Mach number

Builds on Dimensionless numbers in fluid mechanics Speed of sound

Definition

Consider a flow of a compressible fluid. Let $u$ be the flow speed at a point, or the speed of a body relative to the fluid. Let $c$ be the local speed of sound in the fluid. The Mach number is $\mathrm{M} = \frac{u}{c}.$ The flow is subsonic where $\mathrm{M} < 1$ , sonic where $\mathrm{M} = 1$ and supersonic where $\mathrm{M} > 1$ .

Remarks

It is a dimensionless number, as a ratio of two speeds. Example: a body moving at $680\ \mathrm{m/s}$ in air with $c = 340\ \mathrm{m/s}$ has $\mathrm{M} = 2$ , so the flow is supersonic. Non-example: the difference $u - c$ is not a Mach number; it has dimension of speed and depends on the units. For steady flow, density changes are of order $\mathrm{M}^2$ , so flows with small Mach number are well modelled as incompressible. For a steady supersonic flow, the linearised potential equation is hyperbolic, while for subsonic flow it is elliptic.

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Dimensionless numbers in fluid mechanics concept
Speed of sound concept
Mach number definition

Tag	`6NVQFZJWFN`
URI	`m2://6NVQFZJWFN`
Kind	definition
Writing	W0 stub
MSC	76N15, 76M55
Defines	Mach number
Uses	Dimensionless numbers in fluid mechanics, Speed of sound
Changed	3 November 2026

Mach number

Definition

Remarks

Reading path

Further reading

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