Compressible flow

A compressible flow is a situation in which the compressibility of the fluid must be taken into account. In general, this is the case where the Mach number in part or all of the flow approaches or exceeds 1.

For subsonic compressible flows, it is sometimes possible to model the flow by applying a correction factor to the answers derived from incompressible calculations or modelling - for example, the Glauert-Prandtl rule

a _c / a_i ~ 1/sqrt(1 - M ²)

(a _c is compressible lift curve slope, a_i is the incompressible lift curve slope, and M is the Mach number).

For many other flows, their nature is qualitatively different to subsonic flows. A flow where the local Mach number reaches or exceeds 1 will usually contain shock waves. A shock is a discontinuous change in the velocity, pressure and temperature in a flow. Shocks form because information about conditions downstream of a point of sonic or supersonic flow can not propgate back upstream past the sonic point.

The behaviour of a fluid changes radically as it starts to move above the speed of sound (in that fluid). For example, in subsonic flow, a stream tube in an accelerating flow contracts. But in a supersonic flow, a stream tube in an accelerating flow expands.