Sluice-Gate (Underflow) Free-Flow Discharge

The third canal-control structure the flow set was missing.

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Checked against published worked examples from: Sluice gate (contraction cross-check).

Details, formula, and sources

ScopeAlongside the overflow weir (weir-flow, cipolletti-weir) and the submerged orifice (orifice-flow): water drawn UNDER a raised gate. Free-flow Q = Cd x b x a x sqrt(2 g y1), with a the gate opening, b the width, y1 the upstream depth above the floor, and the discharge coefficient Cd = Cc / sqrt(1 + Cc a / y1) from the jet contraction (Cc ~ 0.61 for a sharp-edged vertical gate, so Cd ~ 0.55-0.60). A 1 ft opening on a 5 ft gate under 6 ft of head passes about 57 cfs (Cd 0.58). Free-flow only -- the tailwater must not drown the contracted jet, and the head is the upstream depth above the floor, not the head on the opening. First-principles open-channel hydraulics (Henderson / USBR Water Measurement Manual); the operator of record governs.

Formula or tableQ = Cd x b x a x sqrt(2 g y1), g = 32.2 ft/s^2; Cd = Cc / sqrt(1 + Cc a / y1), Cc ~ 0.61. 1 cfs = 448.831 GPM; MGD = GPM x 1440 / 1e6.

Source and editionFirst-principles open-channel hydraulics - the free-flow sluice (underflow) gate discharge (Henderson, Open Channel Flow) and the USBR Water Measurement Manual submerged-orifice/check-gate section, by name.

Free accessFree at usbr.gov/tsc/techreferences/mands/wmm; the sluice-gate free-flow relation and the ~0.61 contraction coefficient are standard published open-channel hydraulics, and the user may override Cc with a site calibration.

What governsEstimate. AHJ and licensed professional govern.

API field namesgate_opening_ft, gate_width_ft, upstream_depth_ft, discharge_coeff, flow_cfs

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