Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of fluid above it. It increases with depth.

What Is Hydrostatic Pressure?

When you go deeper into water, you feel more pressure — the weight of all the water above you pushes down. This is hydrostatic pressure.

Pressure acts in all directions at a submerged point. It increases with depth h.

Hydrostatic Pressure

P = \rho \cdot g \cdot h

ρ = density of fluid (kg/m³), g = 9.8 m/s², h = depth (m), P in Pascals (Pa).

Key Facts

Pressure depends only on depth, not on the shape or volume of the container
Pressure acts equally in all directions at any given depth
1 Pascal (Pa) = 1 N/m²

Density of Common Fluids

Fluid	Density
Pure water	1 000 kg/m³
Sea water	1 025 kg/m³
Mercury	13 600 kg/m³

Note The pressure at the bottom of a swimming pool and at the bottom of an ocean of the same depth is the same if the water density is the same.

Find the pressure at a depth of 3 m in fresh water.

$P = 1000 \times 9.8 \times 3 = 29\,400 \text{ Pa} = 29.4 \text{ kPa}$

Real world: Dam wall design

A dam holds back a reservoir of water. The pressure at the base of a 50 m deep reservoir:

$P = 1000 \times 9.8 \times 50 = 490\,000 \text{ Pa} = 490 \text{ kPa}$

This is why dam walls are always built much thicker at the base than at the top — the deeper the water, the greater the outward pressure the wall must withstand.

Real world: Diver's ears at depth

A scuba diver descends to 20 m in the sea (ρ = 1025 kg/m³). The extra water pressure on the diver's eardrums:

$P = 1025 \times 9.8 \times 20 = 200\,900 \text{ Pa} \approx 201 \text{ kPa}$

This is about twice atmospheric pressure pressing on the eardrums. Divers must equalise pressure in their ears by swallowing or pinching their nose, otherwise the pressure difference can rupture the eardrum.

Real world: Water towers

A water tower stores water at height to create pressure in the supply pipes below. Water in a tower at h = 30 m creates a pressure at ground level of:

$P = 1000 \times 9.8 \times 30 = 294\,000 \text{ Pa} = 2.94 \text{ bar}$

This is enough to push water up into a building's taps without a pump — gravity does the work.

Tip Where do you see this in real life? Swimming pool pressure on your ears, dam walls, water towers, submarine hulls, and even the design of deep-sea fish are all shaped by hydrostatic pressure!

Practice Problems

What is the hydrostatic pressure at 10 m depth in sea water (ρ = 1025 kg/m³)?

Show answer

P = 1025 × 9.8 × 10 = 100 450 Pa ≈ 100.5 kPa.

At what depth does fresh water exert a pressure of 49 000 Pa?

Show answer

h = P / (ρg) = 49 000 / (1000 × 9.8) = 5 m.