Compressible Flow

What is Compressible flow?

Incompressible flow refers to the fluid flow in which the fluid’s density is constant. For a density to remain constant, the control volume  has to remain constant. Even though the pressure changes, the density will be constant for an incompressible flow. Incompressible flow means flow with variation of density due to pressure changes is negligible or infinitesimal. All the liquids at constant temperature are incompressible.

Compressible flow means a flow that undergoes a notable variation in density with trending pressure. Density r (x, y, z) is considered a field variable for the flow dynamics. When the value of Mach number crosses above 0.3, density begins to vary, and the amplitude of variation spikes when Mach number reaches and exceeds unity.

The control volume (CV) behavior for incompressible and compressible flow is depicted below.

 

Compressible Flow

It can be seen that the CV remains constant for an incompressible flow, and CV is squeezed for compressible flow. Bernoulli’s equation is applicable only when the flow is assumed to be incompressible. In the case of compressible flow, Bernoulli’s equation becomes invalid since the fundamental assumption for Bernoulli’s equation is that density r is constant. For compressible flow,

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