MASS DENSITY, SPECIFIC WEIGHT, SPECIFIC VOLUME - FLUID MECHANICS (StudyCivilEngg.com)

MASS DENSITY, SPECIFIC WEIGHT, SPECIFIC VOLUME

SUBJECT : FLUID MECHANICS

MASS DENSITY

Mass density (or specific mass) of a fluid is the mass which it possesses per unit volume. It is denoted  by a symbol ρ (Greek ‘rho’). In SI units mass density is expressed in kilogram per cubic metre i.e.,  kg/m³. In the metric gravitational system of units mass density is expressed in metric slug per cubic metre i.e., ms1/m³ and in the metric absolute system of units it is expressed in gm (mass) per cubic centimetre i.e., gm/cm³ or gm/cc. The corresponding units in the English gravitational and absolute  systems of units are slugs per cubic foot i.e., slugs/ft³ and pound (mass) per cubic foot i.e., lb (m)/ft³ respectively. The mass density of water at °C in different systems of units is 1000 kg/m³, or 102 msl/m³, or 1 gm/cc, or 1.94 slugs/ft³, or 62.4 lb(m)/ft³.

Since a molecule of a substance has a certain mass regardless of its state (solid, liquid or gas), it then  follows that 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.

SPECIFIC WEIGHT

Specific weight (also called weight density) of a fluid is the weight it possesses per unit volume. It  is denoted by a symbol γ (Greek ‘gama’). As it represents the force exerted by gravity on a unit volume of fluid, it has units of force per unit volume. In SI units specific weight is expressed in newton per cubic metre i.e., N/m³. In the metric gravitational system of units specific weight is expressed in kilogram (f) per cubic metre i.e., kg(f)/m³ and in the metric absolute system of units it is expressed in dynes per cubic centimetre i.e., dynes/cm³ or dynes/cc. The corresponding units in the English gravitational and absolute systems of units are pound (f) per cubic foot i.e., lb (f)/ft³ and poundal per cubic foot, i.e., pdl/ft³ respectively. The specific weight of water at 4°C in different units is 9810 N/m³ (or 9.81 kN/m³), or 1000 kg(f)/m³, or 981 dynes/cm³, or 62.4 lb(f)/ft³, or (62.4 ×  32.2) pdl/ft³.

The mass density ρ and specific weight ω are related as indicated below 

ω = ρg; ρ = ω/g

where g is acceleration due to gravity

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

SPECIFIC VOLUME

Specific volume of a fluid is the volume of the fluid per unit weight. Thus it is the reciprocal of  specific weight. It is generally denoted by v. In SI units specific volume is expressed in cubic metre  per newton i.e., m/N. In the metric gravitational system of units specific volume is expressed in  cubic metre per kilogram (f) i.e., m³/kg(f) and in the metric absolute system of units it is expressed  in cubic centimetre per dyne i.e., cm3/dyne or cc/dyne. The corresponding units in the English  gravitational and absolute systems of units are cubic foot per pound (f) i.e., ft³/lb(f) and cubic foot  per poundal i.e., ft³/pdl respectively.

For the problems involving the gas flow specific volume is generally defined as the volume of the fluid per unit mass, in which case it is reciprocal of mass density. In SI units the specific volume is  then expressed in cubic metre per kilogram i.e., m³/kg. In the metric gravitational system of units it  is expressed in cubic metre per metric slug i.e., m³/msl and in the metric absolute system of units it  is expressed in cubic centimetre per gram(mass) i.e., cm³/gm(m) or cc/gm(m). The corresponding  units in the English gravitational and absolute units are cubic foot per slug i.e., ft³/slug and cubic foot per pound (mass) i.e., ft³/lb (m) respectively.

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.

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