 0.10 69 0.10 0.01244 0.12142 0.4214 0.0517 0.05 0.00304 0.11898 0.4196 0.10 70 0.10 0.01217 0.12142 0.4078 0.0518 0.05 0.00331 0.11898 0.4690 0.10 71 0.10 0.01115 0.12142 0.3606 0.0519 0.05 0.00356 0.11898 0.5103 0.10 72 0.10 0.00771 0.07059 0.2285 0.0520 0.05 0.00188 0.07424 0.2461 0.10 73 0.10 0.00859 0.07059 0.2555 0.0521 0.05 0.00216 0.07424 0.2751 0.10 74 0.10 0.00927 0.07059 0.2811 0.0522 0.05 0.00250 0.07424 0.3240 0.10 75 0.10 0.01092 0.07059 0.3456 0.0523 0.05 0.00290 0.07424 0.3890 0.10 76 0.10 0.01179 0.07059 0.3850 0.0524 0.05 0.00330 0.07424 0.4694 0.10 77 0.10 0.01356 0.07059 0.4687 0.0525 0.05 0.00356 0.07424 0.5110 0.10 78 0.10 0.00600 0.03664 0.1813 0.0526 0.05 0.00221 0.02028 0.2790 0.10 79 0.10 0.00847 0.03664 0.2517 0.0527 0.05 0.00273 0.02028 0.3573 0.10 80 0.10 0.01088 0.03664 0.3410 0.0528 0.05 0.00322 0.02028 0.4470 0.10 81 0.10 0.01341 0.03664 0.4586 0.0529 0.05 0.00353 0.02028 0.5091 0.10 82 0.10 0.01217 0.01654 0.3965 0.0530 0.05 0.00181 0.04559 0.2465 0.10 83 0.10 0.01276 0.01654 0.4332 0.0531 0.05 0.00250 0.04559 0.3286 0.10 84 0.10 0.00917 0.11494 0.3224 0.1032 0.05 0.00343 0.04559 0.4797 0.10 85 0.10 0.01063 0.11494 0.3805 0.1033 0.05 0.00247 0.12348 0.3772 0.15 86 0.10 0.01239 0.11494 0.4621 0.1034 0.05 0.00269 0.12348 0.4140 0.15 87 0.10 0.01372 0.11494 0.5258 0.1035 0.05 0.00290 0.12348 0.4463 0.15 88 0.10 0.00839 0.04202 0.2922 0.1036 0.05 0.00323 0.12348 0.5025 0.15 89 0.10 0.01185 0.04202 0.4272 0.1037 0.05 0.00344 0.12348 0.5394 0.15 90 0.10 0.01274 0.04202 0.4695 0.1038 0.05 0.00155 0.04822 0.2676 0.15 91 0.10 0.00731 0.06702 0.2614 0.1039 0.05 0.00185 0.04822 0.2940 0.15 92 0.10 0.00921 0.06702 0.3215 0.1040 0.05 0.00228 0.04822 0.3475 0.15 93 0.10 0.01119 0.06702 0.3922 0.1041 0.05 0.00269 0.04822 0.4070 0.15 94 0.10 0.01228 0.06702 0.4504 0.1042 0.05 0.00302 0.04822 0.4668 0.15 95 0.10 0.00975 0.02347 0.3374 0.1043 0.05 0.00338 0.04822 0.5334 0.15 96 0.10 0.01192 0.02347 0.4283 0.1044 0.05 0.00144 0.08325 0.2580 0.15 97 0.10 0.01254 0.02347 0.4585 0.1045 0.05 0.00187 0.08325 0.2940 0.15 98 0.10 0.01359 0.02347 0.5103 0.1046 0.05 0.00204 0.08325 0.3171 0.15 99 0.10 0.00593 0.10924 0.2852 0.1547 0.05 0.00239 0.08325 0.3562 0.15 100 0.10 0.00702 0.10924 0.3083 0.1548 0.05 0.00279 0.08325 0.4110 0.15 101 0.10 0.00786 0.10924 0.3346 0.1549 0.05 0.00163 0.05161 0.3147 0.15 102 0.10 0.00905 0.10924 0.3720 0.1550 0.05 0.00191 0.05161 0.3473 0.15 103 0.10 0.00969 0.10924 0.3930 0.1551 0.05 0.00216 0.05161 0.3806 0.15 104 0.10 0.01046 0.10924 0.4225 0.1552 0.05 0.00239 0.05161 0.4125 0.15 105 0.10 0.01096 0.10924 0.4437 0.1553 0.05 0.00257 0.05161 0.4368 0.15 106 0.10 0.01128 0.10924 0.4570 0.15

(continued on next page)

4.2. Effect of various parameters on Cd

Considering the orifice as large, the coefficient of dischargeis computed for each data set collected in the present study forknown values of D,H , and Q using Eq. (6). The effect of thedimensionless parameters B/D,W/D, Ym/D and Fr as obtainedby the dimensional analysis on this computed Cd is examined. Athoroughdata analysis reveals that Fr and B/D are the predominantparameters which affect the Cd. For the range of data used in thepresent study, Cd is unaffected by the parametersW/D and Ym/D.However, for low values ofW/D the Cd is expected to be less dueto the bottom boundary effect. Variation of Cd with Fr for constantB/D is shown in Fig. 4, which clearly indicates a decrease in Cdwith increases in Fr. This is also true for the side weir and sidesluice gate [2,3]. A perusal of Fig. 4 indicates a decrease of Cdwith increase of B/D. Ranga Raju and Asawa [16], based on a large

amount of experimental data for different liquids, found that theeffects of surface tension and viscosity on the discharging capacityof a weir are quite significant at low values of R0.21 W

0.61 and vanish

at R0.21 W0.61 greater than 900. Here R1 = g1/2H3/2/ν and W1 =

ρgH2/σ (ν and µ are surface tension and viscosity, respectively).In the present study, R0.21 W

0.61 is more than 1000 for all the

data sets; therefore, the effect of surface tension and viscosity isnegligible.

4.3. Relationship for coefficient of discharge

164 data sets selected randomly out of 216 data sets collectedin the present study have been used to propose a relationshipfor Cd. The remaining 52 data sets have been used for validatingthe proposed relationship. Using the least squares technique, the

422 A. Hussain et al. / Flow Measurement and Instrumentation 21 (2010) 418–424

Table 2 (continued)

Runno.

D(m)

Q(m3/s)

Qm(m3/s)

Ym(m)

W(m)

Runno.

D(m)

Q(m3/s)

Qm(m3/s)

Ym(m)

W(m)

107 0.10 0.01192 0.10924 0.4867 0.15 162 0.10 0.00698 0.12223 0.4090 0.15108 0.10 0.00629 0.13103 0.2974 0.15 163 0.10 0.00700 0.11312 0.4090 0.15109 0.10 0.00718 0.13103 0.3190 0.15 164 0.10 0.00702 0.11112 0.4090 0.15110 0.10 0.00882 0.13103 0.3675 0.15 165 0.10 0.00709 0.09476 0.4090 0.15111 0.10 0.00935 0.13103 0.3855 0.15 166 0.10 0.00720 0.08053 0.4090 0.15112 0.10 0.00991 0.13103 0.4088 0.15 167 0.15 0.02527 0.15178 0.4040 0.05113 0.10 0.01086 0.13103 0.4454 0.15 168 0.15 0.02655 0.15178 0.4295 0.05114 0.10 0.01151 0.13103 0.4727 0.15 169 0.15 0.02905 0.15178 0.4898 0.05115 0.10 0.00680 0.08087 0.3035 0.15 170 0.15 0.01745 0.09431 0.2615 0.05116 0.10 0.00747 0.08087 0.3218 0.15 171 0.15 0.01977 0.09431 0.2995 0.05117 0.10 0.00866 0.08087 0.3556 0.15 172 0.15 0.02139 0.09431 0.3223 0.05118 0.10 0.00975 0.08087 0.3949 0.15 173 0.15 0.02359 0.09431 0.3623 0.05119 0.10 0.01044 0.08087 0.4230 0.15 174 0.15 0.02793 0.09431 0.4644 0.05120 0.10 0.01132 0.08087 0.4600 0.15 175 0.15 0.02839 0.10338 0.4765 0.05121 0.10 0.00615 0.04801 0.2845 0.15 176 0.15 0.01801 0.06670 0.2660 0.05122 0.10 0.00882 0.04801 0.3598 0.15 177 0.15 0.02017 0.06670 0.3003 0.05123 0.10 0.00987 0.04801 0.3986 0.15 178 0.15 0.02178 0.06670 0.3280 0.05124 0.10 0.01046 0.04801 0.4235 0.15 179 0.15 0.02445 0.06670 0.3813 0.05125 0.10 0.01040 0.03421 0.4167 0.15 180 0.15 0.02754 0.06670 0.4495 0.05126 0.10 0.01069 0.03421 0.4440 0.15 181 0.15 0.02885 0.06670 0.4900 0.05127 0.10 0.00668 0.12545 0.3468 0.20 182 0.15 0.02058 0.03952 0.3077 0.05128 0.10 0.00788 0.12545 0.3788 0.20 183 0.15 0.02252 0.03952 0.3440 0.05129 0.10 0.00855 0.12545 0.4005 0.20 184 0.15 0.02413 0.03952 0.3752 0.05130 0.10 0.00874 0.12545 0.4072 0.20 185 0.15 0.02619 0.03952 0.4200 0.05131 0.10 0.01007 0.12545 0.4580 0.20 186 0.15 0.02756 0.03952 0.4545 0.05132 0.10 0.01067 0.12545 0.4870 0.20 187 0.15 0.02943 0.03952 0.5042 0.05133 0.10 0.00903 0.08651 0.4100 0.20 188 0.15 0.02418 0.15647 0.4340 0.10134 0.10 0.00803 0.08651 0.3829 0.20 189 0.15 0.02555 0.15647 0.4593 0.10135 0.10 0.00725 0.08651 0.3594 0.20 190 0.15 0.02914 0.15647 0.5403 0.10136 0.10 0.00657 0.08651 0.3436 0.20 191 0.15 0.01843 0.11542 0.3270 0.10137 0.10 0.00601 0.08651 0.3300 0.20 192 0.15 0.01992 0.11542 0.3475 0.10138 0.10 0.00967 0.05450 0.4350 0.20 193 0.15 0.02133 0.11542 0.3753 0.10139 0.10 0.00931 0.05450 0.4220 0.20 194 0.15 0.02324 0.11542 0.4104 0.10140 0.10 0.00874 0.05450 0.4030 0.20 195 0.15 0.02464 0.11542 0.4350 0.10141 0.10 0.00805 0.05450 0.3802 0.20 196 0.15 0.02675 0.11542 0.4846 0.10142 0.10 0.00669 0.05450 0.3410 0.20 197 0.15 0.02845 0.11542 0.5235 0.10143 0.10 0.01102 0.03476 0.4870 0.20 198 0.15 0.01752 0.07100 0.3080 0.10144 0.10 0.01005 0.03476 0.4467 0.20 199 0.15 0.01961 0.07100 0.3397 0.10145 0.10 0.00959 0.03476 0.4257 0.20 200 0.15 0.02204 0.07100 0.3816 0.10146 0.10 0.00941 0.11331 0.4795 0.25 201 0.15 0.02361 0.07100 0.4140 0.10147 0.10 0.00868 0.11331 0.4580 0.25 202 0.15 0.02621 0.07100 0.4775 0.10148 0.10 0.00815 0.11331 0.4415 0.25 203 0.15 0.02845 0.07100 0.5235 0.10149 0.10 0.00734 0.11331 0.4181 0.25 204 0.15 0.01646 0.05154 0.2900 0.10150 0.10 0.00645 0.11331 0.3950 0.25 205 0.15 0.02313 0.05154 0.3995 0.10151 0.10 0.00591 0.11331 0.3870 0.25 206 0.15 0.02694 0.05154 0.4825 0.10152 0.10 0.00870 0.08651 0.4600 0.25 207 0.15 0.01916 0.13639 0.4014 0.15153 0.10 0.00770 0.08651 0.4329 0.25 208 0.15 0.02139 0.13639 0.4419 0.15154 0.10 0.00707 0.08651 0.4094 0.25 209 0.15 0.02332 0.13639 0.4830 0.15155 0.10 0.00650 0.08651 0.3936 0.25 210 0.15 0.02700 0.13639 0.5567 0.15156 0.10 0.00596 0.08651 0.3800 0.25 211 0.15 0.02876 0.13639 0.5938 0.15157 0.10 0.00845 0.06336 0.4490 0.25 212 0.15 0.02212 0.09592 0.4530 0.15158 0.10 0.00677 0.06336 0.4017 0.25 213 0.15 0.02391 0.09592 0.4920 0.15159 0.10 0.00577 0.06336 0.3752 0.25 214 0.15 0.02706 0.09592 0.5567 0.15160 0.10 0.00696 0.14235 0.4090 0.15 215 0.15 0.02415 0.06159 0.4976 0.15

following equation is proposed for Cd

Cd = 0.678− 0.072 Fr− 0.130DB. (11)

The remaining 52 data sets, not used in the derivation of Eq.(11), were used to validate the proposed relationship for Cd forthe computation of discharge through the orifice. Observed andcomputed values of discharge through an orifice using Eqs. (6)and (11) for the test data are compared graphically in Fig. 5,which revealed that the computed discharge is within ±5% ofthe observed ones, which is a satisfactory prediction of dischargethrough the orifice. It is to be noted that computation of dischargeusing Eq. (6) requires integration of this equation for given valuesof D and H .Computations of discharge through orifices were also per-

formed treating the used orifices as small. The value of Cd is nowcomputed using Eq. (7) for all data sets collected in the present

study. Using this computed Cd for 164 observed data sets and leastsquares technique a relationship for the Cd was obtained as givenbelow

Cd = 0.670− 0.076 Fr− 0.136DB. (12)

The remaining 52 data sets were used to validate the computationof discharge through Eqs. (7) and (12). Fig. 6 shows comparison ofobserved discharge with computed ones using Eqs. (7) and (12).Even from the concept of a small orifice, the computed dischargeis within 5% of the observed ones.For a numerical measure for selecting best-fit equations that

can represent the agreement between the observed and computedvalues, an average percentage error term ε was defined as [2]

ε =100N

N∑i=1

∣∣∣∣Q (computed)− Q (observed)Q (observed)

∣∣∣∣ . (13)

A. Hussain et al. / Flow Measurement and Instrumentation 21 (2010) 418–424 423

Fig. 3. Water jet issuing out from the side orifice.

Fig. 4. Variation of Cd with Froude number for different values of B/D.

The average percentage error in computation of dischargethrough the orifice considering it as large and small are 1.59% and1.66%, respectively. As these two values are practically the same, itis recommended that computation of discharge through the orificecan be performed considering it as a small orifice within range ofH/D i.e., 0.75–7.86 collected in the present study. Gupta [17] statedthat when the head over an orifice (normal) is less than five timesthe height of the orifice, it is referred to as a large orifice. However,in the present study even for H = 0.75D, the side orifice behaveslike a small orifice.

5. Conclusions

Analytical and experimental studies related to dischargecharacteristics of sharp-crested circular side orifices in openchannels have been reported in this paper. A small decrease inthe water level was observed in the main channel downstreamof the orifice. Specific energy in the main channel was constant.Inclination of the left nappe of water jet was more than theinclination of the right nappe. All other conditions remaining thesame, increase in velocity in the main channel resulted in decreasein the discharge through the orifice. The coefficient of dischargedepends mainly on the approach channel Froude number andratio of the diameter of the orifice and bed width of the channel.The computed discharges using the proposed relationships, byconsidering the orifice as large and small, were within ±5% ofthe observed ones. The average percentage error in computationof discharge through the orifice considering it as large and smallwere, respectively, 1.59% and 1.66%which are practically the same.Therefore, it is recommended that the discharge through the sideorifice can be computed considering it as a small orifice within therange of the ratio of headofwater above the centerline of the orifice

Fig. 5. Comparison of computed discharge through orifice using Eqs. (6) and (11)with observed ones considering orifice as large.

Fig. 6. Comparison of computed discharge through orifice using Eqs. (7) and (12)with observed ones considering orifice as small.

and the diameter of the orifice i.e., 0.75–7.86 studied in the presentstudy. This would, obviously, simplify the prediction of dischargeas one does not have to integrate terms that appear in Eq. (6).

References

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[2] Ghodsian M. Flow through side sluice gate. ASCE Journal of Irrigation andDrainage Engineering 2003;129(6):458–62.

[3] Borghei M, Jalili MR, Ghodsian M. Discharge coefficient for sharp-crested sideweir in subcritical flow. Journal ofHydraulic Engineering 1999;125(1):1051–6.

[4] Swamee PK, Pathak SK, AliMS.Weir orifice units for uniform flow distribution.ASCE Journal of Irrigation and Drainage Engineering 1993;119(6):1026–35.

[5] Tanwar MPS. Flow through side sluice. M.E. thesis. Roorkee (India): Universityof Roorkee; 1984.

[6] Panda S. Characteristics of side sluice flow. M.E. thesis. Roorkee (India):University of Roorkee; 1981.

[7] Gill MA. Flow through side slots. ASCE Journal of Environmental Engineering1987;135(21874):1047–57.

[8] Ojha CSP, Subbaiah D. Analysis of flow through lateral slot. ASCE Journal ofIrrigation and Drainage Engineering 1997;123(5):402–5.

[9] Bryant DB, Khan AA, Aziz NM. Investigation of flow upstream of orifices. ASCEJournal of Hydraulic Engineering 2008;134(1):98–104.

[10] Emiroglu ME, Kisi O, Bilhan O. Predicting discharge capacity of triangularlabyrinth side weir located on a straight channel by using an adaptive neuro-fuzzy technique. Advances in Engineering Software 2010;41(2):54–160.

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[11] Bilhan O, Emiroglu ME, Kisi O. Application of two different neural networktechniques to lateral outflow over rectangular side weirs located on a straightchannel. Advances in Engineering Software 2010;41(6):831–7.

[12] Ahmad Z. End-depth-discharge relationship for circular free overfall. Journalof the Institution of Engineers 2002;83:21–4.

[13] Prohaska PD. Investigation of the discharge coefficient for circular orifices inriser pipes. Thesis submitted for the degree of Master of Science. US: GraduateSchool of Clemson University; 2008.

[14] Brater EF, KingHW, Lindell JE,Wei CY. Handbook of hydraulics. NewYork (NY):McGraw-Hill; 1996.

[15] Mostkow MA. A theoretical study of bottom type water intake. La HouilleBlanche 1957;4:570–80.

[16] Ranga Raju KG, Asawa GL. Viscosity and surface tension effects on weir flow.ASCE Journal of Hydraulic Engineering 1977;103(10):1227–31.

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A. Hussain is currently a post graduate student of Civil Engineering at IIT Roorkee,India. He obtained his B.Tech. (Civil) from AMU, Aligarh, India. His areas of interestare hydro power, computational hydraulics and hydraulic structures.

Z. Ahmad is currently Associate Professor of Civil Engineering at IIT Roorkee, India.He obtained his B.Tech. (Civil) degree fromAMUAligarh,M.Tech. (Hyd) degree fromUniv. of Roorkee and Ph.D. degree from T.I.E.T., Patiala. He has published about 56papers in referred national and international journals and conference proceedings.His areas of research are surface water quality management, computationalhydraulics and hydraulic structures. He has written two Monographs on Transportof Pollutants in Open Channels and Control Section in Open Channels for AICTE,New Delhi. He has been a recipient of G.N. Nawathe, Jal Vigyan Puraskar (twice);Department of Irrigation Award.

G.L. Asawa joined the Department of Civil Engineering at the Indian Institute ofTechnology Roorkee (formerly University of Roorkee) in 1971 and is presently Pro-fessor. He has been teaching hydraulic engineering courses at both undergraduateand postgraduate levels, and also is associatedwith research and consultancy activ-ities in different aspects of water resources engineering and wind engineering. Hehas published 04 books, about 65 research papers, and written as many reports onconsultancy projects. He is a member of the Monitoring Committee for ISO/TC 113works and also other committees at the national level. He led the Indian delegationfor ISO/TC 113 committee meetings in October 1994 and has travelled abroad forvarious academic programmes.