395

2.31 Weirs and Flumes

W. H. HOWE

(1969, 1982)

B. G. LIPTÁK

(1995)

A. V. PAWLOWSKI

(2003)

Types

Open-channel flow can be measured by detecting level in front of primaries. Bubblers,capacitance, float, hydrostatic, and ultrasonic devices are used as level sensors. Open-channel flows can also be measured without primaries by calculating flow from depthand velocity using ultrasonic and magnetic sensors.

Operating Conditions

Atmospheric

Applications

Waste or irrigation water flows in open channels

Flow Range

From 1 GPM (3.78 l/m), no upper limit

Rangeability

Most devices provide 75:1; V-notch weirs can reach up to 500:1

Inaccuracy

Laboratory devices: 2 to 3% of full scaleField installations: 5 to 10% of full scale

Costs

Primaries used in pipe inserts cost less than $1000. A 6-in. (150-mm) Parshall flumecosts about $1500, and a 48-in. (1.22-m) one costs about $5000. Primaries forirrigation applications are usually field-fabricated. Manual depth sensors can beobtained for $300; local bubbler or float indicators for $750 to $1500; and program-mable, transmitting, capacitance,

ultrasonic

, or bubbler units from $2000 to $3000.Open-channel flowmeters calculating flow (based on depth and velocity) range from$5000 to over $10,000.

Partial List of Suppliers

ABB Automation, Instrumentation Division (www.abb.com/us/instrumentation) (primaries)

Badger Meter Inc. (www.badgermeter.com) (Parshall or manhole flume, ultrasonicand open-channel computing)

Endress+Hauser Inc. (www.us.endress.com) (ultrasonic and capacitance)Fischer Controls Int. (ultrasonic)Flow Technology Inc. (www.ftimeters.com)GLI International (www.gliint.com)Hays Cleveland (www.hayscleveland.com)Kay-Ray/Sensall Inc. (www.thermo.com) (ultrasonic)Manning Environmental Corp. (www.manning-enviro.com) (primaries)Marsh-McBirney Inc. (www.marsh-mcbirney.com) (electromagnetic)Milltronics Inc. (www.milltronics.com) (ultrasonic)Montedoro-Whitney Corp. (open-channel flow by ultrasonics)MSR Magmeter Mfg. Ltd. (www.magmeter.com) (robotic magmeter probe for open channel)

Princo Instruments Inc. (www.princoinstruments.com) (capacitance)Robertshaw Ind.Royce Instrument Corp.Sponsler Co. (www.sponsler.com)Thermal Instrument Co. (www.thermalinstrument.com)Thermo Polysonics (www.thermopolysonics.com)

Flume

WeirFlow Sheet Symbol

© 2003 by Béla Lipták

396

Flow Measurement

WEIRS

Weirs are apertures in the top of a dam, across a channelthrough which flows the liquid to be measured (Figure 2.31a).The aperture may be rectangular (Figure 2.31b), trapezoidal(Figure 2.31c), or V-notch (Figure 2.31d). The special caseof a trapezoidal weir with side slopes of 1:4 (Figure 2.31c)is known as a

Cippoletti weir

; this form leads to a simplifiedflow calculation. V-notch weirs generally have a notch anglefrom 30 to 90

°

, depending on required flow capacity.The head is measured as the difference in level of the pool

at an adequate distance upstream from the weir as comparedto the horizontal crest of a rectangular or trapezoidal weir, orthe bottom point of the V of a V-notch weir. Heads less than0.1 ft (30 mm) for minimum measured flow or more than 1.0ft (300-mm) for maximum flow are generally to be avoided,

although a 1.25-ft (380-mm) head can be tolerated under favor-able conditions. These limits are easily met by practical design,given that a 30

°

V-notch will measure a minimum flow of 1GPM (3.8 l/m), whereas the maximum value for a rectangularor trapezoidal weir is limited only by practical crest length.

V-notch weirs are used for smaller flows. A 30

°

V-notchweir has a practically constant coefficient from 3.0 to 300GPM (11.4 to 1140 l/min) with flow proportional to the five-halves power of the head. Coefficient increases roughly 2%for flow down to 1 GPM (3.8 l/min) and changes relativelylittle for flow up to 500 GPM (1893 l/min). For notch angleup to 90

°

, flow varies as the tangent of half the notch angle.Notch angle exceeding 90

°

is not recommended.Rectangular or Cippoletti weirs are used for larger flows.

A rectangular weir with a crest 2 ft (0.6 m) long develops ahead of about 0.2 ft (60 mm) for 250 GPM (946 l/min) and1.0 ft (305 mm) for 2700 GPM (10,221 l/min). For this weir,flow is directly proportional to crest length and to the three-halves power of the head.

The weir plate may be located in a dam in a natural channelor in a weir box (Figure 2.31e). The stilling basin ahead of theweir should be large enough so that the upstream velocity doesnot exceed 0.33 ft/sec (0.01 m/sec). Width and depth immedi-ately ahead of the weir should be sufficient so that the walleffect of the bottom and sides of the channel has negligible

FIG. 2.31a

Flow over a weir.

FIG. 2.31b

Rectangular weir.

FIG. 2.31c

Cippoletti (trapezoidal) weir.

Drawdown

Nappe

AerationUnder Nappe

H

BottomContraction

CrestL

End Contractions

Q = 3.33 (L−0.2H)H3/2

Crest

L

4

Q = 3.367 LH3/2

FIG. 2.31d

V-notch weir.

FIG. 2.31e

Weir box.

No crest

Angle of notch (θ)

Q = 2.48 tan(θ/2) H5/2

Flow15

10

0

© 2003 by Béla Lipták

2.31 Weirs and Flumes

397

effect on the pattern of flow through the notch. It is importantthat the flow break clear from the sharp edge of the notch withan air pocket maintained immediately beyond and below theweir plate. The channel downstream from the weir must besufficiently wide and deep so that, at maximum flow, there isample clearance between flow through the notch to downstreamliquid level so that this air pocket is maintained (Figure 2.31a).The upstream edge of the weir should be sharp and straight. Itis usual practice to bevel the downstream edge of the weir at45

°

to about a 1/32-in. (0.8-mm) edge. For rectangular andCippoletti weirs, the crest must be carefully leveled.

Accuracy of the relation between flow and head (level)to

±

2% is attainable, based on the dimensions of the primarydevice. Reference 1 gives full data on installation and oper-ation of weirs.

The following equations establish the relationshipsbetween flow and measured head, provided that the installa-tion and operation of the weir are as recommended in thissection and also in the cited references.

For a V-notch weir

2.31(1)

For a rectangular weir

2.31(2)

For a Cippoletti weir

2.31(3)

where

Q

=

rate of flow in cubic feet per second

θ

=

V-notch angle in degrees

H

=

head* in feet of following liquid

L

=

crest length in feet

THE PARSHALL FLUME

Developed by R.L. Parshall at the Colorado Experiment Stationof the Colorado Agricultural College, in cooperation with theDivision of Irrigation of the U.S. Department of Agriculture,

2

this device is a special type of venturi flume (Figure 2.31f).The loss of head is about one-quarter of that for a weir of equalcapacity. Compared to weirs, approach velocity effects arepractically eliminated so that a large upstream stilling basin isnot required. The relatively high velocities in the system tendto flush away deposits of silt and other solids that might accu-mulate and alter measurement. There are no sharp edges, nopockets, and few critical dimensions; also, the device can be

locally fabricated from available materials. Calibration databased on physical dimensions are available from 3 in. (76 mm)throat width with minimum range of 0.03 second-feet (13 GPMor 49 l/m) up to 50 ft (15.2 m) throat width with maximumcapacity of 3300 second-feet (1,485,000 GPM/5,619,900 l/m).Flow is approximately proportional to the three-halves powerof level with flow capacity of a single unit covering a range of35:1 or more, depending on size.

Extreme accuracy is not claimed for flow measurementusing this device; however, measurement is very dependablewith minimal maintenance and good repeatability. Accuracyis adequate for most applications to irrigation, waste, andsewage flows.

Downstream level has minimal effect on the measurementas long as the level near the downstream end of the throat doesnot exceed 70% of the level measured near the upstream endof the converging section (Figure 2.31f). (Both levels arereferred to the floor section of the flume.) For flumes less than1 ft (305 mm) wide, the ratio of levels is 60% maximum. Thisis the preferred and more usual mode of operation. It providesbest accuracy. Only one measurement of level is required, withflow computed directly from this upstream level measurement;direct, continuous readout of flow rate is readily provided.

Where operating conditions (available head, maximumflow rate, weir size, and so on) result in a throat level greaterthan 70% of upstream level, so-called

submersion

results.Measurement can be obtained with a downstream level as greatas 95% of upstream level. However, this requires a correctionfactor based on both upstream level and downstream level inthe flow computation, accuracy suffers, and special equipmentis usually required for direct readout of flow.

The simplified equations based on a single measurementat the upstream location are as follows:

* Head is measured between the level in the stilling pond and the crest ofa rectangular or Cippoletti weir, or the bottom of the V of a V-notch weir.

Q H= 2 4812

2 5. tan .θ

–Q L H H= 3 33 0 2 1 5. ( . ) .

Q LH= 3 367 1 5. .

FIG. 2.31f

Parshall flume.

ConvergingSection

Plan

ThroatSection

DivergingSection

o o

Flow

LevelFloor

Section O-O

Water Surface SubmergedOperation

Normal Operation

© 2003 by Béla Lipták

For conditions other than exactly as recommended, see ref-erences for correction factors.

398

Flow Measurement

For

L

=

0.25 ft,

2.31(4)

For

L

=

0.5 ft,

2.31(5)

For

L

=

0.75 ft,

2.31(6)

For

L

=

1 to 8 ft,

2.31(7)

For

L

=

>

8 ft,

2.31(8)

where

L

=

width of throat section in feet

Q

=

volume flow rate in cubic feet per second

H

=

head in feet*

Parshall flumes are available in plastic construction. Onevariation of the plastic units is the nested, dual-range config-uration in which two flumes are nested inside each other.This configuration is used in installations where the start-upconditions are substantially lower than the final operatingflow rates (Figure 2.31g). With these units, the flow initiallypasses through the inner flume; then, when the flow exceedsits capacity, the inner flume is removed while the outer flume

remains in place permanently. Dimensions of fiberglass-reinforced resin Parshall flumes are given in Table 2.31h.

THE PALMER BOWLUS FLUME

Palmer-Bowlus flumes provide the advantages of rounded bot-toms and relatively small size. Compared with other flumes,this makes for easier installation in pipe inverts, ends, andsewer manholes. They also have a smaller head change vs.

TABLE 2.31h

Dimensions and Capacities of One-Piece Parshall Flumes*

†

Free Flow (GPM)

Throat Width Depth (inches) Length Weight (pounds) Minimum Maximum

2 in. 12 2 ft, 6.5 in. 35 9.0 210

3 in. 24 3 ft, 0 in. 40 13.5 494

6 in. 24 5 ft, 0 in. 100 22.4 1750

9 in. 30 5 ft, 4 in. 130 40.4 3950

12 in. 36 9 ft, 4.875 in. 280 157.0 7225

18 in. 36 9 ft, 7.875 in. 305 228.9 11,040

24 in. 36 9 ft, 10.875 in. 330 296.2 14,855

3 ft, 0 in. 36 10 ft, 4.075 in. 385 435.3 22,619

4 ft, 0 in. 36 10 ft, 10.375 in. 450 565.5 30,473

5 ft, 0 in. 36 11 ft, 10.25 in. 515 996.3 38,417

6 ft, 0 in. 36 11 ft, 10.375 in. 575 1180.3 46,450

7 ft, 0 in. 36 12 ft, 4.25 in. 650 1831.1 54,484

8 ft, 0 in. 36 12 ft, 10.125 in. 730 2073.5 62,607

*Units in table can be converted using 1 in.

=

25.4 mm, 1 lb.

=

0.45 kg; 1 in. H

2

O

=

249 Pa; 1 GPM

=

3.785 l/min.†Courtesy of ABB Inc.

*

H

(head) is measured at a designated point in the upstream convergingsection, referred to the level floor of this section.

Q LH= 3 97 1 547. .

Q LH= 4 12 1 58. .

Q LH= 4 10 1 53. .

Q LH L= 4 0 1 522 0 026. . ( . )

Q L H= +( . . .2 5 3 69 1 6 )

FIG. 2.31g

Dual-range Parshall flume. (Courtesy of ABB - Fischer & Porter Co.)

© 2003 by Béla Lipták

2.31 Weirs and Flumes

399

flow, and their dimensions are scalable to throat width, whichmakes rating of off-size flumes possible. A disadvantage is thatthe throat is raised; therefore, the possibility exists for upstreamsilt deposition at low flows. Reference 3 provides data on this.

These flumes are available for installation in existinground pipe using the type of insert shown in Figure 2.31i.

THE KENNISON NOZZLE, PARABOLIC FLUME, AND LEOPOLD LAGCO FLUME

These are typical proprietary products that were designedprimarily for end-of-pipe flow measurement of waste, sew-age, and the like, where the liquid flow to be measuredemerges from a cylindrical pipe or conduit that usually is notcompletely full of liquid. All are designed to flush solidsthrough the device without accumulations and to allow acces-sibility for inspection and cleaning if necessary.

These devices develop heads that are a function of flow rate.In the Kennison nozzle, head is almost linear with flow above10% of maximum flow rate. Accuracy is stated as 2% in thisrange. For the parabolic flume and the Leopold Lagco flume,flow varies approximately as the three-halves power of head.

These devices are available in medium to large sizes.Details as to structure, application, and characteristics areavailable from the manufacturers.

DETECTORS FOR OPEN-CHANNEL SENSORS

The level rise generated by flumes or weirs can be measured bynearly any of the level detectors described in Chapter 3, includingsuch simple devices as the air or nitrogen bubblers (Section 3.2).

It is also possible to detect the flow in open channelswithout the use of flumes, weirs, or any other primary devices.One such design computes flow in round pipes or open chan-nels by ultrasonically measuring the depth, calculating the flow-ing cross-sectional area on that basis, and multiplying the areaby the velocity to obtain volumetric flow (Figure 2.31j).

Another open-channel flowmeter that does not need aprimary element uses a robot-operated magnetic flowmeterprobe to scan the velocity profile in the open channel (Figure2.31k). In this design, the computer algorithm calculates and

FIG. 2.31i

Flume insert elements. (Courtesy of Manning Environmental Corp.)

FIG. 2.31j

Volumetric flow computer measures depth and velocity in open chan-nel and does not require a primary device. (Courtesy of Montedoro-Whitney Corp.)

FIG. 2.31k

Robot-operated magnetic flow meter probe sensor is used to computechannel flow. (Courtesy of MSR Magmeter Mfg. Ltd.)

I

Q = Flow

f v

Example of aVelocity Profile

© 2003 by Béla Lipták

400

Flow Measurement

separately adds up the flow segments through each slice ofthe velocity profile as the velocity sensor moves down to thebottom of the channel.

References

1. Streeter, V. L., The kinetic energy and momentum corrections for pipesand open channels of great width,

Civil Eng.,

12(4), 212, 1942.2. Measuring water in irrigation channels,

Farmers Bulletin 1682,

U.S.Dept. of Agriculture, Washington, D.C.

3. Paper Number 1948, in

Proc. Inst. Civil Eng.,

101, 1195, 1936.4. Wells, E. A. and Gotaas, H. B., Design of Venturi tubes in circular

conduits, in

Proc. Am. Soc. Civil Eng., J. Sanitary Eng. Div.,

82, 1956.5.

Water Measurement Manual,

4th ed., U.S. Dept. of the Interior, Bureauof Reclamation, Washington D.C.

Bibliography

Boyes, W. H., Pumps and flowmeters hand in hand,

Flow Control,

September2001.

Cushing, M., The future of flow measurement,

Flow Control,

January 2000.Eren, H., Flowmeters, in

Survey of Instrumentation and Measurement,

S. A.Dyer, Ed., John Wiley & Sons, New York, 2001, 568–580.

Lipták, B. G., Flow measurement trends,

Control,

June 2000.Miller, R. W.,

Flow Measurement Engineering Handbook,

3rd ed., McGraw-Hill, New York, 1996.

Open channel flowmeters,

Meas. Control,

December 1992.Shinskey, G., Characterizers for flume and weirs,

Instrum. Control Syst.,

111,

September 1974.Spitzer, D. W.,

Flow Measurement Practical Guide Series,

2nd ed., ISAPress, Research Triangle Park, NC, 2001.

Thorsen, T. and Oen, R., How to measure industrial wastewater flow,

Chem-ical Eng.,

97–100, February 17, 1975.

© 2003 by Béla Lipták