The Mach number is the ratio of flow speed, V, to the speed of sound, a. It reflects the importance of the compressibility of the fluid. This ratio is important because pressure disturbances propagate in a fluid at the local speed of sound and the compressibility of a fluid permits a sound wave to travel. The speed of sound in a fluid is related to the way in which density and pressure vary: a

Assuming isentropic flow and a perfect gas: a

The flow pattern and pressures can change dramatically with Mach number as the applicable differential equation changes form. (See later sections.) At low subsonic speeds, the effect of compressibility is not large and the flow behaves almost as if pressure disturbances traveled with infinite speed. As the flow speed is increased, but remains subsonic the effects of compressibility start to appear slowly. As the flow velocity approaches Mach 1 (transonic flow) more significant compressibility effects appear quickly. Because of the increase in local velocity over parts of an airfoil, the local Mach number can be much higher than the freestream Mach number. In fact, compressibility effects can be important for high-lift sections at freestream Mach numbers as low as 0.3. As the flow velocity increases beyond Mach 1.0, it becomes supersonic and its characteristics change greatly. Very high velocity flows (usually above Mach 5 or 6) are called hypersonic. These types of flow are of great importance in the aerodynamics of rockets and re-entry vehicles, which achieve Mach numbers as high as 25.