Hydrodynamic calculations are considerably simplified when the fluid is incompressible.
Incompressibility is a reasonably good assumption under certain situations.
When a gas is compressed in some localized region, the excess pressure generates sound waves which act to return the matter distribution to a uniform one. Hence only objects moving at speeds comparable to or faster than the sound speed are capable of producing appreciable compressions. When an object moves slowly, the gas in front of it can dissipate the compression at a speed faster than the speed at which the object is trying to build up the compression. A gas can therefore be regarded as incompressible as long as all the motions inside have velocities small compared to the sound speed. For an incompressible fluid the equation of continuity yields If is small for a flow pattern, then we are justified in regarding the fluid as incompressible.