Orifice Discharge Flow
The flow through a sharp-edged hole that sizes a detention-pond outlet, a tank drain, or a restrictor plate: Q = Cd A sqrt(2 g h), Cd about 0.6 sharp-edged, head to the orifice center. A 6 in orifice under a 4 ft head sheds 1.89 cfs (849 gpm); the flow scales with the square root of the head, so a 2.25x head raises it only 1.5x - the gentle stage-discharge control that holds a post-development peak to the pre-development rate. Free/submerged, steady head, small orifice; the falling-head time-to-drain is separate. A design aid; the engineer of record governs.
Formula and source
A = pi/4 (d/12)^2; Q_cfs = Cd A sqrt(2 g h) (g = 32.2 ft/s^2); Q_gpm = 448.831 Q_cfs.
The orifice discharge equation Q = Cd A sqrt(2 g h) with g = 32.2 ft/s^2 and the sharp-edged discharge coefficient (~0.6), a standard hydraulics result, by name.
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