# compressible flow

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## Compressible flow

Flow in which density changes are significant. Pressure changes normally occur throughout a fluid flow, and these pressure changes, in general, induce a change in the fluid density. In a compressible flow, the density changes that result from these pressure changes have a significant influence on the flow. The changes in the flow that result from the density changes are often termed compressibility effects. All fluids are compressible. However, compressibility effects are more frequently encountered in gas flows than in liquid flows.

An important dimensionless parameter in compressible flows is the Mach number, *M*. This is defined by Eq. (1),

*a*is the speed of sound and

*V*is the velocity of the flow. For a gas, the speed of sound is given by Eq. (2),

*R*is the gas constant,

*k*=

*c*,

_{p}/c_{v}*c*and

_{p}*c*being the specific heats at constant pressure and constant volume respectively, and

_{v}*T*is the temperature. If

*M*< 0.3 in a flow, the density changes in the flow will usually be negligible; that is, the flow can be treated as incompressible. Compressible flows are, therefore, as a rough guide, associated with Mach numbers greater than 0.3.

When *M* < 1, the flow is said to be subsonic; when *M* = 1, the flow is said to be sonic; when *M* varies from slightly below 1 to slightly above 1, the flow is said to be transonic; and if *M* > 1, the flow is said to be supersonic. When the Mach number is very high, this usually being taken to mean *M* > 5, the flow is said to be hypersonic.

Compressible flows can have features that do not occur in low-speed flows. For example, shock waves and expansion waves can occur in supersonic flows. Another important phenomenon that can occur due to compressibility is choking, where the mass flow rate through a duct system may be limited as a result of the Mach number being equal to 1 at some point in the flow. *See* Choked flow, Shock wave, Sonic boom

Another effect of compressibility is associated with the acceleration of a gas flow through a duct. In incompressible flow, an increase in velocity is associated with a decrease in the cross-sectional area of the duct, this in fact being true as long as *M* < 1. However, when *M* > 1, that is, when the flow is supersonic, the opposite is true; that is, an increase in the velocity is associated with an increase in the cross-sectional area. Therefore, in order to accelerate a gas flow from subsonic to supersonic velocities in a duct, it is necessary first to decrease the area and then, once the Mach number has reached 1, to increase the area, that is, to use a so-called convergent-divergent nozzle. An example is the nozzle fitted to a rocket engine. *See* Fluid flow, Mach number, Supersonic flow