Practice Question: Flow over a Rectangular Contracted Weir

NCEES Civil PE Specification Hydraulics and Hydrology: Open-channel flow

Problem

Water in the open channel pictured flows through a rectangular weir contracted on two sides. Given dimensions provided by the elevation view and a discharge coefficient of 0.6, determine the flow over the weir in cubic feet per second.

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Solution

Answer: A) 15.4 cfs
Basic flow equation for a rectangular weir:
$$ Q=2/3\ Cb\sqrt2g\ H^{3/2} $$
Discharge coefficient (given):
$$ C=0.6 $$
Head above weir bottom:
$$ H=1\ ft $$
Effective width based on weir width:
$$ b=b_{weir}-0.1\ast\ N\ast\ H $$
where:
$$ N=number\ of\ contractions=2 $$
$$ b_{weir}=weir\ length=5\ ft $$
$$ b=5\ ft-0.1\ast2\ast1\ ft=4.8\ ft $$
Gravity constant:
$$ g=32.2\frac{ft}{s^2} $$
Flow:
$$ Q=15.4\frac{ft^3}{s} $$