Mach number#

Named after: Ernst Mach (1838-1916).

$$\text{Ma} \stackrel{\text{def}}{=} \frac{U}{c} \sim \frac{\text{flow speed}}{\text{sound speed}}$$

Measures flow speed relative to the speed of sound. It indicates whether compressibility, acoustic waves, and shocks are important.

Name	Symbol	SI units	Dimension
velocity	$U$	$\mathrm{m}\,\mathrm{s}^{-1}$	$\text L\,\text T^{-1}$
speed of sound	$c$	$\mathrm{m}\,\mathrm{s}^{-1}$	$\text L\,\text T^{-1}$

Compressible flow

Range	Regime	Description
0 – 0.3	incompressible	Density variations are negligible. Flow can be treated as incompressible.
0.3 – 0.8	weakly compressible	Compressibility effects are small but may be noticeable in some cases.
0.8 – 1.2	transonic	Flow speed approaches the speed of sound. Shock waves and strong compressibility effects occur.
1.2 – 5	supersonic	Flow speed exceeds the speed of sound. Strong shock waves and compressibility effects dominate.
5 – ∞	hypersonic	Flow speed is much greater than the speed of sound. Extreme shock waves, high temperatures, and ionization may occur.

Name	Symbol	SI units	Dimension
velocity	\(U\)	\(\mathrm{m}\,\mathrm{s}^{-1}\)	\(\text L\,\text T^{-1}\)
speed of sound	\(c\)	\(\mathrm{m}\,\mathrm{s}^{-1}\)	\(\text L\,\text T^{-1}\)