Pressure in Liquids

The pressure at a depth in a liquid is caused by the weight of the liquid above pressing down.

The pressure difference between two depths:

p = ρ g h

with pressure in pascals, density in kg/m³, g the gravitational field strength (10 N/kg) and h the vertical depth in metres.

Three things that follow from this equation, and one that does not appear in it:

• Pressure increases with depth — twice as deep is twice the pressure from the liquid.
• Pressure increases with the density of the liquid. Mercury produces far more pressure than water at the same depth.
• Pressure depends on the vertical depth, not the distance along a slope.
• Pressure does not depend on the shape or width of the container. A narrow tube and a wide tank of the same depth have the same pressure at the bottom. This surprises people, and it is a favourite examination point.

Pressure in a liquid acts in all directions — not merely downwards. This is why a hole in the side of a container squirts water sideways, and why a diver feels pressure equally on every part of their body.

Why a dam is thicker at the base. Pressure rises with depth, so the water pushes hardest at the bottom. The wall must be thickest where the force per unit area is greatest.

Total pressure. At a depth h beneath the surface of an open liquid, the total pressure is the atmospheric pressure pushing down on the surface plus ρgh from the liquid itself. Questions usually ask only for the pressure due to the liquid, but read carefully — if a question says "total pressure" the atmospheric term must be added.

Example: at 20 m down in seawater of density 1030 kg/m³, the pressure from the water is ρgh = 1030 × 10 × 20 = 206 000 Pa. Adding atmospheric pressure of about 100 000 Pa gives a total of around 306 000 Pa — roughly three times what a diver experiences at the surface.