Orifice Discharge Flow
The flow through a sharp-edged hole that sizes a detention-pond outlet, a tank drain, or a restrictor plate.
Example
You enter
- Orifice diameter (in) 6
- Head to orifice center (ft) 4
- Discharge coefficient Cd 0.6
You get
- Orifice area 0.196 ft^2
- Discharge 1.89
- Q (GPM) 849
Details, formula, and sources
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.
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.
The orifice equation is a public closed-form hydraulics result; the discharge coefficients are in the standard references.
Estimate. AHJ and licensed professional govern.
Field names used by the API: d_in, h_ft, cd, a_ft2, q_cfs, q_gpm
- Discharge Q = Cd A sqrt(2 g h) at the head to the orifice centroidorifice hydraulics
- Coefficient Cd about 0.6 sharp-edged (0.8 short tube, 0.98 rounded), enteredstandard hydraulics tables
- Steady head small orifice under a steady head; the falling-head drain time is separatescope of this tile