# Mach number

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## Mach number

(mäk) [for E. Mach**Mach, Ernst**

, 1838–1916, Austrian physicist and philosopher, b. Moravia. He taught (1864–67) mathematics at Graz and later, until his retirement in 1901, was professor of physics at Prague and Vienna.

**.....**Click the link for more information. ], ratio between the speed of an object and the speed of sound in the medium in which the object is traveling. An airplane that has the velocity of Mach 3.0 is traveling at three times the speed of sound as measured in the prevailing atmospheric conditions.

## Mach number

In the flow of a fluid, the ratio of the flow velocity, *V*, at a given point in the flow to the local speed of sound, *a*, at that same point. That is, the Mach number, *M*, is defined as *V*/*a*. In a flowfield where the properties vary in time and/or space, the local value of *M* will also vary in time and/or space. In aeronautics, Mach number is frequently used to denote the ratio of the airspeed of an aircraft to the speed of sound in the freestream far ahead of the aircraft; this is called the freestream Mach number. The Mach number is a convenient index used to define the following flow regimes: (1) subsonic, where *M* is less than 1 everywhere throughout the flow; (2) supersonic, where *M* is greater than 1 everywhere throughout the flow; (3) transonic, where the flow is composed of mixed regions of locally subsonic and supersonic flows, all with local Mach numbers near 1, typically between 0.8 and 1.2; and (4) hypersonic, where (by arbitrary definition) *M* is 5 or greater.

Perhaps the most important physical aspect of Mach number is in the completely different ways that disturbances propagate in subsonic flow compared to that in a supersonic flow. Shock waves are a ubiquitous aspect of supersonic flows. *See* Compressible flow, Shock wave, Sonic boom

## Mach Number

a fundamental characteristic of a gas flow, equal to the ratio of the velocity of the flow v to the velocity of sound *a* at the same point in the flow: *M = v/a*. For a body moving in a gas, the Mach number is equal to the ratio of the velocity of the body to the velocity of sound in the medium.

Named after E. Mach, the Mach number is also one of the fundamental criteria of aerodynamic similarity for cases in which the compressibility of the gas cannot be disregarded. In air the compressibility must be taken into account for velocities v > 100 m/sec, to which the number *M* > 0.3 corresponds. For *M* < 1, the flow is called subsonic; for *M =* 1, sonic; and for *M >* 1, supersonic. One of the principal features of supersonic flow is the formation of shock waves in the flow around bodies or on braking the gas flow. Wave drag, which increases with the Mach number, arises in shock waves as a result of the dissipation of energy. Flow regions with *M* > 5 (hypersonic flows) have a number of unique features; in particular, physicochemical changes in a gas compressed in a shock wave become significant.

M. IA. IUDELOVICH

## Mach number

[′mäk ‚nəm·bər]*N*

_{Ma }. Also known as relative Mach number.

## Mach number

*relative Mach number*.