CE 195 2009
Measuring Discharge with a Rectangular Weir
TA: Caliente
Introduction
Discharge is a critical parameter
necessary for designing
hydraulic structures, evaluating
aquatic habitat, and any general
river or stream studies.
Measuring the flow of water is
an easy task when you have a
controlled environment such as a
pipe or a flume. There are
precision instruments that
measure flow in these controlled
environments such as venturi
meters. These situations involve
steady, uniform flow, and
idealized conditions. In realFigure 1: 6 meter re-circulating flume
world situations, there is the added
with rectangular weir installed.
complication that flows can be nonuniform and unsteady. The main techniques used in rivers and other open channels are
hydraulic structures (i.e. weirs), velocity-area methods, and slope-hydraulic radius-area
methods (i.e. Manning’s equation; Ackers et al., 1978).
Weirs are structures that control and measure flow. Water flowing over a weir is forced
into critical depth in which there is a relationship between discharge and the depth above
the weir. There are several types of weirs such as v-notch weirs, broad-crested weirs, and
rectangular weirs. Rectangular weirs can be further classified as full width, partially
contracted, or fully contracted, based on the weir width opening. The selection of weir
type is chosen based on the range of flows to be measured, the accuracy of measurement
needed, and the most economical geometry that fits in the given channel (Ackers et al.,
1978).
Purpose: To measure flows in the flume using three different methods in order to
compare results between the different methods and the venturi meter.
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CE 195 2009
Materials
 6 meter re-circulating flume with
high-flow venturi
 Plexi-glass weir plate
 Aluminum cross plate
 2 L-brackets
 Nuts, bolts and washers
 Wrench and socket-wrench
 Two clamps
 Athletic tape (for sealing weir)
 Rubber Ducky or other floating
object
 Measuring tape
 Point gage
Figure 2: Lab Materials
Procedure
Rubber Ducks (or citrus)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Make sure that the insert is in the flume.
Turn the main power switch on, located behind the flume.
Set the frequency to 15 Hz on the operator interface.
Make sure the tailgate is lowered completely.
Set the slope to 1%.
Once the flow has equilibrated, place a rubber duck (or orange) in the flume at
a marked location, and record how long it takes to travel a distance of 4m.
(Please catch all duck or citrus fruit before it exits the flume!)
Measure the water depth upstream of the insert using the point gage.
Determine the velocity using v = 0.8 x/t, and then calculate the flow using the
continuity equation (see below).
Record the inches of H2O from the high-range venturi meter and determine
the flow using the venturi meter equation (see equations below).
Repeat steps 3 through 9 two more times using frequencies of 20 Hz and 25
Hz.
Manning’s Equation (calculation)
1.
2.
3.
4.
Using the water depth measured when the frequency was set to 15 Hz,
determine the hydraulic radius.
Use Manning’s equation to determine the velocity (using, n = 0.008).
Calculate the flow using the continuity equation.
Repeat steps 1 through 3 using the depths recorded from the 20 Hz and 25 Hz
frequencies.
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CE 195 2009
Figure 3: Rectangular thin-plate weir with side contractions
(adapted from Ackers et al., 1978)
Weir Method
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Stop the flow in the flume and allow it to drain completely.
Measure the dimensions of the weir plate including the width opening (b), the
height to the opening (P), and the total width (B; see Figure 3).
Place the aluminum cross plate across the flume and underneath the flume’s
bars at approximately the midpoint of the flume.
Connect the weir to the aluminum cross plate using two L-brackets and twelve
bolts, nuts and washers, and then clamp the aluminum cross plate to the flume
walls.
Using the athletic tape, seal the downstream side of the weir plate to the flume
walls and floor.
Start the flume using the same frequency and slope as in the first method.
When the flow has equilibrated, measure the depth of the water just upstream
from the weir opening using the point gage.
Record the inches of H2O from the high-range venturi meter and determine
the flow using the venturi meter equation (see below).
Using the weir equation, compute the flow.
Repeat steps 6 through 9 using frequencies of 20 Hz and 25 Hz.
Equations
Continuity equation: Q = AV, where A = cross-sectional area and V = average
velocity.
Hydraulic radius: RH = A/Pw, where Pw = wetted perimeter.
Manning’s equation: V = 1/n RH 2/3 S1/2, where S = the slope of the energy grade line,
which for uniform open channel flow = channel slope and n = roughness coefficient.
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CE 195 2009
High Range Venturi meter flow equation:
Q(m 3 / s)  3.360 x10 3 H or
Q(cfs)  0.1187 H , where H = ft of H2O.
Kinksvater and Carter weir equation (Ackers et al., 1978):
Q  C KC (1  a KC
h
)(b  k b ) g (h  0.001) 3 / 2 (metric units only)
P
where, CKC, aKC, and kb are coefficient values, h = height of water above the weir
plate, P = height of the weir plate, and b = width of the weir opening. Coefficients for
the Kinkvater and Carter equation can be determined from the following table:
b/B
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2 - 0
CKC
0.567
0.564
0.562
0.560
0.559
0.558
0.557
0.556
0.555
aKC
0.125
0.107
0.076
0.050
0.030
0.022
0.010
0.003
-0.003
Kb
-0.0010
0.0038
0.0042
0.0040
0.0035
0.0030
0.0027
0.0025
0.0025
Type of weir
Full width
Partially contracted
Fully contracted
Discussion questions
1. How do the flows compare when plotted against each other (Qweir and Qduck and
QMannings vs. Qventuri)? Include a 1:1 line on your plot or plots to help interpret the
similarities or differences between the different flow measurement methods.
2. Which method produces the most accurate flow measurements when compared to
the venturi results? What might cause differences between the flow measurement
methods?
3. Which of these methods would you recommend for replication in a stream or
river?
References
Ackers, P., White, W. R., Perkins, J. A., and A. J. M. Harrison. (1978). Weirs and flumes
for flow measurement. John Wiley & Sons, Chichester.
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