Mechanical Properties of Fluids
Fluids—liquids and gases—flow and deform easily, fundamentally different from rigid solids. Yet physics governs their behavior just as rigorously.
Start with the simplest version: this lesson is about Mechanical Properties of Fluids. If you can explain the core idea to a friend using everyday language, examples, and one clear reason why it matters, you have moved from memorising to understanding.
Fluids—liquids and gases—flow and deform easily, fundamentally different from rigid solids. Yet physics governs their behavior just as rigorously. Pressure in a fluid distributes force; streamlines reveal flow patterns; Bernoulli's principle connects pressure and velocity in startling ways. Understanding fluid mechanics explains why ships float, how planes fly, and why water flows from a tap.
Pressure in Fluids
Pressure P = F/A acts perpendicular to surfaces; SI unit pascal (1 Pa = 1 N/m²). At depth h below the surface of a liquid of density ρ, the pressure is P = P₀ + ρgh. Atmospheric pressure ≈ 1.013 × 10⁵ Pa = 760 mm of Hg.
Pascal's Principle
An external pressure applied to an enclosed incompressible fluid is transmitted undiminished to every part of the fluid and the walls of the container. This powers hydraulic lifts: a small force F₁ on a small piston of area A₁ produces F₂ = F₁ (A₂/A₁) on the large piston.
Archimedes' Principle and Buoyancy
A body partly or wholly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced: F_B = ρ_fluid V_displaced g. Floating equilibrium: weight of displaced fluid equals weight of the body. Apparent weight in fluid = true weight − buoyant force.
Continuity Equation
For steady incompressible flow, mass conservation gives A v = constant along a streamline. Where the pipe narrows, the speed increases.
Bernoulli's Principle
Along a streamline of an ideal incompressible fluid in steady flow: P + ½ρv² + ρgh = constant. Where speed is high, static pressure is low — explains aerofoil lift, the Venturi meter, and Torricelli's law for the speed of efflux: v = √(2gh).
Viscosity
For laminar flow, the viscous force between layers is F = ηA (dv/dz), where η is the coefficient of viscosity (SI unit: Pa·s). For a sphere of radius r moving slowly with velocity v through a fluid: Stokes' law F = 6πηrv. Terminal velocity: v_t = (2/9) r²(ρ − σ)g/η.
Reynolds Number
Re = ρ v D / η classifies flow: Re ≲ 1000 is laminar; Re ≳ 2000 becomes turbulent. Above the critical Reynolds number, smooth flow gives way to chaotic eddies.
Surface Tension and Capillarity
Surface tension T (N/m) is the force per unit length acting in the surface of a liquid. Excess pressure inside a spherical drop = 2T/R; inside a soap bubble (two surfaces) = 4T/R. Capillary rise h = 2T cos θ /(ρ g r), where θ is the contact angle and r the tube radius.
Socratic Questions
- Why does pressure increase with depth in a liquid, but the gas pressure in a closed container is essentially the same at all heights?
- A ship made of dense steel floats while a steel ball sinks. How is Archimedes' principle consistent with both?
- Use Bernoulli's principle to explain why a spinning cricket ball can swing in mid-air.
- Why does the viscosity of liquids decrease with temperature while the viscosity of gases increases?
- Why does a small water drop tend to be spherical, while large drops flatten under gravity?