# Draining a Tank

on . Posted in Fluid Dynamics

These formulas for draining a tank assumes ideal conditions and doesn't account for factors like friction losses, turbulence, or changes in pressure over time as the tank drains.  Depending on the specifics of your tank and the fluid being drained, more complex formulas might be needed to provide a more accurate estimate.

The time it takes to drain a tank depends on several factors such as the volume of the tank, the size of the outlet (orifice) through which the liquid is draining, and the height of the liquid in the tank.

### Time it takes to Drain a Tank formula

$$t \;=\; ( A_1 \;/\; A_2 ) \; \sqrt{ 2 \; h_0 \;/\; g }$$
Symbol English Metric
$$t$$ = time to drain a tank $$min$$ $$min$$
$$A_1$$ = tank area cross-section $$ft^2$$ $$m^2$$
$$A_2$$ = area of outlet $$ft^2$$ $$m^2$$
$$h_0$$ = height of liquid in tank $$ft$$ $$m$$
$$g$$ = gravitational acceleration $$ft \;/\; sec^2$$ $$m \;/\; s^2$$

### Velocity to Drain a Tank formula

$$v_2 \;=\; \sqrt{ 2 \; g \; h_0}$$
Symbol English Metric
$$v_2$$ = velocity to draiin a tank $$ft \;/\; sec$$ $$m \;/\; s$$
$$g$$ = gravitational acceleration $$ft \;/\; sec^2$$ $$m \;/\; s^2$$
$$h_0$$ = height of liquid in tank $$ft$$ $$m$$