Definition
Compressible flow describes the behaviour of fluids that experience significant variations in density. For flows in which the density does not vary significantly, the analysis of the behaviour of such flows may be simplified greatly by assuming a constant density. This is an idealization, which leads to the theory of incompressible flow. However, in the many cases dealing with gases (especially at higher velocities) and those cases dealing with liquids with large pressure changes, the significant variations in density can occur, and the flow should be analysed as a compressible flow if accurate results are to be obtained.
Allowing for a change in density brings an additional variable into the analysis. In contrast to incompressible flows, which can usually be solved by considering only the equations from conservation of mass and conservation of momentum. Usually, the principle of conservation of energy is included. However, this introduces another variable (temperature), and so a fourth equation (such as the ideal gas equation) is required to relate the temperature to the other thermodynamic properties in order to fully describe the flow.
When defining what is meant by a compressible flow, it is useful to compare the density to a reference value, such as the stagnation density, which is the density of the fluid if it were to be slowed down isentropically to stationary. As a general rule of thumb, if the change in density relative to the stagnation density is greater than 5%, then the fluid should be analysed as a compressible flow. For an ideal gas with a ratio of specific heats of 1.4, this occurs at a Mach number greater than approximately 0.3. Below this value, however, whether or not a specific case should be treated as compressible or incompressible depends largely on the level of accuracy that is required.
Read more about this topic: Compressible Flow
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