Tank Fill and Drain Time Calculator

How long does a tank take to drain?

The velocity of water leaving an orifice at the bottom of a tank open to atmosphere follows Torricelli's law: v = √(2 × g × h). As the level falls so does the velocity, which is why the time is not simply volume over a fixed flow rate. For a tank of constant section the result is t = At / (Cd × Ao) × √(2 / g) × (√h1 − √h2), where At is the tank section area, Ao the orifice area, Cd the discharge coefficient and h1, h2 the initial and final water levels measured from the orifice centreline.

Discharge coefficient

Real flow is lower than the theoretical figure because the jet contracts as it leaves the orifice and there is friction. Cd is about 0.61 for a sharp edged orifice and close to 1 for a well rounded nozzle. A pipe or valve on the outlet adds its own loss and lengthens the time further. Enter a measured value where you have one.

Example

A vertical cylindrical tank 2 metres in diameter holds water 3 metres deep above a sharp edged orifice of 50 mm at the bottom. The diameter ratio squared is 1600, and with Cd = 0.61 the time is 2052 seconds, about 34 minutes. The flow starts at 9.2 litres per second and falls with the level. The average flow is half the initial flow.

Fill time

For filling, divide the volume by the net flow: t = V / (Qin − Qout). The same tank fills in 2.36 hours with 5 cubic metres per hour coming in and 1 drawn off.

Limits

The formula covers vertical cylinders and prisms. Horizontal cylinders, conical bottoms, pressurised tanks and siphons are outside this calculation.