8.2 - Pressure in Liquids

Pressure in a liquid increases with depth and density

• At a point inside a liquid, the pressure comes from the weight of the column of liquid directly above that point.
• In a fluid at rest, the pressure at any point acts equally in all directions.

Pressure increases with depth

• Going deeper means a taller column of liquid sits above the point.
• The extra weight adds to the pressure, so the deeper you go, the higher the pressure.

Pressure increases with density

• A denser liquid has more mass in a given volume, so the column above a point weighs more - creating a higher pressure at the same depth.
• Liquids can be squashed only slightly, so their density is treated as constant throughout.

Formula for the change in pressure with depth

Where:

• $\mathrm{\Delta }p$ = Change in pressure, in pascals (Pa)
• $\rho$ = Density of the liquid, in kilograms per cubic metre (kg/m³)
• $g$ = Gravitational field strength, in newtons per kilogram (N/kg)
• $\mathrm{\Delta }h$ = Change in depth (or height) between the two points, in metres (m)

Worked example - Change in pressure using Δp = ρgΔh

Calculate the change in pressure between a point 42 m below the surface of a lake and a point 12 m below the surface. The density of water is 1,000 kg/m³ and $g$ = 9.8 N/kg.