Fluids and pressure

Liquids and gases can flow, so both are called fluids. Flowing is the basic property that separates them from solids.

A fluid has no shape of its own. A solid or a liquid keeps a fixed volume (at atmospheric pressure), while a gas spreads to fill whatever container holds it.

Solids and liquids have far lower compressibility than gases: a change of outside pressure alters their volume only slightly.

Fluids resist shear stress very weakly: a tiny shear stress changes their shape. Their shearing stress is roughly a million times smaller than that of solids.

The same force does more damage when it is spread over a smaller area: a needle pierces skin, the back of a spoon does not. A wide plank on a performer's chest protects him from an elephant's foot.

A fluid at rest pushes on any surface in contact with it at right angles to that surface. A parallel component would, by Newton's third law, make the fluid flow along the surface, which a fluid at rest cannot do.

Average pressure P_av = F/A, with F the normal force on area A. Taking the area to zero gives the pressure at a point: P = lim (ΔF/ΔA) as ΔA → 0.

Pressure is a scalar: only the normal component of force appears in its definition. Dimensions [ML⁻¹T⁻²]; SI unit N m⁻², named the pascal (Pa) after Blaise Pascal.

1 atm is the pressure of the atmosphere at sea level: 1 atm = 1.013 × 10⁵ Pa.

Density ρ = m/V, dimensions [ML⁻³], unit kg m⁻³, a positive scalar. A liquid's density hardly changes with pressure; a gas's density changes a great deal.

Water at 4 °C (277 K) has density 1.0 × 10³ kg m⁻³. Relative density = density ÷ density of water at 4 °C, a pure number. Aluminium: relative density 2.7, so ρ = 2.7 × 10³ kg m⁻³.

Two thighbones, each 10 cm² in cross-section, holding up 40 kg of upper body (g = 10 m s⁻²): A = 20 × 10⁻⁴ m², F = 400 N, so the average pressure is 2 × 10⁵ N m⁻².