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Tank Drain Time Calculator

Estimate how long a cylindrical tank takes to drain through a hole in its base, using Torricelli's law.

Time to drain
11 min
Initial flow rate
6.86 L/min
Average flow rate
3.43 L/min

How it works

Torricelli's law says fluid escaping through a small hole under a head of height h leaves with velocity v = Cd√(2gh), where Cd is a discharge coefficient correcting for real-world orifice losses (an ideal, frictionless hole has Cd = 1; a typical sharp-edged round hole is closer to 0.6). The instantaneous flow rate out of the hole is then Q(h) = Cd × A_orifice × √(2gh).

For a tank with a constant cross-sectional area, the volume draining out must equal the drop in the tank's own volume: A_tank × dh/dt = −Q(h). Solving this differential equation from the starting height h₁ down to a target height h₂ gives a closed form for the drain time: t = 2 × A_tank × (√h₁ − √h₂) ÷ (Cd × A_orifice × √(2g)) — notice it depends on the square root of height, so draining slows down noticeably as the tank empties rather than proceeding at a constant rate.

Both areas are computed from the diameters you enter (A = π × (diameter/2)²), and the discharge coefficient defaults to 0.6, the commonly cited value for a plain sharp-edged circular hole in a thin tank wall.

FAQ

Why does draining slow down near the end instead of finishing at a constant rate?

Because the exit velocity depends on √h — with less water above the hole, there's less pressure pushing it out, so the flow rate drops even though the hole size never changes. This is the same reason a draining sink or bathtub trickles out slowly at the very end rather than stopping abruptly.

What discharge coefficient should I use?

0.6–0.62 is the standard textbook value for a sharp-edged circular orifice in a thin wall, which is what this calculator defaults to. A smoothly rounded, bell-mouthed opening can approach 0.95–0.98 (much closer to the ideal, frictionless 1.0), while a very short tube or an irregular, jagged hole can be lower than 0.6 — if you know a more specific value for your setup, use it instead of the default.

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