Tank Drain Time Calculator
Time to drain a round or rectangular tank by gravity through an orifice (Torricelli), with your discharge coefficient, the initial outflow and a profile.
How long a tank takes to empty, or to fall to a given level, with the outflow at every stage — from the orifice equation and a coefficient you supply, not a rule of thumb.
Example: A 2 m diameter tank with 3 m of liquid over a 50 mm orifice (Cd 0.62) drains in 33.6 minutes; the outflow starts at 33.6 m³/h and the first half of the height takes only 9.9 minutes.
The outflow slows
as the level falls.
Torricelli's law, what the discharge coefficient stands for, and which tanks this page can and cannot handle.
Torricelli's law
Liquid leaves an orifice at the speed it would reach falling freely through the head above it: v = √(2gh). The outflow is that speed times the orifice area, reduced by the discharge coefficient: Q = Cd × A × √(2gh). Because the flow falls with the square root of the head, a tank does not drain at a steady rate — the first half of the height goes in far less than half the time, which the profile table shows step by step.
Drain time
For a tank whose cross-section does not change with height (a vertical cylinder or a box), the level equation integrates exactly: t = (A_tank ÷ (Cd × A_orifice)) × √(2/g) × (√h₁ − √h₂). Set the end head to zero for a full drain or to a level to find the time to reach it. Heads are measured from the orifice centreline to the liquid surface.
The discharge coefficient is yours
Cd accounts for the jet contracting after a sharp edge and for friction; it depends on the orifice shape, edge, size and on what is attached (a short pipe, a valve, a nozzle). The 0.62 shown at first is a labelled sample for a sharp-edged round orifice as given in the cited textbook, not a general value: take yours from the orifice or valve manufacturer or from a measured flow. A coefficient of 1 is the frictionless ideal and is flagged. The page also warns when the orifice exceeds 1 % of the tank area, where the simple law starts to overstate the flow.
Out of scope
Horizontal cylinders, cones, spheres and tanks with sloped floors have an area that changes with height and need a numerical integration; pressurised or vented-poorly tanks, viscous liquids where the orifice Reynolds number is low, and long drain lines with their own friction are also outside this page. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Çengel, Y. A. & Cimbala, J. M., Fluid Mechanics: Fundamentals and Applications — §5-4 Bernoulli equation, Torricelli’s law and discharge coefficients (Example 5-11, draining a tank)
Last reviewed 19 September 2026. How results are checked: How we verify.