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Hydrostatic pressure

The pressure in a fluid at rest increases with depth, because every column of fluid must support the weight of everything above it. The gauge pressure depends only on density, gravitational acceleration and depth, not on the container's shape or total volume – this is the hydrostatic paradox.

p = p_0 + \rho gh

hydrostatic pressure, absolute

p_{abs} = p_{atm} + p_{gauge}

absolute pressure from gauge pressure

Symbols

$\rho$	density	kg/m³
$h$	depth	m
$p_{atm}$	atmospheric pressure	$\approx 101.3 kPa$

Example

A dam holds water $h = 12$ m deep. The gauge pressure at the bottom is $\rho gh = 1000\cdot 9.81\cdot 12 \approx 117.7$ kPa.

The pressure depends only on the depth – a narrow and a wide tank with the same depth have the same pressure at the bottom.

Practise hydrostatics for free →

Archimedes' principle →

Part of Fluid Mechanics: Hydrostatics.