Density, Mass Density, Specific Weight, Specific Volume and Relative Density

1) Density (r)

The basic definition of the density of a substance is the ratio of the mass of a given amount of the substance to the volume it occupies. Thus, density of a fluid is its mass per unit volume and the SI unit is kg/m³.The density of a fluid, denoted by ‘r’ (lowercase Greek letter ‘rho’).

Fluid density is temperature dependent and to a lesser extent it is pressure dependent. For example the density of water at sea level at 4^oC is 1000 kg/m³ , whilst at 50^oC is 988 kg/m³.

2) Mass Density (r)

The mass density of a fluid is its mass per unit volume, normally stated in kilograms per cubic metre (kg/m³ ). The symbol used for mass density is `rho’ (r).

Typical mass densities are:

Material	Mass density (kg/m3)
Water	1000
Sea water	1024
Mercury	13.6 x 10^3
Oil	800 - 900
Air	1.23

Since a molecule of a substance has a certain mass regardless of its state (solid, liquid or gas), the mass density is proportional to the number of molecules in a unit volume of the fluid. As the molecular activity and spacing increase with temperature, fewer molecules exist in a given volume of fluid as temperature rises. Therefore, the mass density of a fluid decreases with increasing temperature. Further by application of pressure a large number of molecules can be forced into a given volume, it is to be expected that the mass density of a fluid will increase with increasing pressure.

3) Weight Density/Specific Weight (w or g)

The weight density (also called specific weight) of a fluid is its weight per unit volume, with unit of Newton per cubic metre (N/m³). The weight density is calculated by multiplying the mass density by 9.8, the value for the gravitational acceleration. It is denoted by a symbol ‘w’ or ‘g’ (Greek letter ‘gama’). As it represents the force exerted by gravity on a unit volume of fluid, it has units of force per unit volume.

Weight Density = Mass Density x g

The mass density ‘r’ and specific weight ‘w’ are related as indicated below.

where g is acceleration due to gravity.

The specific weight depends on the acceleration due to gravity and the mass density. Since the acceleration due to gravity varies from place to place, the specific weight will also vary. Further the mass density changes with temperature and pressure, hence the specific weight will also depend upon temperature and pressure.

4) Specific Volume (v)

Specific volume of a fluid is the volume of the fluid per unit mass. Thus it is the reciprocal of mass density. It is generally denoted by ‘v’. In SI units specific volume is expressed in cubic meter per kilogram i.e., m³/kg. The specific volume of water is 

                                                   1 /ρ=1/1000 = 0.001 m³ /kg

For liquids the mass density, the specific weight and specific volume vary only slightly with the variation of temperature and pressure. It is due to the molecular structure of the liquids in which the molecules are arranged very compactly (in contrast to that of a gas). The presence of dissolved air, salts in solution and suspended matter will slightly increase the values of the mass density and the specific weight of the liquids.

For gases the values of the above properties vary greatly with variation of either temperature, or pressure, or both. It is due to the molecular structure of the gas in which the molecular spacing (i.e., volume) changes considerably on account of pressure and temperature variations.

5) Relative Density (RD)

The relative density is the ratio of the density of a substance to some standard density. The standard density chosen for comparison with the density of a solid or a liquid is invariably that of water at 4°C. The relative density of a fluid is the mass density of the fluid compared to the mass density of water at 4°C. RD is a pure ratio. So, it has no units. It is also sometimes referred as specific gravity.

Example Question

If a 25 litre volume of oil has a mass of 20 kilograms, determine the oil’s mass density, weight density, relative density and specific volume.

     Mass density = mass/volume

                           = 20/0.025

                           = 800 kg/m³

  Weight density = mass density x g

                           = 800 x 9.8

                           = 7840 N/m

Relative density = mass density of oil/ mass density of water

                           = 800/1000

                           = 0.8

Specific volume = 1/r

                           = 1/800

                           = 1.25 x10 ^ -3 m³ /kg