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 an objects mass per unit volume. Mass is a property.

The 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 lb/ft3 (slugs/ft3). While people often use pounds per cubic foot as a measure of density in the U.S., 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.

The higher the density, the tighter the particles are packed inside the substance. Density is a physical
property constant at a given temperature and density can help to identify a substance.

Relative Density (Specific Gravity)

SubstanceRelative Density
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 - 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 be calculated as

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

   = 1184 kg/m3

Example - Use the Density to Identify the Material:

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

The density 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 can find that ethyl alcohol, or ethanol, has a density of 789 kg/m3. The liquid may be ethyl alcohol!

Example - Use Density to Calculate the Mass of a Volume

The density of titanium is 4507 kg/m3. Calculate the mass of 0.17 m3 titanium!

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 (9.81 m/s2, 32.174 ft/s2)

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

Specific weight for water at 39 oF (4 oC) is 62.4 lb/ft3 (9.81 kN/m3) in imperial units.

With a density of water 1000 kg/m3 - specific weight in SI units can be calculated as

γ = (1000 kg/m3) (9.81 m/s2)

    = 9810 (N/m3)

    = 9.81 (kN/m3)

With a density of water 1.940 slugs/ft3 - specific weight in SI units can be calculated as

γ = (1.940 slugs/ft3) (32.174 ft/s2)

    = 62.4 (lb/ft3)

Example - Specific Weight Some other Materials

ProductSpecific Weight - γ
Imperial Units
(lb/ft3)
SI Units
(kN/m3)
Aluminium 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)

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

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 reference since at this point the density of water is at the highest - 1000 kg/m3 or 62.4 lb/ft3.

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

Since Specific Weight is dimensionless it has the same value in the metric SI system as in the imperial English system (BG). At the reference point the Specific Gravity has same numerically value as density.

It is common to use relate specific gravity for both liquids and solids to water.

Example - Specific Gravity

If the density of iron is 7850 kg/m3, 7.85 grams per cubic centimeter (cm3), 7.85 kilograms per liter, or 7.85 metric tons per cubic meter - the specific gravity of iron related to water is

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

    = 7.85

  • water density is 1000 kg/m3

Specific Gravity Gases

The Specific Gravity - SG - of gases relates to air and is a dimensionless unit defined as the ratio of density of the gas to the density of air at a specified temperature and pressure. In general conditions according NTP - Normal Temperature and Pressure - defined as air at 20oC (293.15 K, 68oF) and 1 atm ( 101.325 kN/m2, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr), where density of air is 1.205 kg/m3 - is used. 

Specific Gravity of a gas can be calculated as

SG = ρgas / ρair         (3)

where

SG = specific gravity of gas

ρgas = density of gas (kg/m3)

ρair = density of air (kg/m3)

Note that when the densities of the gas and the air are evaluated at the same pressure and temperature - the SG can be calculated utilizing only the molecular weights.

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

Related Documents

Key Words

  • en: density specific weight gravity
  • es: la gravedad peso específico densidad
  • de: Dichte spezifische Gewicht der Schwerkraft

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