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Tank Drain Time Calculator

Time to empty — or lower to any level — a vertical cylindrical or rectangular tank draining by gravity through a bottom orifice, from Torricelli's law with a discharge coefficient. Also reports the initial flow rate and the volume released.

ft
ft
ft
in
—
ft
ft
—ft²
—ft³/s
—gpm
—min
—hours
—gal

Heads are measured from the orifice centreline to the water surface. Set h₂ = 0 to empty the tank. The orifice should be small relative to the tank for the quasi-steady assumption to hold.

$$ Q = C_d\,a\,\sqrt{2 g h} \qquad t = \frac{2A}{C_d\,a\,\sqrt{2g}}\left(\sqrt{h_1} - \sqrt{h_2}\right) $$
A tank plan area · a orifice area · Cd discharge coefficient · h head above the orifice · g = 32.174 ft/s² or 9.80665 m/s². Integrated from A·dh/dt = −Cd·a·√(2gh).

Discharge coefficients for tank outlets

Typical Cd for small outlets under free discharge
OutletCd
Sharp-edged orifice in a thin wall0.60 – 0.62
Short square-edged tube (2–3 diameters long)≈ 0.80
Re-entrant (Borda) tube, flowing free≈ 0.50
Well-rounded bell-mouth entrance0.95 – 0.98

Typical textbook ranges. Coefficients vary with Reynolds number and edge condition; use a calibrated value where accuracy matters.

Worked examples

Example 1 — Emptying a vertical storage tank

Given: D = 10 ft, h₁ = 12 ft, h₂ = 0, 2-in sharp-edged outlet, Cd = 0.61.
A = π × 10² / 4 = 78.54 ft²; a = π × (2/12)² / 4 = 0.02182 ft²
Q₀ = 0.61 × 0.02182 × √(2 × 32.174 × 12) = 0.3698 ft³/s = 166 gpm
t = 2 × 78.54 × √12 / (0.61 × 0.02182 × √64.348) = 5,097 s
t = 85.0 min (1.42 h) to release 7,050 gal

Example 2 — The first half is the fast half

Same tank, drained only from 12 ft to 6 ft.
t = 5,097 s × (√12 − √6) / √12 = 1,493 s
24.9 min for the top 6 ft; the remaining 6 ft takes 60.1 min

Example 3 — Rectangular basin (SI)

Given: 4 m × 3 m basin, h₁ = 2.0 m, h₂ = 0.5 m, 50-mm orifice, Cd = 0.61.
A = 12 m²; a = 1.963×10⁻³ m²
t = 2 × 12 × (√2 − √0.5) / (0.61 × 1.963×10⁻³ × √19.613) = 3,199 s = 53.3 min

References: Brater, E.F., King, H.W., Lindell, J.E., Wei, C.Y. (1996). Handbook of Hydraulics, 7th ed., McGraw-Hill. Streeter, V.L., Wylie, E.B. (1985). Fluid Mechanics, 8th ed.

Common mistakes

When this calculator doesn’t apply

This is Torricelli’s law integrated for free discharge through a small outlet, with constant Cd and no inflow. Tanks with inflow need level-pool routing. Very low heads, viscous liquids and outlets that vortex or draw air at the end of draining all slow the last part of the drawdown. For detention ponds with multi-stage outlets, use a reservoir routing calculation.

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