Two principles distinguish compressible flow: gases heat when compressed and cool when expanded; disturbances propagate at the speed of sound. The first alludes to thermodynamics. The second alludes to gas dynamics.

Thermodynamics

Heating by compression converts work into thermal energy. This is a reversible conversion in the sense that the thermal energy can be converted back into work. Heating also occurs by frictional dissipation of fluid kinetic energy into thermal energy. That is an irreversible process; viscosity cannot convert the thermal energy back into ordered flow. Friction increases entropy.

Compression and expansion occur in the course of the motion of a gas. For instance, on approaching a blunt body, the flow will slow, and fluid elements will be compressed. That is the ultimate motive for reviewing basic thermodynamics: the governing equations of compressible flow must be consistent with thermodynamics, extended to a spatially distributed system. However, we start with the thermodynamic description of compression and expansion of a homogeneous gas and then proceed to discuss compressible fluid dynamics. Comprehensive texts (Saad, 1997) can be consulted if the reader desires a thorough treatment of thermodynamics. The following is an informal treatment that provides background to compressible flow analysis.

Define a fluid element as a fixed mass, M, of gas. This occupies a volume element, V, which contains that mass. The volume defined in this way is termed specific volume – specific properties are those associated with a given quantity of mass. The mass of the fluid element is invariant, because that is how the element is defined: its volume can change. Indeed, compressibility is the property of volume change in consequence of pressure variations.