Density, Specific Weight and Specific Gravity

An introduction and definition of density, specific weight and specific gravity - formulas with examples

Density

Density is defined as mass per unit volume. Mass is a property.

Density can be expressed as

ρ = m / V = 1 / vg         (1)

where

ρ = density (kg/m3, slugs/ft3)

m = mass (kg, slugs)

V = volume (m3, ft3)

vg = specific volume (m3/kg, ft3/slug)

The SI units for density are kg/m3. The Imperial (U.S.) units are slugs/ft3.

Pounds per cubic foot - lb/ft3 - is often used as a measure of density in the US, but pounds are really a measure of force, not mass. Slugs are the correct measure of mass. You can multiply slugs by 32.2 for a rough value in pounds (lbm).

On atomic level - particles are packed tighter inside a substance with higher density. Density is a physical property - constant at a given temperature and pressure - and may helpful for identification of substances.

Example - Density of a Golf ball

A golf ball has a diameter of 42 mm and a mass of 45 g. The volume of the golf ball can be calculated as

V = (4 / 3) π ((42 mm) (0.001 m/mm) / 2)3

   = 3.8 10-5 m3

The density of the golf ball can then be calculated as

ρ = (45 g) (0.001 kg/g) / (3.8 10-5 m3)

   = 1184 kg/m3

Example - Density to Identify a Material

An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml (milliliter).

The density of the substance can be calculated as

ρ = [(18.5 g) / (1000 g/kg)] / [(23.4 ml) / (1000 ml/l) (1000 l/m3)]

    = (18.5 10-3 kg) / (23.4 10-6 m3)

    = 790 (kg/m3)

If we look up densities of some common liquids, we find that ethyl alcohol - or ethanol - has a density of 789 kg/m3. The liquid may be ethyl alcohol!

Example - Density to Calculate Volume Mass

The density of titanium is 4507 kg/m3. The mass of 0.17 m3 volume titanium can be calculated as

m = (0.17 m3) (4507 kg/m3)

    = 766.2 (kg)

Specific Weight

Specific Weight is defined as weight per unit volume. Weight is a force.

Specific Weight can be expressed as

γ = ρ g         (2)

where

γ = specific weight (N/m3, lb/ft3)

ρ = density (kg/m3, slugs/ft3)

g = acceleration of gravity (9.807 m/s2, 32.174 ft/s2)

The SI units for specific weight are N/m3. The imperial units are lb/ft3.

Local acceleration g is (under normal conditions) 9.807 m/s2 in SI units and 32.174 ft/s2 in imperial units.

Example - Specific Weight Water

The density of water is 1000 kg/m3 at 4 oC (39 oF). The specific weight in SI units is

γ = (1000 kg/m3) (9.81 m/s2)

    = 9810 (N/m3)

    = 9.81 (kN/m3)

The density of water is 1.940 slugs/ft3 at 39 oF (4 oC). The specific weight in Imperial units is

γ = (1.940 slugs/ft3) (32.174 ft/s2)

    = 62.4 (lb/ft3)

Specific Weight for Some common Materials

ProductSpecific Weight
- γ -
Imperial Units
(lb/ft3)
SI Units
(kN/m3)
Aluminum 172 27
Brass 540 84.5
Copper 570 89
Ethyl Alcohol 49.3 7.74
Gasoline 42.5 6.67
Glycerin 78.6 12.4
Mercury 847 133.7
SAE 20 Oil 57 8.95
Seawater 64 10.1
Stainless Steel 499 - 512 78 - 80
Water 62.4 9.81
Wrought Iron 474 - 499 74 - 78

Specific Gravity  (Relative Density)

Specific Gravity - SG - is a dimensionless unit defined as the ratio of the density of a substance to the density of water - at a specified temperature, and can be expressed as

SG = ρsubstance / ρH2O         (3)

where

SG = Specific Gravity of the substance

ρsubstance = density of the fluid or substance (kg/m3)

ρH2O = density of water - normally at temperature 4 oC (kg/m3)

It is common to use the density of water at 4 oC (39oF) as a reference since water at this point has its highest density of 1000 kg/m3 or 62.4 lb/ft3.

Specific Gravity - SG -  is dimensionless and has the same value in the SI system and the imperial English system (BG). Water is normally also used as reference when calculating the specific gravity for solids.

  • Thermal Properties of Water - Density, Freezing temperature, Boiling temperature, Latent heat of melting, Latent heat of evaporation, Critical temperature ...

Specific Gravities for some common Materials

SubstanceSpecific Gravity
- SG -
Acetylene 0.0017
Air, dry 0.0013
Alcohol 0.82
Aluminum 2.72
Brass 8.48
Cadmium 8.57
Chromium 7.03
Copper 8.79
Carbon dioxide 0.00198
Carbon monoxide 0.00126
Cast iron 7.20
Hydrogen 0.00009
Lead 11.35
Mercury 13.59
Nickel 8.73
Nitrogen 0.00125
Nylon 1.12
Oxygen 0.00143
Paraffin 0.80
Petrol 0.72
PVC 1.36
Rubber 0.96
Steel 7.82
Tin 7.28
Zinc 7.12
Water (4oC) 1.00
Water, sea 1.02

Example - Specific Gravity of Iron

The density of iron is 7850 kg/m3. The specific gravity of iron related to water with density 1000 kg/m3 is

SG = (7850 kg/m3) / (1000 kg/m3)

    = 7.85

Specific Gravities of Gases

The Specific Gravity of a gas is normally calculated with reference to air - and defined as the ratio of the density of the gas to the density of the air - at a specified temperature and pressure.

Specific Gravity can be calculated as

SG = ρgas / ρair         (3)

where

SG = specific gravity of gas

ρgas = density of gas (kg/m3)

ρair = density of air (normally at NTP - 1.205 kg/m3)

Molecular weights can be used to calculate the Specific Gravity if the densities of the gas and the air are evaluated at the same pressure and temperature.

Related Topics

  • Basics - Basic Information as SI-system, Unit converters, Physical constants
  • Fluid Mechanics - The study of fluids - liquids and gases. Involves various properties of the fluid, such as velocity, pressure, density and temperature, as functions of space and time.
  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
  • Beams and Columns - Deflection and stress, moment of inertia, section modulus and technical information of beams and columns
  • Material Properties - Material properties - density, heat capacity, viscosity and more - for gases, fluids and solids
  • Statics - Loads - force and torque

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