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
| Outlet | Cd |
|---|---|
| Sharp-edged orifice in a thin wall | 0.60 – 0.62 |
| Short square-edged tube (2–3 diameters long) | ≈ 0.80 |
| Re-entrant (Borda) tube, flowing free | ≈ 0.50 |
| Well-rounded bell-mouth entrance | 0.95 – 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.
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