Broad-Crested (Critical-Flow) Weir Discharge

The critical-flow weir that completes the weir family alongside the sharp-crested V-notch, rectangular.

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Details, formula, and sources

The critical-flow weir that completes the weir family alongside the sharp-crested V-notch, rectangular, and Cipolletti weirs. A broad, level crest forces the flow through critical depth, so Q = Cd (2/3)^1.5 sqrt(g) L H^1.5, with L the crest width, H the upstream head over the crest, and g = 32.2 ft/s^2. The theoretical coefficient (2/3)^1.5 sqrt(g) = 3.089 is well below the 3.33 of a sharp-crested (Francis) weir, and Cd ~ 0.85-0.95 trims it further, so the effective coefficient is about 2.6-2.9. A 10 ft crest at 1 ft of head with Cd 0.90 passes about 27.8 cfs. Broad crests run spillways, embankment/road-overtopping checks, and long-throated flumes because the rating is stable and the crest tolerates debris and submergence. Free-flow (modular) rating; approach-velocity head neglected. First-principles critical-flow hydraulics / USBR Water Measurement Manual; the engineer of record governs.

Q = Cd (2/3)^1.5 sqrt(g) L H^1.5, g = 32.2 ft/s^2; theoretical coefficient (2/3)^1.5 sqrt(g) = 3.0888 (ft units); effective C = Cd x 3.0888, Cd ~ 0.85-0.95. 1 cfs = 448.831 GPM; MGD = GPM x 1440 / 1e6.

First-principles critical-flow open-channel hydraulics - the broad-crested weir discharge - and the USBR Water Measurement Manual (public domain), by name.

Free at usbr.gov/tsc/techreferences/mands/wmm; the critical-flow (2/3)^1.5 sqrt(g) = 3.089 coefficient is a first-principles constant and the user may override Cd with a site calibration.

Estimate. AHJ and licensed professional govern.

Field names used by the API: crest_length_ft, head_ft, effective_coeff, flow_cfs

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