Question 1

What is the sluice gate discharge equation?

Accepted Answer

For free outflow under a vertical gate: Q = Cd·b·a·√(2g·y1), where b is gate width, a the gate opening, y1 the upstream depth, and Cd the discharge coefficient. Cd combines the jet contraction and the approach velocity: Cd = Cc/√(1 + Cc·a/y1) with contraction coefficient Cc ≈ 0.61 for a sharp-edged vertical gate.

Question 2

What is the vena contracta?

Accepted Answer

The jet issuing under the gate contracts to a minimum depth y2 = Cc·a a short distance downstream — the vena contracta. For a sharp-edged vertical gate Cc ≈ 0.61, nearly constant over the usual range of a/y1. The supercritical jet at the vena contracta is the starting point for downstream hydraulic-jump analysis.

Question 3

How do I know if the gate is flowing free or submerged?

Accepted Answer

Compute the conjugate (sequent) depth of the vena-contracta jet. If the tailwater depth y3 is less than that conjugate depth, a free jump forms downstream and the gate discharges free — upstream depth alone controls. If y3 exceeds the conjugate depth, the jump drowns back against the gate, the outflow is submerged, and the free-flow equation over-predicts Q. This calculator performs exactly that check.

Question 4

What happens to discharge when the gate is submerged?

Accepted Answer

Discharge depends on both upstream and tailwater levels and drops below the free-flow value — sometimes drastically. Submerged-flow solutions (e.g., Henry's chart, Swamee's fitted equations, or a momentum-energy analysis between the gate and tailwater) are required. This tool flags submergence and reports the free-flow value as an upper bound; for rating a permanently submerged gate use the full submerged analysis.

Question 5

Can I use this for a low-level outlet or head gate on a dam?

Accepted Answer

The equation applies to a rectangular vertical lift gate discharging into an open channel. Dam low-level outlets that flow full as pressurized conduits behave as orifices/short culverts instead — use the orifice tool or a conduit analysis. Radial (Tainter) gates have different Cc values that vary with trunnion geometry and lip angle; USBR and USACE publish those coefficients.

Question 6

How accurate is Cc = 0.61?

Accepted Answer

For sharp-edged vertical gates with a/y1 below about 0.5, experimental Cc ranges roughly 0.59–0.62 and 0.61 is the standard design value (Henderson 1966; Rajaratnam & Subramanya 1967). Rounded gate lips raise Cc toward 0.7–0.8, increasing discharge for the same opening. If the gate lip is not sharp, adjust Cc accordingly.

Gate lip	C_c
Sharp-edged (standard)	0.59–0.62 (use 0.61)
Rounded lip	0.70–0.80
45° bevel, downstream face	≈ 0.70

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