Tank Drain Time Calculator
Estimate the time for a vertical cylindrical tank to drain by gravity from one level to another through an outlet at the bottom.
- t = Atank ÷ (Cd × Aoutlet) × √(2/g) × (√h₁ − √h₂)
- = 7.069 ÷ (0.61 × 0.001963) × √(2/9.807) × (√4 − √0) = 5,330 s
Tank Drain Time Formula
Outflow q = Cd × Ao × √(2gh)
Atank is the tank cross section, Ao the outlet area, Cd the discharge coefficient (about 0.61 for a sharp edged hole, near 0.97 for a well rounded nozzle), h₁ and h₂ the start and end liquid heights above the outlet and g = 9.80665 m/s². The tank is open to atmosphere.
Worked example
A 3 m diameter tank with 4 m of water draining through a 50 mm sharp edged outlet (Cd 0.61) empties in about 1 h 29 min. The top 2 m drain in only 26 min; the bottom 2 m take the other 63 min, because outflow falls as the level drops.
Frequently Asked Questions
What is Torricelli law?
Liquid leaves an opening at v = √(2gh), the speed of a body falling through the height h. The discharge coefficient corrects for the contraction of the jet.
Does the liquid density matter?
No. For an open tank draining by gravity, density cancels out. Viscosity matters only for very viscous liquids or small outlets.
What if the tank is pressurised?
Add the gas pressure as an equivalent liquid head to h. This calculator assumes an open tank.
Learn more on the blog
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