Pressure in a liquid at rest

The fundamental law of fluid statics

In a liquid at rest, pressure increases with depth. The fundamental law of hydrostatics is written:

P = P0 + rho * g * h

where:

• P0 is the pressure at the surface of the liquid (often atmospheric pressure)
• rho is the density of the liquid, in kg/m^3
• g is the acceleration of gravity (g ~ 9.8 m/s^2)
• h is the depth considered, in meters

Example: scuba diving

For water (rho = 1000 kg/m^3), each 10 m layer of depth adds about 1 bar (100,000 Pa) of pressure. A diver at 20 m therefore experiences a total pressure of about 3 bar: 1 atmospheric bar + 2 bar due to the water.

The hydrostatic paradox

A classic pitfall is believing that the pressure at the bottom of a container depends on its shape or the volume of liquid it contains. In reality, P depends only on the depth h, rho, and g: a thin tube and a wide basin, filled with the same liquid to the same height, have exactly the same pressure at the bottom.

Depth h	Pressure due to water (rho = 1000)
0 m	0 Pa
10 m	100,000 Pa
20 m	200,000 Pa

Don't forget to add P0 if the problem asks for it!