How this calculator works
A broad horizontal crest can bring free surface flow to critical depth. Enter the total energy head above the crest and its width measured across the stream. The coefficient is dimensionless and equals one for the ideal energy model. Head based on a water level alone neglects approach velocity; use an appropriate calibrated coefficient. Tailwater must not drown the control.
Formula
Q = Cd b sqrt(g) (2H/3)^(3/2). The ideal critical depth is 2H/3. All inverse modes use this same coefficient convention.
Worked example
With Cd = 1, b = 1 m, H = 1 m and g = 9 m/s2, discharge is 1.632993162 m3/s. Doubling width doubles this to 3.265986324 m3/s.
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Frequently asked questions
Which length is the width?
Use the crest dimension across the stream. The crest length along the stream establishes whether the broad-crest assumption holds.
Can I use a coefficient of 1.7?
That value may include gravity and unit factors. This page uses a dimensionless Cd with the theoretical factor written separately.
What happens under submergence?
Downstream water affects discharge and this free-flow relation is no longer sufficient.