Minimum Height Requirement for a Critical Flow Broad Crested Weir
The water velocity will increase whenever the flow in an open channel passes over an obstruction like a broad crested weir, because of the decrease in cross-sectional flow area. Within limits, the higher the obstruction, the greater the water velocity will be going over the obstruction. If the approach flow is subcritical, then the flow over a broad crested weir will become critical at some particular weir height. That height needed to give critical flow over the weir crest can be calculated using some basic hydraulics equations, Using the terminology in the broad crested weir figure above, along with B for the width of the channel, the energy equation becomes:
y1 + V12/2g = y2 + P + V22/2g
From the definition of average velocity in an open channel, assuming that the channel is approximately rectangular:
V1 = Q/y1B and Vc = Q/ycB
From the fact that the specific energy is a minimum for critical flow conditions:
yc = [Q2/gB2]1/3
If the channel width, B, the flow rate through the channel, Q, and the approach depth, y1, are known, the depth required to give critical flow over the broad crested weir crest can be calculated with the above three equations. If a broad crested weir has the minimum height needed for critical flow, then the simple equation, Q = 1.6 L H3/2, can be used for flow rate calculations over that broad crested weir.
This is illustrated with example calculations in the next section. In order to ensure critical flow over the weir for all flow conditions, the maximum anticipated flow rate through the channel should be used to calculate the required weir height, P.