Module 2.2.4 Fluid dynamics

Knowledge levels

Item	A	B1	B2 / B2L	B3
2.2.4(a) Specific gravity and density	2	2	2	2
2.2.4(b) Viscosity, fluid resistance, streamlining; compressibility; static, dynamic and total pressure, Bernoulli's theorem, venturi	1	2	2	1

Note that all categories have level 2 for density and specific gravity - expect calculations even in the A paper.

Density and specific gravity

• Density ρ = mass / volume (kg/m³). Water at 4 °C: 1 000 kg/m³ (1 g/cm³, 1 kg/L).
• Specific gravity (relative density) = density of substance / density of water. It has no unit.
• Typical SG: jet fuel about 0.8; avgas about 0.72; mercury 13.6; aluminium 2.7; steel about 7.8.
• Density of liquids falls as temperature rises (they expand), which is why fuel is measured by mass for performance.
• A hydrometer measures SG (e.g. battery electrolyte in lead-acid batteries, about 1.28 fully charged).

Worked example - fuel mass

A tank holds 5 000 L of jet fuel with SG 0.8. What is the fuel mass?

• Density = 0.8 × 1 000 = 800 kg/m³ = 0.8 kg/L
• Mass = 5 000 × 0.8 = 4 000 kg

Trap: dividing by 0.8 (6 250 kg).

Worked example - specific gravity

A 2 L sample of hydraulic fluid has a mass of 1.7 kg. Find SG.

• Density = 1.7 / 2 = 0.85 kg/L → SG = 0.85

Viscosity

• Viscosity is a fluid's resistance to flow (internal friction). Honey is highly viscous; petrol is not.
• Liquids become less viscous when heated; gases become more viscous when heated.
• Oil viscosity grades (e.g. SAE numbers) indicate how thick an oil is at a reference temperature. Viscosity index describes how little viscosity changes with temperature.