Pressure and hydrostatics

Pressure: definition and units

Pressure P in a fluid is defined as the normal force per unit area: P = F/S, expressed in pascals (Pa = N/m²). Unlike a force, pressure is a scalar quantity: at a point in a fluid at rest, it is the same in all directions (Pascal’s principle).

The fundamental equation of hydrostatics

For an incompressible fluid of density ρ, at rest in a gravitational field g, the pressure varies with depth h according to:

P = P₀ + ρ * g * h

where P₀ is the pressure at the free surface. This relationship explains why pressure increases with depth in a lake or an ocean, and why it decreases with altitude in the atmosphere.

Practical example

At a depth of 10 m in water (ρ = 1000 kg/m³), the excess pressure due to the weight of the water is: rho * g * h = 1000 * 9.81 * 10 = 98,100 Pa, or approximately 0.98 bar. Adding atmospheric pressure (approximately 1 bar), the total absolute pressure is therefore around 2 bar.

Common pitfall

Do not confuse absolute pressure (measured relative to a vacuum) with relative pressure (measured relative to atmospheric pressure, also known as gauge pressure). A pressure gauge generally displays relative pressure.

Quantity	Symbol	SI unit
Pressure	P	Pa
Density	ρ	kg/m³
Depth	h	m

This principle forms the basis of Archimedes’ principle and of hydraulic systems (cylinders, hydraulic presses) which utilise the complete transmission of pressure within a confined fluid.