Orifice Discharge Calculator (Tank Outlet & Detention Orifice)

How it works

Q = C × A × √(2 g h); required area A = Q ÷ (C √(2gh)); drain time from h₁ to h₂ with constant surface area A_t: t = 2 A_t ÷ (C A √(2g)) × (√h₁ − √h₂)

Water leaving a hole under pressure accelerates to the velocity a body would reach falling through the head (Torricelli’s theorem), √(2gh), and the flow is that velocity times the opening times a discharge coefficient that accounts for the jet contracting as it leaves a sharp edge — about 0.61 for a thin plate, higher for a short tube or a rounded entrance. The square-root dependence on head makes orifices ideal flow controllers: a detention pond’s outlet orifice releases more as the pond fills but only gently, which is how post-development runoff is throttled back to pre-development rates. The same formula, integrated as the level drops, gives the time to drain a tank or pond, and rearranged it sizes the orifice for a permitted release rate. Head is measured to the orifice centre, or to the downstream water level when the outlet is submerged.

Worked example

A 6-inch sharp-edged orifice (0.196 ft², C 0.61) under 4 ft of head releases 1.92 cfs (860 gpm) with a 16 ft/s jet. To limit release to 1.5 cfs at that head the opening should be 5.3 inches; a 20,000 ft² pond would take about 15 hours to fall from 4 ft to 0.5 ft through the 6-inch orifice.

Frequently asked questions