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.

• Mass and Weight - the Difference! - What is weight and what is mass? An explanation of the difference between weight and mass.

The density can be expressed as

ρ = m / V = 1 / v_g         (1)

where

ρ = density (kg/m³)

m = mass (kg)

V = volume (m³)

v_g = specific volume (m³/kg)

The SI units for density are kg/m³. The imperial (BG) 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.

• Unit converter for other units

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.

• Densities and material properties for common materials

Relative Density

Relative density of a substance is the ratio of the substance to the density of water, i.e.

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 substances, we can find that ethyl alcohol, or ethanol, has a density of 790 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.

• Mass and Weight - the difference! - What is weight and what is mass? An explanation of the difference between weight and mass.

Specific Weight can be expressed as

γ = ρ g         (2)

where

γ = specific weight (N/m³)

ρ = density (kg/m³)

g = acceleration of gravity (m/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. Specific weight in SI units can be calculated like

γ = (1000 kg/m³) (9.81 m/s²)

    = 9810 N/m³

    = 9.81 kN/m³

Example - Specific Weight Some other Materials

• Material Properties

Specific Gravity

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

SG = = ρ / ρ_H2O         (3)

where

SG = specific gravity

ρ = density of fluid or substance (kg/m³)

ρ_H2O = density of water (kg/m³)

It is common to use the density of water at 4 ^oC (39^oF) as reference - 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.

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 is:

SG = (7850 kg/m³) / (1000 kg/m³)

    = 7.85

• water density is 1000 kg/m³

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