97

TRAPEZOIDAL FLUMES FOR MEASURINGFLOW IN IRRIGATION CHANNELS

MARCH 1968 ARS 41-140Agricultural Research Service

UNITED STATES DEPARTMENT OF AGRICULTURE

CONTENTS

Page

Introduction

Flume design

Operation

Free flow

Submerged flow

Accuracy of measurement

Construction

Materials

Flume setting

Summary

Appendix

3

5

8

10

10

10

10

13

14

TRAPEZOIDAL FLUMES FOR MEASURINGFLOW IN IRRIGATION CHANNELS 1

By A. R. Robinson Z

INTRODUCTION

Experience and research have shown that,in many respects, trapezoidal flumes aresuperior to the rectangular or Parshall-typeflumes, particularly for measuring_ smallerflows. The shape conforms to the normalshape of ditches, particularly those that arelined. This minimizes the amount of transitionsection needed as compared to that requiredwhen changing from a trapezoidal shape to arectangular one and back to the trapezoidal.The trapezoidal shape is also desirable sincethe sidewalls expand as the depth increases.This means that one structure can convey alarger range of flow. Also, the entire rangeof depth for a given range of discharge issmaller.

Operational characteristics of trapezoidalflumes are also superior. Generally, lessbackwater will result and a shallower sectionWill be required than for a rectangular shape.Another desirable feature of the trapezoidalflume is the flat bottom throughout ratherthan a dropped section such as with theParshall flume. No particular advantage of acrest section with a drop in the floor suchas that in the Parshall flume has been found.

The trapezoidal flume will operate under ahigher degree of submergence than the Parshallflume without corrections being necessary.The loss in head, i.e., total-head loss, throughthe trapezoidal structure, may be less forcomparable discharges.

FLUME DESIGN

Since the trapezoidal flume cross sectioncorresponds to the shape of common irrigationchannels or ditches, the flumes can be adaptedto standard trapezoidal, lined ditches. A stand-ard size, concrete-lined ditch has a 1-footbottom width, 1:1 sidewall slope, and is usuallyfrom 15 to 18 inches deep. A larger size hasa 2-foot bottom width and a 1.25:1 sidewallslope. The two trapezoidal flumes presentedherein for 1-foot and 2-foot irrigation channelswere designed with similar dimensions in

order that they may be made an integral partof lined canals. The flumes may also be usedin unlined ditches with cutoff walls attachedto each end. The flumes can be constructedof metal,' fiberglass, precast from concrete,or poured and formed in place as an integralpart of a lined channel. Techniques have alsobeen developed for casting the flume withinan existing lined canal utilizing a portableform. In this case the canal lining acts as theouter form. Figure 1 shows the flumes in use.

'Soil and Water Conservation Research Division, Agricultural Research Service, U.S. Department of Agriculture,in cooperation with the Idaho Agriculture Experiment Station,

2 Research agricultural engineer, Kimberly, Idaho,

3

A

C

Figure 1--Trapezoidal flumes installed for flow measurement; A. concrete; B., steel; g fiberglass.

4

The design and dimensions of the two flumesare given in figures 2 (flume No. 1) and 3(flume No. 2). Essentially, these designs in-volve a simple contraction from the standardditch dimension with all surfaces plane andflat for simplified construction. Flume No. 1has a flow range from 0.16 to 7.1 c.f.s. andflume No. 2, 0.67 to 53.2c.f.s. Although the twoflumes discussed in this publication cover themost usable range of discharges, many other

sizes and designs of small trapezoidal flumeshave been developed. s. 4' 5

Two positions for measuring flow depththrough the flumes are used. The standardupstream location is hi , where a staff gage ismounted. A fitting can be provided for usewith a stilling well and recorder. Normally,the h i depth is all that is required. The h 4depth is used only for correcting the indicateddischarge for submergence.

OPERATION

Free Flow

The simplest and most accurate flow meas-urement using trapezoidal flumes is obtainableunder "free-flow" conditions. Free flow occurswhen the flow passes through critical depth(flow at minimum specific energy) in thethroat section. With free flow, a unique re-lationship exists between the depth at anupstream point, designated as h i in figures 2and 3, and the discharge. For this conditionand a particular design and size of flume, theh i scale can be graduated in flow units. Thedischarge is then read directly from the scale.

For free flow, the relationship betweendepth and discharge is expressed by thefollowing equations:

Flume No. 1

Q = 3.23 h i " + 0.63 h i" + 0.05 (1)

Flume No. 2

Q= 4.27 h i " + 1.67h1 1 ' 5 + 0.19 (2)

where Q is the discharge in cubic feet persecond and h i is the upstream vertical depthin feet as shown in figures 2 and 3. Theserelationships are tabulated in tables I and 3for vertical depth and in tables 2 and 4 fordepths along the sloping sidewall. Both dis-charge equations were determined from labo-ratory calibrations where the discharge wasmeasured through standard Venturi meters,Gentile flow tubes, and precise weirs. Thedata were analyzed by means of a digitalcomputer by the method of least squares.

Recent tests were made utilizing a fiber-glass trapezoidal flume (No. 1) to determinethe effect of upstream conditions on the free-flow calibrations. For one condition, the flumewas installed as an integral part of a linedditch (fig. I,A). The other condition wassimilar to that in figure 1,C where there wasa sharp corner entrance. The flume bottomwas 4 inches above the bottom of the channel.The ratings for the two conditions wereidentical.

It is usually neither possible nor desirableto maintain a low water depth downstreamfrom the flume such as that shown in figure 4as condition a. With this condition an exces-sive energy loss occurs when the kineticenergy (velocity head) is converted back topotential energy (water depth). Because of thisenergy dissipation, channel protection may beneeded to prevent erosion. Maximum waterdepth downstream with free-flow conditionsmaintained is desired. If the downstreamdepth is too large, the flow does not gothrough critical depth. In this case the up-stream depth is greater than normal for thefree-flow discharge. This is the submergedflow condition, and corrections are necessaryto determine the correct discharge.

thamberIain, A, R. Measuring water in smallchannels with the WSC flume. Wash. Agr, Expt, Sta.Cir. 200, 12 pp. 1952.

4 Robinson, A. R, Water measurement in small irri-gation channels using trapezoidal flumes. Amer, Soc.Agr, Engin, Trans, 9(3): 382-385, 388, 1966,

5 Robinson, A. R„ and Chamberlain, A. R. Trapezoidalmeasuring flumes for open-channel flow measurement.Amer, Sac, Agr, Engin, Trans, 3(2): 120-124, 128.1960.

5

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20

Nw-co

0)

II

LL

H

7

"sr IL

ContractedSection

Flow

YIV/A9/7 /746)\77 \>>47/1/4417/7 if

Figure 4.--Flow regimes through trapezoidal flumes ( and b are free flow, c and d are submerged flow).

Submerged Flow

Submerged flow is defined as the conditionwhere the flow in the control section does notgo through critical depth, i.e., the downstreamdepth is great enough that the flow throughoutthe flume is subcritical. For a given dis-charge, the depth upstream at the h 1 measur-ing point is increased so that the free-flowrelationship does not apply. An accurate meas-urement with the flume is still possible butnow two depth readings are needed, h 1 andh4 (fig. 2 and 3). By use of the two depths,corrections can be made to determine thecorrect flow.

The flow profiles shown in figure 4 for aconstant discharge illustrate free and sub-merged flow. Water surface profiles a andb are free flow, whereas c and d representsubmerged flow. Profile g represents a lowtailwater condition with a high-velocity jet ofwater emerging from the flume. Profile hrepresents a condition where the downstreamdepth is approaching the point where sub-mergence must be considered in determiningthe correct discharge. Degree of submergenceis expressed as the ratio of depth at the down-stream point to that at the upstream gagepoint, i.e., h 4/11 1. Between profiles a and bthere is a wide range of downstream condi-tions where free flow occurs. The water sur-face profiles c and d represent submergedflow conditions, with profile c having a sub-mergence slightly greater than 75 percent,and d much greater. At flow conditions c andd, the upstream depth at the h 1 location hasincreased.

The effect of submergence and the correc-tion factors necessary for determining theactual discharge for the two flumes are givenin figure 5. This figure shows the effect ofdownstream water depth, 114 , on the head-discharge relationship determined under free-flow conditions. Recent tests have shown thatthe submergence effect is essentially thesame for both flumes. Submergence beginsto become a significant factor as VIII ex-ceeds 75 percent. The ordinate of figure 5 isa ratio of the actual discharge, Q, to observeddischarge, Q0, for the h 1 depth which has beenincreased owing to submergence. The use ofthis increased depth and the rating table forfree flow, results in a determination of dis-charge (Q 0) which is greater than actual. Theratio QIN is a correction factor and can beused for determining the actual discharge.

Example:

For flume No. 2

Given: h1 = 1.61 ft.

h4 = 1.43 ft.

Submergence= x 100• n

= 89 percent

From table 3, the observed discharge forh 1 = 1.61 ft. is 17.63 c.f.s.

From figure 5:

Qo - 0.92

8

__Ar----Free Flow

FlumesNo.land2

10

0.9

0.89/go

0.7

0.6

0.550 60 70

80 90 100

Percent Submergence— fx1001

Figure 5,--Effect of submergence on dis&harge, flumes Nos. 1 and 2.

therefore, the actual discharge under sub-merged conditions is

Q 0.92 x 17.63 = 16.2 c.f.s.

Although submergence' actually begins toaffect the head-discharge relationship when

hilt), exceeds 70 percent, there is only a3-percent difference from the free-flow re-lationship at 80 percent. Since this deviationis within the usual expected error of meas-urement with a flume, a correction may notbe necessary until submergence exceeds 80percent.

9

ACCURACY OF MEASUREMENT

As with most measuring devices, the ac-curacy of measurement depends to a greatextent on the precision of construction, flumesetting, and determining depths of flow. Usinga device under conditions different from thoseunder which it was calibrated results in errors.

The flumes must be constructed to thedimensions shown in figures 2 and 3. Afterconstruction, all dimensions should be checkedto see that lengths and widths are correct andthe staff gages are located in the properposition. The throat section is the controlsection and, therefore, the dimensions in thisarea are very important. If this sectiondeviates from exact dimensions, then the dis-charge will also deviate from the standard.The equation of continuity applies, and thedischarge is directly proportional to the area.For example, if the area is 3 percent smallerthan standard in the throat section, then the dis-charge is also 3 percent less for the h 1 depth.

Flumes should normally be installed hori-zontally but may be installed on slopes within

the determined limits if cast within concreteditches. For those with bottom slope, the staffgages must be installed with the zero refer-enced to the elevation of the center of thethroat section. It is important that the flumesbe leveled transversely so that the staff gagesare on the exact side slope specified for theflume.

The reading of depth is important since theaccuracy of reading may determine the ac-curacy of the device. During calibration testsof flume No. 1 over the entire range of dis-charge, more than 80 individual readings weremade both with staff gages mounted on theflume and with a hook gage in a stilling well.The staff gage differed from the hook gagereadings by an average of 10.004 foot and hada standard deviation of 0.004 foot. An errorof ± 0.01 foot in reading the staff gage wouldresult in an error of ± 4.3 percent in dis-charge for low flows and 2.0 percentfor highflows through flume No. 1.

CONSTRUCTION

Materials

The flumes can be constructed of differentmaterials. Flume No. 1 has been constructedof concrete, sheet metal, and fiberglass asshown in figure 1. Because of its larger size,flume No. 2 should generally be constructedof concrete. Since both flumes conform to thedimensions of standard concrete ditches, theflumes can be cast in an existing ditch by theuse of a portable form as shown in figure 6.For temporary installations the flumes couldbe constructed of plywood.

Flume Setting

The flumes should normally be set so thatthey operate in the free-flow range. The flumeinvert elevation relative to the natural bedlevel can be important. Flumes No. I and 2were basically designed to become an integralpart of a lined channel, and if there is suf-ficient slope, the bottom of the flumes cor-responds to the elevation of the channel bottom

and there is no step. For this situation, theslope of the channel and the correspondingnormal depth determine the degree of sub-mergence that may be encountered.

There is a lower limit to channel slopewhere flume submergence might exceed 80percent. As an example, consider flume No. 1

at approximately maximum flow.

Assume: Q = 5.98 c.f.s.

h i = 1.20 ft. (table 1)

For 80-percent submergence, normal depth inthe downstream section of a standard slipform,concrete ditch should be

hn 11 4 = 0.80 X 1.20 = 0.96 ft.

A 4 = 1.88 ft. 2 (area)

p4 = 3.72 ft. (wetted perimeter)

R 4 0.505 ft. (hydraulic radius)

V4 Q/A 4 = 3.18 f.p.s. (mean velocity)

10

2 2yA nThen: so _

Assume: n 0.015 (Manning coefficient forconcrete channel)

(3.18) 2(0.015)2

(2.22) n 4 )4/3- 2.22(0.505)1. 33

= 0.0025 (channel slope)

The following tabulation gives the minimumslopes for a range of roughness values n for

limits in the standard 1-foot

Figure 6.--Portable form used to pour trapezoidal flumes inconcrete ditches

c. f. s. so

5.98 0.015 0.00255.98 .018 .0034.54 .015 .0013.54 .018 .0019

The values of n represent those for smooth(0.015) to rough (0.018) concrete surfaces.

Slipform concrete ditches are generally

slope of 0.0025 for the smooth ditch or elsemake submergence corrections at the higherflows. The foregoing procedure can be usedto determine the minimum slope require-ments for other channels in order to insurefree-flow conditions through the flume.

There is also an upper limit on the slopeof a concrete ditch for placing a trapezoidalflume. Since the flume is a critical depthdevice, flow approaching the structure mustbe at subcritical velocity. Critical slope canbe determined for a channel of given size witha particular roughness coefficient. The upperlimit of discharge gives the upper limit ofslope. The following tabulation gives the uppercritical slopes for ditches conforming in shapeto each of the measuring flumes:

Critical slope

Flume No. 1 Flume No. 2

the dischargeditch.

placed on slopes ranging from 0.00075 to 0.015 0,0053 0.00400.0015. It would be necessary to require a .018 .0076 .0057

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The invert height above channel bed levelcan be chosen arbitarily, although it must bekept in mind that the higher the invert, thehigher will be the upstream water level and,therefore, the higher the ditchbanks that willbe required. For earth ditches, the flumesshould always be placed higher than the ditchbottom. When a concrete ditch has a flat slopeso that the flume would operate more than80 percent submerged most of the time,then the flume should be raised above thebottom.

Figures 7 and 8 can be used to determinethe head loss through the flumes and also togive an approximate elevation for setting theflume above the natural bed to insure that theflow will generally be free. If the canal slopeis very flat, i.e., below the slopes determinedin the previous section, then the setting of the

flume can be determined. For flume No. 1assume the maximum flow is

Q-= 4.98 c.f.s.,

h i = 1.11 ft. (table 1)

and maximum submergence is to be 80 percent.From figure 7

= 0.22 ft.

and the flume bottom should be raised 0.22foot above the canal invert.

Figures 7 and 8 can also be used to deter-mine the drop in water surface through thestructures for design or operational needs.For a flow of 6 c.f.s. at 80-percent sub-mergence, the head loss for flume No. 1 is0.24 foot. For the same conditions, the lossthrough flume No. 2 is 0.20 foot (fig. 8).

0.6 0.8 ID003 0.04 0.06 008 0.1

02 0.3 04

Head Loss (N)- ft.

Figure 7,—Head loss through trapezoidal flume No. 1,

ODI

Q02

12

Trapezoidal flumes can be constructed asan integral part of a lined canal or made ofmetal, fiberglass, or wood and installed in thechannel. The flumes can be used where headloss must be kept to a minimum. Submer-

Head Loss (hil -ft.

Figure 8,--Head loss through trapezoidal flume No, 2,

SUMMARY

gence to a maximum of 80 percent can beallowed before corrections are necessary.For flows with submergence in excess of 80percent, flow corrections can easily bemade.

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13

APPENDIX

TABLE 1.--Free-flow discharge, in cubic feet per second, through trapezoidal flume No. 1

1bl measured in vertical•direction Q 3.23 hi. 2.5 + 0.63 hi. 1.5 + 0.05)

h, (ft.) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.20 0.16 0.18 0.19 0.20 0.22 0.23 0.24 0.26 0.28 0.30.30 .40

.31

.54.33.56

.35

.59.37.62

.39

.65.42.68

.44 .46

.71 .74.48.78

.51

.81.50 .60

.841.24

.881.29

.921.34

.951.38

.991.43

1.031.48

1.07 1.111.53 1.58

1.161.64

1.201.69

.70 1.74 1.80 1.86 1.92 1.97 2.03 2.10 2.16 2.22 2.29

.80 2.35 2.42 2.49 2.56 2.63 2.70 2.77 2.84 2.92 3.00

.90 , 3.07 3.15 3.23 3.31 3.39 3.48 3.56 3.65 3.74 3.821.00 3.91 4.00 4.10 4.19 4.28 4.38 4.48 4.58 4.68 4.781.10 4.88 4.98 5.09 5.20 5.30 5.41 5.52 5.63 5.75 5.861.20 5.98 6.10 6.21 6.33 6.46 6.58 6.70 6.83 6.96 7.08

TABLE 2.--Free-flow discharge, in cubic feet per second, through trapezoidal flume No. 1

[h, measured along sloping aidewal/ Q = 1.36 h„ 2 ' 5 + 0.37 h, + 0.05]

hi (ft.) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0. 07 0.08 0.09

0.30 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27.40 .28 .29 .31 .32 .33 .35 .36 .38 .39 .4150 .42 .44 .46 .47 .49 .51 .52 .54 .56 .5860 .60 .62 .64 .66 .69 .71 .73 .76 .78 .80

.70 .83 .85 .88 .90 .93 .96 .98 1.01 1.04 1.07

.80 1.10 1.13 1.16 1.19 1.22 1.25 1.28 1.31 1.35 1.3890 1.41 1.45 1.48 1.52 1.56 1.59 1.63 1.67 1.71 1.74

1.00 1.78 1.82 1.86 1.91 1.95 1.99 2.03 2.08 2.12 2.161.10 2.21 2.25 2.30 2.35 2.40 2.44 2.49 2.54 2.59 2.641.20 2.69 2.74 2.79 2.84 2.90 2.95 3.00 3.06 3.11 3.171.30 3.23 3.28 3.34 3.40 3.46 3.52 3.58 3.64 3.70 3.761.40 3.82 '3.89 3.95 4.02 4.08 4.15 4.22 4.28 4.35 4.421.50 4.49 4.56 4.63 4.70 4.77 4.84 4.92 4.99 5.06 5.141.60 5,21 5.29 5.37 5.44 5.52 5.60 5.68 5.76 5.84 5.921.70 6.01 6.09 6.17 6.26 6.34 6.43 6.52 6.60 6.69 6.781.80 6.87 6.96 7.05 7.14 7.23 7.33 7.42 7.51 7.61 7.70

TABLE 3.--Free-flow discharge, in cubic feet per second, through trapezoidal flume No. 2

[hi measured in vertical direction Q = 4.27 hl 2.5 + 1.67 hi. 1 ' 5 + 0.19]

hl (ft.) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.30 0.67 0.70 0.74 0.77 0.81 0.84 0.88 0.92 0.96 1.0040 1.04 1.09 1.13 1.18 1.22 1.27 1.32 1.37 1.42 1.48

.50 1.53 1.59 1.65 1.70 1.76 1.83 1.89 1.95 2.02 2.0960 2.15 2.22 2.30 2.37 2.44 2.52 2.59 2.67 2.75 2.8370 2.92 3.00 3.09 3.17 3.26 3.35 3.44 3.54 3.63 3.73

.80 3.82 3.92 4.03 4.13 4.23 4.34 4.45 4.56 4.67 4.7890 4.89 5.01 5.12 5.24 5.36 5.49 5.61 5.74 5.86 5.99

1.00 6.12 6.26 6.39 6.53 6.66 6.80 6.95 7.09 7.23 7.381.10 1.20

7.539.11

7.689.28

7.839.45

7.989.62

8.149.80

8.309.98

8.4610.15

8.6210.33

8.7810.52

8.9510.70

1.30 10.88 11.07 11.26 11.45 11.65 11.84 12.04 12.24 12.44 12.641.40 12.85 13.06 13.26 13.48 13.69 13.90 14.12 14.34 14.56 14.791.50 15.01 15.24 15.47 15.70 15.94 16.17 16.41 16.65 16.89 17.141.60 17.38 17.63 17.88 18.13 18.39 18.65 18.91 19.17 19.43 19.701.70 19.96 20.24 20.51 20.78 21.06 21.34 21.62 21.90 22.19 22.481.80 22.76 23.06 23.35 23.65 23.95 24.25 24.55 24.86 25.17 25.481.90 25.79 26.10 26.42 26.74 27.06 27.39 27.71 28.04 28.37 28.712.00 29.04 29.38 29.72 30.07 30.41 30.76 31.11 31.46 31.82 32.172.10 32.53 32.90 33.26 33.63 34.00 34.37 34.74 35.12 35.50 35.88

2.20 36.26 36.65 37.04 37.43 37.82 38.22 38.62 39.02 39.42 39.832.30 40.24 40.65 41.06 41.48 41.90 42.32 42.74 43.17 43.60 44.032.40 2.50

44.4648.95

44.9049.41

45.3449.87

45.7850.34

46.2350.81

46.6751.28

47.1251.76

47.5852.24

48.0352.72

48.4953.20

14