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 / ai ~ 1/sqrt(1 - M 2)
(a c is compressible lift curve slope, ai 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.