Tank Drain Time Calculator
Calculate how long it takes to drain a tank from one liquid level to another through a bottom orifice. Ideal for sizing drain valves, planning tank cleanouts, or verifying emergency drainage rates.
About this calculator
Torricelli's law states that the velocity of fluid exiting an orifice at the bottom of a tank is v = √(2gh), where h is the current fluid height above the orifice and g = 9.81 m/s². Because the head h decreases as the tank empties, the drain rate slows continuously — making this a differential equation problem. Integrating over the height change from h₁ to h₂ gives the total drain time: t = (A_tank / (C_d × A_orifice)) × (√(2/g)) × (√h₁ − √h₂). Here A_tank is the tank cross-sectional area, A_orifice is the orifice area, and C_d is the discharge coefficient (typically 0.6–0.65 for a sharp-edged orifice), which accounts for flow contraction and real-world losses. A larger orifice or smaller tank drains faster; a lower starting head means slower initial flow.
How to use
A cylindrical tank has a cross-section of 2 m², draining through an orifice of 0.005 m² (C_d = 0.62) from an initial height of 3 m down to 0.5 m. Plug into the formula: t = (2 / (0.62 × 0.005)) × (2 / √(2 × 9.81)) × (√3 − √0.5). Calculate each part: A_tank/(C_d×A_orifice) = 2/0.0031 = 645.2; 2/√19.62 = 0.4515; √3 − √0.5 = 1.732 − 0.707 = 1.025. So t = 645.2 × 0.4515 × 1.025 ≈ 298 seconds, or about 5 minutes.
Frequently asked questions
What is the discharge coefficient and what value should I use for my tank drain?
The discharge coefficient (C_d) accounts for the fact that real fluid jets contract and experience friction losses as they pass through an orifice, so the actual flow is less than the theoretical maximum. For a sharp-edged circular orifice, C_d ≈ 0.61 is the standard engineering value. Rounded or well-contoured orifices can have C_d up to 0.98, while very rough or irregular openings may be as low as 0.50. When in doubt, use 0.61 for a drilled hole and 0.80–0.90 for a short nozzle. Using a higher C_d than the true value will underestimate drain time, which can be dangerous in safety-critical applications.
Why does a tank drain slower as the water level drops?
As the liquid level falls, the hydrostatic pressure driving the flow through the orifice decreases proportionally. Since exit velocity is proportional to the square root of head (v = √(2gh)), the flow rate continuously decreases as the tank empties. This non-linear relationship means the last fraction of liquid takes disproportionately longer to drain than the first fraction. That is why drain time calculations require integration over the full height range rather than a simple division of volume by an average flow rate.
How do I calculate the orifice area if I only know the drain pipe diameter?
The orifice area is simply the cross-sectional area of the circular opening: A = π × (d/2)², where d is the internal diameter of the drain hole or pipe in metres. For example, a 50 mm (0.05 m) diameter drain gives A = π × (0.025)² ≈ 0.00196 m². If the drain is a pipe rather than a thin-plate orifice, additional pipe friction losses apply and the simple Torricelli model becomes less accurate. In that case, a combined orifice-and-pipe friction analysis, or using C_d values calibrated for pipe inlets, will give more accurate results.