Tank Drain Time (Falling-Head Orifice)
How long a tank takes to empty through an orifice, integrating the falling head the steady orifice tile leaves out: t = 2 A_t (sqrt(h1) - sqrt(h2)) / (Cd A_o sqrt(2 g)) for a constant-cross-section tank. A 100 ft^2 tank draining a 6 in orifice empties from 9 ft in 10.6 min, but reaches the last foot in only 7.1 - the flow slows as sqrt(h), so the final foot alone takes another 3.5 minutes. Prismatic tank, free discharge, steady Cd (~0.6). A design aid; the engineer of record governs.
Formula and source
A_o = pi/4 (d/12)^2; t = 2 A_t (sqrt(h1) - sqrt(h2)) / (Cd A_o sqrt(2 g)), g = 32.2 ft/s^2.
The falling-head (Torricelli) tank drain-time integral of the orifice equation, a standard hydraulics result, by name.
Audience
This tile is built for plumbers and the adjacent professions in the Plumbing and Gas group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.