Mach number

The Mach number (symbol: ) is a dimensionless parameter of fluid mechanics for velocities. It indicates the ratio of the speed ( for example, a body or a fluid ) to the sound velocity of the surrounding fluid. It is named after the physicist and philosopher Ernst Mach.


The following applies:

Where you can use the speed of sound in gases in general, which leads to the following expression:

Is the isentropic exponent set, the specific gas constant and the temperature for the observed gas (eg air) dar. It should be noted that the isentropic exponent is a function of pressure and temperature for a specific fluid. Within a certain range but it may be assumed to be constant, which is sufficient as an approximate solution in most cases. Under Mach number = 1, colloquially also " Mach 1 ", it is understood, therefore the speed of sound ( which is dependent on a particular medium to a good approximation only on the temperature ). Accordingly, " Mach 2 " ( twice the speed of sound), Mach 3, etc., can not convert speeds in " exact " also without knowing the reference speed of sound.

Using the Mach number can, however, divide flows in different areas, such as:

  • Subsonic flow,
  • Transonic flow,
  • Supersonic flow.

From one also speaks of hypersonic flow.

These areas require different approaches, because the local physical phenomena occur in the areas. For example, enter for compressible effects in the currents on ( compressible flow ), while such effects usually for no role play ( incompressible flow ).


In aviation, the Mach number is used for the dimensionless indication of airspeed fast -flying aircraft. It is the ratio of airspeed to the speed of sound in the air and is indicated by a special flight instrument, the Mach meter.

At a temperature of -50 ° C (usually in about 10,000 m altitude ) is the sound velocity 299.8 m / s = 1079.3 km / h A passenger airplane flying at a cruising speed of Mach 0.85 under these conditions, has a speed of 254.83 m / s = 917.39 km / h