A compressible flow is a situation in which the compressibility of a 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. Under these circumstances, it is usual to neglect viscosity and the Euler equations are used (rather than the Navier-Stokes equations). Mach number (Ma) (pronounced as mack in International English or mock in the American English) is defined as a ratio of speed to the speed of sound in the medium in case. ... In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. ... Jump to: navigation, search The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances like liquids and gases. ...

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 is compressible lift curve slope, a_i is the incompressible lift curve slope, and M is the Mach number). Mach number (Ma) (pronounced as mack in International English or mock in the American English) is defined as a ratio of speed to the speed of sound in the medium in case. ...

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 an abrupt change in the velocity, pressure and temperature in a flow; the thickness of a shock scales with the molecular mean free path in the fluid (typically a few micrometers). Mach number (Ma) (pronounced as mack in International English or mock in the American English) is defined as a ratio of speed to the speed of sound in the medium in case. ... In fluid dynamics, a shock wave is a nonlinear or discontinuous pressure wave. ...

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. To interpret this in another way, consider steady flow in a tube that has a sudden expansion: the tube's cross section suddenly widens, so the cross-sectional area increases.

In subsonic flow, the fluid speed drops after the expansion (as expected). In supersonic flow, the fluid speed increases. This sounds like a contradiction, but it isn't: the mass flux is conserved but because supersonic flow allows the density to change, the volume flux is not constant.