Result

Hydrostatic pressure

P = P_{0} + ρ g h

Statement

The pressure at depth h below a surface with pressure P₀, in a fluid of density ρ.

Symbols and units

$P$	pressure at depth h	Pa
$P_{0}$	pressure at the surface	Pa
$ρ$	fluid density	kg/m³
$h$	depth	m
$g$	gravitational acceleration	9.8 m/s²

When it applies

An incompressible fluid in static equilibrium.

Don't use when

Assumes an incompressible fluid in static equilibrium — does not apply to flowing or compressible fluids (e.g. gases over large height changes).

Derivation

Consider a column of fluid of cross-section A and height h; in equilibrium, the pressure difference across it supports the column's weight:

(P - P_{0}) A = ρ A h g

Cancel A:

P = P_{0} + ρ g h

Worked examples

Pressure at 10 m depth in water

P = P_{0} + ρ g h = 1.013 \times 1 0^{5} + (1000) (9.8) (10) \approx 1.99 \times 1 0^{5} Pa

About double atmospheric pressure — depth alone adds roughly 1 atm every 10 m in water.

Watch out for

Pressure depends only on depth, not on the shape or width of the container — a narrow tube and a wide tank at the same depth have the same pressure.