Mechanical Properties of Fluids

Complete revision notes

1. Introduction

A fluid flows and cannot sustain static shear stress. Density is ρ=m/V; relative density compares a substance's density to a reference.

2. Pressure

Pressure is normal force per area. In a stationary fluid at depth h, p=p₀+ρgh. At equal depth, connected fluid pressure is equal irrespective of vessel shape.

3. Streamline flow

Streamline flow is smooth; steady flow means velocity at a point does not vary with time. For steady incompressible flow A₁v₁=A₂v₂. Turbulence is more likely at high Reynolds number.

4. Bernoulli's principle

Bernoulli's relation p+½ρv²+ρgh=constant applies to steady, incompressible, non-viscous flow along a streamline. At comparable height, faster flow has lower static pressure under these assumptions.

5. Viscosity

Viscosity describes internal resistance between fluid layers. Stokes' drag on a small sphere in slow laminar flow is 6πηrv; terminal speed occurs when drag balances effective weight.

6. Surface tension

Surface tension is force per length or energy per area. Excess pressure is 2S/r for a liquid drop and 4S/r for a soap bubble because it has two surfaces.

Formula sheet

Use SI units, state assumptions and directions before substitution, show working and round only the final result.

Worked example

Common errors and exam checklist

Distinguish absolute from gauge pressure; Bernoulli has assumptions; a soap bubble has two surfaces unlike a liquid drop.

• Write the relevant law before substituting values.
• Show steps, units and signs/directions.
• Check that the final answer is physically reasonable.