A weir is an obstruction in an open-channel
that can be used to determine the flow rate.
a sharp-crested weir is a vertical plate with sharp edges placed across
shapes of weirs (e.g., rectangular, triangular, and trapezoidal) are
shown in the figures.
The weir discharge can be derived from Bernoulli's equation. The details of the derivation process are omitted
for brevity. The volumetric flow rate for a rectangular weir is given
where L is the width of the weir, and H is the head of the weir (see figure).
As expected, the actual flow rate deviates from that obtained
from theory (Eqn. 10). Hence, an experimentally-determined
the flow rate:
where the discharge coefficient for a rectangular channel is given by (Henderson,
Cd = 0.611 + 0.075 (H/Pw) 
where Pw is the height of the weir above the channel bed, as
shown in the figure.
Similar expressions for determining the flow rate of triangular and trapezoidal
weirs can be derived, and discharge coefficients are available
for various shapes of the weirs. For more information, students are
referred handbooks on hydraulics.
[ *Reference: Henderson, F. M., "Open
Channel Flow," Macmillan, New York, 1966.]