# Mach number

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The Mach number, $M$, is the local flow-speed, $u$, divided by the local speed of sound, $a$:

$M \equiv \frac{u}{a} \equiv \frac{\mbox{local flow speed}}{\mbox{local speed of sound}}$

The Mach number can be used to categorise compressible flows into different Mach number regimes

The name "Mach number" originates from the famous pioneer in compressible fluid dynamics Ernst Mach