6.1 Density & Specific Gravity

Density & Specific Gravity

Fluid dynamics builds on the static fluid ideas of pressure and buoyancy by asking how much mass occupies a given volume and how that mass behaves when the fluid moves. Density and specific gravity (relative density) are the bookkeeping tools for fuel loads, hydraulic oil mass, and any calculation that converts tank volume into mass or weight. Module 2 expects the SI definitions, the water reference, and straightforward aviation-style calculations without a calculator.

Density: Mass per Unit Volume

Density (symbol ρ, Greek rho) is defined as:

ρ = m / V

• m = mass (kilograms, kg)
• V = volume (cubic metres, m³)
• ρ = density (kilograms per cubic metre, kg/m³)

Rearrangements you will use constantly:

• m = ρ V
• V = m / ρ

Density is an intensive property of a material at a stated temperature and pressure: a litre of pure water has the same density whether it sits in a cup or a tank. Compressing a gas increases its density; heating a liquid usually expands it slightly and lowers density. For Module 2 liquids at ordinary temperatures, treat density as constant unless the question mentions temperature change.

SI and practical units

The coherent SI unit is kg/m³. You will also meet g/cm³ and kg/L (kilograms per litre). Useful identities:

• 1 g/cm³ = 1000 kg/m³
• 1 kg/L = 1000 kg/m³ (because 1 L = 0.001 m³)
• Pure water near 4 °C has density ≈ 1000 kg/m³ = 1 g/cm³ = 1 kg/L

Convert carefully. A tank volume of 2000 L is 2000 × 0.001 = 2 m³. Fuel density of 0.80 g/cm³ is 800 kg/m³.

Typical aviation densities (order of magnitude)

Exam questions often use rounded values (water 1000 kg/m³, fuel 800 kg/m³) so arithmetic stays clean.

Specific Gravity and Relative Density

Specific gravity (SG) — also called relative density (RD) — is the ratio of a substance’s density to the density of a reference substance under stated conditions:

SG = ρ_substance / ρ_reference

For liquids and solids, the reference is almost always water (ρ_water ≈ 1000 kg/m³). Then:

SG ≈ ρ (in kg/m³) / 1000

or equivalently SG = density in g/cm³ numerically.

Examples:

• Fuel with ρ = 800 kg/m³ → SG = 0.80
• Sea water ≈ 1025 kg/m³ → SG ≈ 1.025
• Mercury ≈ 13 600 kg/m³ → SG ≈ 13.6

SG is dimensionless (a pure number). Saying “SG is 0.8 kg/m³” is wrong — units belong to density, not specific gravity.

For gases, relative density is often referenced to air at the same temperature and pressure (e.g. hydrogen is much less dense than air). Module 2 liquid/fuel work almost always uses the water reference.

Why SG is useful

SG lets you compare fuels and oils without repeating full SI density each time. If SG of fuel is 0.78, mass of volume V is m = 0.78 × 1000 × V = 780 V (with V in m³, m in kg). Load sheets, hydrometer scales, and many manuals quote SG or density in kg/L interchangeably for liquids near the water scale.

Weight of a Fluid Volume

Mass and weight are not the same. Weight is the gravitational force on the mass:

W = m g = ρ V g

• W in newtons (N) when m is in kg and g ≈ 9.81 m/s²
• On Earth, “weight in kg” in casual speech often means mass; exam physics uses newtons for weight/force

Worked example — fuel mass and weight. A wing tank holds 1.5 m³ of jet fuel with density 800 kg/m³.

• Mass m = ρ V = 800 × 1.5 = 1200 kg
• Weight W = m g = 1200 × 9.81 = 11 772 N (≈ 11.8 kN)

If the same tank is filled with water instead: m = 1000 × 1.5 = 1500 kg; W = 14 715 N. The denser fluid loads structure more for the same full-volume fill.

Worked example — from litres and SG. Fuel uplift 2500 L; SG = 0.79; g = 9.81 m/s².

V = 2500 L = 2.5 m³
ρ = 0.79 × 1000 = 790 kg/m³
m = 790 × 2.5 = 1975 kg
W = 1975 × 9.81 ≈ 19 375 N

These numbers feed mass and balance: fuel mass (and its station) changes aircraft total mass and centre of gravity as fuel is burned or uplifted.

Temperature, Fuel Grade, and Density Variation

Liquid density falls as temperature rises (thermal expansion). Cold winter fuel can be measurably denser than the same fuel grade on a hot ramp. A tank that is “full” by volume can therefore contain more mass when the fuel is cold than when it is warm. Operators and fuelers use density (or SG) measured or tabulated at the uplift temperature to convert volume to mass for accurate loading.

Different grades (Jet A-1 vs avgas, etc.) have different nominal density bands. Never assume “fuel = 0.8” blindly if the question states a different SG; always use the given density.

Density, Pressure, and Buoyancy Links

You already used density in statics:

• Hydrostatic pressure: p = ρ g h
• Buoyant force: F_b = ρ_fluid V_displaced g

Higher fluid density at the same depth means higher pressure and stronger buoyancy. Fuel denser than air-displaced space in a tank contributes more hydrostatic head at the bottom fittings. These relations reuse the same ρ from this section.

Density altitude (awareness only)

Density altitude is the altitude in the standard atmosphere at which the actual air density would occur. Hot, high, and humid conditions reduce air density, degrading engine and aerodynamic performance. Conceptually it is still ρ = m/V for air, but performance tables and Module 8 aerodynamics develop the operational use. For Module 2, know that air density is far smaller than liquid density (~1.225 kg/m³ vs ~1000 kg/m³ for water) and that density appears in both fluid statics and later fluid-flow formulas.

Measurement Awareness

• Hydrometer: a weighted float that sinks to a depth depending on liquid density/SG; scale read at the liquid surface (temperature correction may apply).
• Densitometer / density meter: instruments used in fuel quality and uplift contexts to obtain density for mass calculation.
• Known volume + weighed mass: laboratory density from m/V directly.

For the exam, the definition and the calculation chain volume → mass → weight matter more than instrument brand names.

Formula Recap

• ρ = m / V (kg/m³)
• SG = ρ_substance / ρ_water (dimensionless; water ≈ 1000 kg/m³)
• m = ρ V; W = ρ V g
• 1 L = 0.001 m³; 1 g/cm³ = 1000 kg/m³

Keep water as the liquid reference, convert volumes to m³ before SI density arithmetic, and treat fuel density as a measured or given input for mass-and-balance and hydrostatic work.