I'NCINEER - Vol. XXXX, No. 03, pp. 31-38,2007O Tlie Institution of Engineers, Sri Lanka

Discharge Measurements in Open Channels usingCompound Sharp-Crested Weirs

M. Piratheepan, N.E.F. Winston and K.P.P. Pathirana

Abstract: Compound sharp-crested weirs have been widely used for measuring discharges in openchannels accurately with a reasonable sensitivity over a wide flow range. The flow characteristic over acompound sharp-crested weir is completely different to that over a single sharp-crested weir. The mostcommon type of compound sharp-crested weir used in irrigation canals is the combination of arectangular notch and a 'V notch with a small notch angle. However, the continuity of flow andprecision of this type of compound weirs are reported to be poor in the transition region between twosections. As an improvement, a compound sharp-crested weir composed of two triangular parts withdifferent notch angles has been designed and experimentally validated which proved to be accurate inmeasuring a wide range of discharges without any discontinuity. Several methods are also proposed toestimate the flow over the double 'V notch compound sharp-crested weir and one method isexperimentally validated as most suitable.

Keywords: Compound sharp-crested weir, Discharge coefficient, Steady uniform flow

1. Introduction

Accurate flow measurement in open channels isvery important in many civil engineeringapplications. There are different types ofstructures available for flow measurements suchas weirs, orifice, flumes, sluice gates etc. Thestructures used for flow measurements shouldhe accurate, economical and easy to use(installation, operation and maintenance). Weirsallow water to be routed through a structure ofknown dimensions, permitting flow rates to bemeasured as a function of depth of flow throughthe structure. Among different types of weirs, a.sharp-crested weir has been widely used fordischarge measurements in open channels. Thecommonly used cross sections of sharp-crestedweirs are rectangular, trapezoidal andtriangular. A triangular weir with a small notchangle is found to be accurate in dischargemeasurements; however, it can only be used tomeasure small discharges. When measuringhigh discharges by using the single sharp-crested weirs, backwater effects might affect thestructures located upstream of the weir.

When the discharge is to be measuredaccurately with a reasonable sensitivity over awide range of flows, the use of compoundsharp-crested weirs could be an appropriatesolution. The most commonly used compoundsharp-crested weirs used in irrigation canalshave a combination of rectangular notch and a

'V notch with a small notch angle. But it hasbeen already found that the accuracy of flowmeasurements of this type of structure is poor inthe transition region between the two parts.Therefore, in order to overcome this problemand also to measure flow rates accurately for awide range of discharges, the use of acompound sharp-crested weir having acombination of two triangular weirs withdifferent notch angles has been studied. Thispaper presents the details of the experimentalinvestigations conducted with a compoundsharp-crested weir having two triangular 'Vnotches with different notch angles forestimating discharge accurately over a widerange of flows.

2. Literature Review

Many studies have been carried out in the pastto investigate the discharge over sharp-crestedweirs with fully and partially developed flows.Henderson [8] presented an elementary analysisfor discharge over a sharp-crested weir byassuming that the flow does not contract as itpasses over the weir. By assuming that thepressure across the whole water column over

M.Piratheepan, B.Sc. Eng. (Hons), Department of Civil Engineering,University of Peradeniya.

N.E.F.Winston, B.Sc. Eng. (Hons), Department of Civil Engineering,University of Peradeniya.

Eng.(Dr.) K.P.P. Pathirana, B.Sc. Eng. (Hons.) (Peradeniya), M.Eng.,Ph.D., C.Eng., FIE(SL), MICE (London), Senior Lecturer, Departmentof Civil Engineering, University of Peradeniya.

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the weir is atmospheric the following equationwas derived for discharge as,

o r a—Qtan-15 d \2

2.5(1)

Where, Q= discharge; C= discharge coefficient;g = gravitational acceleration; 6 = notch angle;and h = head over the weir.

Some of the researchers adjust the head over theweir to eliminate the effects of lateral andvertical contractions with the limitation ofapplicability (Bos [4], Brater et al. [5],Kindswater et al. [9] and Chow [7]). Later acorrection factor (K) has been introduced to thehead over the weir by considering the surfacetension and viscous effects (USER [13]). Thedischarge coefficient solely depends on thenotch angle for fully developed flow anddepends on many other parameters for partiallydeveloped flow. It is recommended in BSI [6]that the head over the weir need to be adjustedfor both partially and fully contracted flows. Asall the references show similar curves for C,andK without providing the equations for them,LMNO Engineering [12] used a curve fittingprogram to obtain the following relationshipsfor Cd and K, both of which are related to notchangle of weir,

=0.6072-0.000874<9 + 6.

£=4.42-0.10350+1.005x10~36'2-3.24xlO~66'3

(2)

(3)

Where, 6 is the notch angle. The specificationsand the proper installation of weirs for flowmeasurements in both partially and fullycontracted flow conditions are clearly discussedin BSI and USER [13].

Very few studies are reported in the past oncompound sharp-crested weirs with the aim ofimproving the performance of single sharp-crested weir. Abdel-Azim et al. [1] discussed thecharacteristics of the combined flow over weirsand below gates of equal contraction for thepurpose of avoiding the problem of sedimentaccumulation upstream from the weir. On theother hand, the characteristics of a compoundweir consisting of a rectangular notch with a V-notch cut into the centre of the crest arediscussed in the USER [13], and this couldhandle the normal range of discharges by lower

V-notch and the occasionally occurring largerflows by the rectangular weir. However, thediscontinuity in the discharge curve has been amajor problem in the above stated combinationof notches when measuring discharge in thetransition range. To avoid this problem Martinezet al. [10] proposed a compound sharp-crestedweir which has two triangular weirs withdifferent notch angles. They proposed andvalidated a theoretical discharge equation forfully contracted flow condition by conductingthe experiment with different combinations ofnotch angles.

In this paper various methods of estimatingdischarge over the compound sharp-crestedweir, having a combination of two triangularweirs in partially contracted flow conditions arecompared based on the experimentalinvestigations. The most suitable method ofcomputing discharge over the compound weir isproposed. The accuracy and continuity ofdischarge measurements using this type ofcompound weirs are also discussed.

3. Theoretical Aspects

A weir is considered to be a sharp-crested weir,when the crest thickness is between 1 mm and 2mm. when the thickness exceeds the specifiedlimits, it is required to be bevelled to at least 600for triangular weirs and at least 450 forrectangular weirs. The bevelled section shouldbe faced towards the downstream. The tailwater level should be low enough to ensure thefree fall of the nappe.

The discharge equation for the sharp-crestedweir is obtained by integrating the flow througha small elemental strip over the nappe at theweir; where each flow strip, is considered with adifferent head. The discharge equation for atypical triangular weir is given in Eq.(l). Thedischarge over the compound weir with twotriangular weir sections is calculated by addingthe flow through the triangular areas 1 & 2 andsubtracting the flow through the intersectedtriangular area as shown in Figure-1. The Cdvalues for the lower 'V notch and the upper 'Vnotch are calculated separately and used topredict the flow. Eq.l can be used to predict theflow over the weir when head over the weir (h)is less than the lower weir height (hO) and in thiscase, the discharge coefficient corresponding tothe lower 'V notch is used. When the head over

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the weir is greater than hff six different methodsarc proposed to estimate the flow over thecompound weirs, which are presented in detailin the following sections.

e = [T] (* -

\'\%ure 1- Typical cross section of the compoundsharp-crested-weirs (a & b)

Method -1

I lore, the intersection triangle is in the upper 'Vnotch and hence, the Cd corresponding to thisarea is taken as the lower 'V notch dischargecoefficient.

(4)

Where Cd = discharge coefficient of the lower 'Vnotch, Ca= discharge coefficient of the upper 'Vnotch, 9j = lower notch angle and 92 = uppernotch angle.

Method -2

I lere, the intersection triangle is in the lower 'Vnotch and hence, the Cd corresponding to thisarea is taken as the upper 'V notch dischargecoefficient (see Figure 1 (b)).

(5)

Where, x is the height of the intersectiontriangle.

Method-3

It is the same as 'Method -1' but replacing the Cd

of the intersection triangle corresponding to theupper 'V notch.

(6)

Method -4

It is the same as 'Method -2' but replacing the C1

of the intersection triangle corresponding to thelower 'V notch.

(7)

.,2.5

In Method-5 & Method-6, it is considered thatthe intersection triangles do not contact withany solid boundaries and therefore, the Cd

values for the intersection triangles areeliminated.

4. Experimental Details

The experiments were carried out in theHydraulics Laboratory of the Faculty ofEngineering, University of Peradeniya. Theexperimental set-up mainly consists of arectangular circulating open channel of 12 mlong, 0.3 m wide and 0.3 m deep and a collectingtank at the downstream end of the channel. Thecompound sharp-crested weirs were built of GIplates and attached at the end of the openchannel with the help of G-clamps and watersealant to prevent leakages.

The downstream collecting tank consists of twoperforated plates to avoid the turbulence causedby the nappe from the elevated channel. A

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From overheadtank Upstream tank

To overhead

"1Main channel

(a.} Plan view

„ , .Compound Weir

From overhead tank Upstream tank Main channel

U / / Compound'=31 , / / ^

/ /' _'V- notch Sump

Downstream tank

V-notch

(b) End elevationTo sump

Figure 2. Schematic diagram of the experimental set-up (-not to scale-).

schematic diagram of the experimental set-up isshown in Figure 2.

Water was supplied to the main channel from anoverhead tank at constant head and the flowwas controlled by a gate valve. The flow wasconfirmed as steady uniform by the help of thebackwater height measurements at subsequentintervals. The actual discharge through thechannel was measured by means of the 'V notchattached to the downstream collecting tank. Forthis purpose, initially it was calibratedaccurately by using a volumetric method. Thewater depth was measured from a fixed heightalong the centre line of the main channel using apoint gauge with an accuracy of 0.0508 mm (0.02inch).

Initially, several experimental runs were carriedout with single 'V notches having 60°, 90°, 120°& 150° notch angles to find out their dischargecoefficients. Due to the proximity of the walls ofthe approach channel, the contractions are notfully developed. So the notch is defined as apartially contracted, triangular thin-plate weir.As the flow conditions exceed the limitationprescribed for partially contracted flow in BSI(1965) and USER (1997), the effect of the weirheight (p) on the discharge coefficients was

checked by conducting the trials with different'rj values for these single 'V notches.

Altogether eight combinations of double 'Vnotches were tested by changing 6^, 62 and lower'V notch height (see Table 1). Discharge in thechannel was increased in steps of nearly 1 L/sduring experiments. Table 2 shows a summaryof experimental data used for different testcases.

Table 1: Combinations of 'V notches

Compoundweir type

12345678

Height ofthe lower'V notch

(fc/cm)

1515151010101010

Lowernotch

angle (0t)

60°60°60°90°90°60°60°60°

Uppernotchangle

(0.)90°

120°150°120°150°

90°120°150°

Table 2: Summary of experimental data

Parameter

Main channel discharge, (L/s)Upstream depth of flow, (m)Weir height, p (cm)

Range

0.30 - 13.120.09 - 0.232.5 - 10.0

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3. - The experimental set-up

5. Data Analysis

The analysis of experimental data is aimed atchecking the continuity of flow over thecompound weir, suitability of the equationsproposed for discharge computations (Sec. 3)and the accuracy of the proposed weir fordischarge measurements. The 'V notch attachedto the downstream collecting tank is calibratedprecisely and Qis calculated as 0.627. As statedearlier, the Cd values for the single 'V notchesare computed by changing the weir height p.The Cd values for the 90° *V notch are given inTable 3 as a typical result.

Tible 3: Cd values of 90° 'V notch with changingweir heights

Height of the weir p/(cm)

2.54.05.07.510.0

£10.70610.70050.69430.69420.7035

By considering the values given in Table 3, it canbe noted that there is not much deviation of Cd

values for different values of p. Therefore, theeffect of p value on the discharge coefficient isrtssumed to be negligible within theexperimental range covered in this study.I lence, the p value is not taken as a variable forthe remaining test cases. The C, values for single' V notches are tabulated in Table 4.

Table 4: Cd values of single 'V notches

Notch Angle60°90°120°150°

Discharge Coefficient (C,)0.6540.6940.6630.761

5.1 Continuity of flow

The continuity of flow over the compound weirsfor variation of head is checked usingexperimental data. As a typical result, thevariation of measured discharge with head forcompound weir types 6, 7 and 8 is shown inFigure 4.

14 -,

12 -

8 -

oco

^

2 -

) 50 100 150Head o\«r the weir(mm)

--«--Type6 —*—Type7 --•-•Type8

200

Figure 4 - Variation of measured discharge with headfor compound weir types 6, 7 and 8.

As can be noted, there is no discontinuity offlow shown at the transition region of the twotriangular notches. This is not the case withcompound weirs having a rectangular notchwith a V notch at the centre, where the dischargeversus head relationship is not continuous andas a result, when the head is near the transitionregion the flow measurements are not veryaccurate. Such difficulties could be overcomewith the use of compound weirs having double'V notches as suggested during this study.

5.2 Selection of best method

Discharges over the compound sharp-crestedweirs for all test cases are computed by using sixdifferent methods outlined in section 3. Thecomparison between measured and computeddischarges is shown in Figure 5.

It can be seen that the discharge computed byusing methods 2, 4 and 6 have highly under-estimated the discharge over the compoundweirs, whereas methods 1, 3 and 5 appear to bemore suitable for estimating the discharge overthe compound weir.

In order to compare the six different methodssuggested in this study for estimating the

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4 6 8 1 0 1 2

Measured Discharges (L/s). Mtd 1 Mtd 2 4 Mtd 3! ; Mtd 4l x Mtd 5 Mtd6i

figure 5. Comparison between measured andcomputed discharges using six different methods.

discharge over the compound sharp-crestedweir, the gradients obtained from the graphs ofcomputed discharge versus actual discharge foreach double 'V notch combinations are takeninto consideration. The gradient reaches onewhen the method is more accurate. The varianceof the gradients with one is calculated by usingthe Eq.(8).

V = -(H-1)

(8)

Where, V is the variance with 1 and y is thegradient of the measured versus computeddischarge graph for a specific method in eachcombination and n is the number of test runs.

The average percentage error (E) between theactual and computed discharges is alsocomputed using Eq.(9).

0.03835

0.00309 • 0.00307 II 0.00415

Mtd CD Mtd 2 Mtd 3 Mtd * Mtd 5J Mtd Q

Figure 6. The variance of the gradients with methodsof computing discharges

E =100

N

- Gc

G(9)

Where Ga and Gc are the actual and computeddischarges, respectively. N is the number of testruns examined for a particular method.

According to the Figures 6 and 7, it can be notedthat the method 3 is the most accurate one forcomputing discharge over compound sharp-crested weirs having double 'V 'notches. Figure8 illustrates the comparison between measureddischarges with the discharge computed usingmethod 3.

18 -,

16 -

14 •

b 12 -

§ 8 -

I 6 -

4 •

2

0 •

©

• R• •

*o

m

9

m «» 5 g

» " 1 * *i I «

1 2 3 4 5 6 7 8

Compound Weir type

o Mtd n • Mtd 2i A Mtd Si x Mtd «! x Mtd a o Mtd 6i

Figure 7. The average percentage errors betweenmeasured and computed discharges for differentmethods

19 -

§.E?ro n .oVIbo

1.

O

o .

n -/

/

jft

/

/'/

/

0 2 4 6 8 1 0 1 2 1 4Measured Discharge (L/s)

Figure 8. Comparison between measured andcomputed discharges using method-3

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5.3 Accuracy of discharge measurements

The accuracy of flow measurements usingcompound weirs, having a 60° lower notch angleis compared with the accuracy of flowmeasurements by a single 'V notch of 60°. Thepercentage error that can be expected in flowmeasurements is computed according to Eq.(lO)based on the accuracy of the point gauge usedfor head measurements which is 0.0508 mm.

2fi(A)

Where, the function Q(H) is taken according tothe Method-3 and the variation of accuracy withhead over the weir is shown in Figure 9. As canbe seen in the figure, the accuracy of flowmeasurements using compound weirs withdouble 'V notches whose lower triangle ishaving a notch angle of 60° is almost the same asthe accuracy with a single 'V notch of 60°.

0.18-|

0.16 -

0.14-

0.12 -0.10-0.08

0.06

0.04-

0.02-

0.00

-60-

500 1000 1500 2000

head over the w eir/(mm)- 60/150 60/120 60/90

Figure 9. Variation of percentage error with head overthe weir

6. Summary and Conclusions

A compound sharp-crested weir composed oftwo triangular parts with different notch angleshas been analysed and experimentally validatedto provide accurate measurements for a widerage of flow without discontinuity. The mostsuitable method to estimate the flow over thedouble 'V notch compound sharp-crested weirin partially contracted flow conditions, is foundto be the procedure given in Method-3. Here, theintersection triangle is in the upper 'V notchand the Cd of that part is taken as the dischargecoefficient of the upper 'V notch and thedischarge can be computed using the Eq. 6. Thisequation can be simplified in the form of;

Where,2.5

(11)

So, when there is a requirement to measure awide range of flows accurately with reasonablesensitivity, the above compound sharp-crestedweir can be selected due to its simplicity, easymaintenance and good flow measurementprecision.

Figures 10, 11 and 12 illustrate the finaldischarge coefficients (Cdc) for different headsabove the weir for various combinations of 'Vnotches tested during this study. These curvescan be used to obtain a correct dischargecoefficient depending on the combination of 'Vnotches in sharp-crested compound weirs.

O

1.25 -1.15 -1.050.95 -]

•8 0.850.750.65 -0.55 -0.45 -0.35

0.1 0.15 0.2h(m)

0.25 0.3

Figure 10. Cd values for compound weirs having 60°lower notch angle & 10 cm lower weir height

0.85-|

0.75-

0.65-J

' 0.55-

0.45

0.35

150°

0.15 0.2 0.25h(m)

0.3

Figure 11. Cd values for compound weirs having 60°lower notch angle & 15 cm lower weir height

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1.45-1.35-1.25

01.150"1.05-

0.95-0.85-0.750.65

150°

120°

0.1 0.15 0.2 0.25 0.3h(m)

Figure 12. Cd values for compound weirs having 90"lower notch angle & 10 cm lower weir height

References

1. Abdel-Azim, M.N., Al-Brahim, A.M., andAlhamid, A.A (2002). "Combined free flow overweirs and below gates", Journal of HydraulicResearch, Vol.40(3), pp.359-365.

2. Aydin, I., Metin Ger, A., and Hincal, o. (2002)"Measurement of small discharges in openchannels by slit weir", Journal of HydraulicEngineering, Vol.l28(2), pp.234-237.

3. Borghei, S.M., Jalili, M.R., and Ghodsian, M.(1999) "Discharge coefficient for sharp-crestedside weir in subcritical flow", Journal ofHydraulic Engineering, Vol.125 (10), pp.1051-1056.

4. Bos, M.G. (1989) "Discharge measurementstructures", International Institute for landReclamation and Improvement (ILRI),publication 20, Wageningen, The Netherlands.

5. Brater, E.F., King, H.W., Lindell, J.E., and Wei,C.Y. (1996) "Handbook of Hydraulics", Mcgraw-Hill, New York.

6. British Standards Institution (BSI). (1965). "Thinplate weirs and venture flumes in methods ofmeasurement of liquid flow in open channel",Part 4A, BSI 3680, London.

7. Chow, V.T. (1959) "Open channel Hydraulics",Mcgraw-Hill, New York.

8. Henderson, EM. (1966) "Open channel flow"Prentice-Hall, Englewood Cliffs, N.J.

9. Kindswater, C.E., and Carter, R.W. (1959)"Discharge characteristics of rectangular thinplate weirs", Trans. American Society of CivilEngineering, Vol. 124, pp.772-822.

10. Martinez, J., Reca, J., Morillas, M.T., and Lopez,J.G (2005) "Design and calibration of acompound sharp-crested weir", Journal ofHydraulic Engineering, Vol. 131, No. 2, pp.112-116.

11. Swamee, P.K., qha, C.S.P., and Kumar, S. (1998)"Discharge equation for rectangular slots",Journal of Hydraulic Engineering, Vol. 124(9),pp.973-974.

12. LMNO Engineering Research and Software Ltd.(1999) "Focus on open channel flowmeasurement: V-notch weirs" Newsletter, Vol. 1,Athens, Ohio.

13. United States Department of the Interior, Bureauof Reclamation (USER). (1997), Watermeasurement manual, 3rd Ed., Denver.

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