Compressibility

The change in volume of a fluid associated with change in pressure is called compressibility. When a fluid is subjected to pressure it gets compressed and its volume changes. The bulk modulus of elasticity is a measure of how easily the fluid may be compressed, and is defined as the ratio of pressure change to volumetric strain associated with it. The bulk modulus of elasticity, K, is given by:

Pressure increment dp

K = ———————– = -V—

Volume strain dV

It may also be expressed as:

where v is specific volume. Since dp/p represents the relative change in density brought about by the pressure change dp, it is apparent that the bulk modulus of elasticity is the inverse of the compressibility of the substance at a given temperature. For instance, K for water and air are approximately 2 GN/m2 and 100 kN/m2, respectively. This implies that air is about 20,000 times more compressible than water. It can be shown that, K = a2/p, where a is the speed of sound. The compressibility plays a dominant role at high-speeds. Mach number M (defined as the ratio of local flow velocity to local speed of sound) is a convenient nondimensional parameter used in the study of compressible flows. Based on M the flow is divided into the following regimes. When M < 1 the flow is called subsonic, when M & 1 the flow is termed transonic Bow, M from 1.2 to 5 is called supersonic regime, and M > 5 is referred to as hypersonic regime. When flow Mach number is less than 0.3, the compressibility effects are negligibly small, and hence the flow is called incompressible. For incompressible flows, density change associated with velocity is neglected and the density is treated as invariant.