Torricelli's theorem

Intermediate

Speed of efflux from a tank depends on depth.

Key relationv = √(2gh)

Speed of liquid leaving a hole at depth h below the surface is v = √(2gh), the same as free fall through h.

Worked example

Hole 1.25 m below the surface: 5 m/s.

Common mistake

Range of a jet is maximum at mid-depth.

In more detail

Torricelli's theorem gives the speed of fluid flowing out of a hole in a tank, v = sqrt(2gh), where h is the depth of the hole below the surface.

Estimating how fast water leaves a tank or dam through an outlet.
Designing drainage and outlet structures.
A water tank's outlet pipe delivers water faster when the tank is full, which is a direct use of Torricelli's theorem.

Does the hole size affect the speed?

No. The speed depends only on depth, though the flow rate depends on the area.

Is it the same as free fall?

Yes, the result matches the speed of an object dropped through the same height.

Why does the flow slow down as the tank empties?

The water depth falls, which reduces the pressure at the outlet and the speed of the efflux.