formula for Mach number

Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is derived from Bernoulli's equation for M<1:[3]

{M}=\sqrt{\frac{2}{\gamma-1}\left[\left(\frac{q_c}{P}+1\right)^\frac{\gamma-1}{\gamma}-1\right]}

where:

\ M is Mach number
\ q_c is impact pressure and
\ P is static pressure
\ \gamma is the ratio of specific heat of a gas at a constant pressure to heat at a constant volume (1.4 for air).

The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:

{M}=0.88128485\sqrt{\left[\left(\frac{q_c}{P}+1\right)\left(1-\frac{1}{[7M^2]}\right)^{2.5}\right]}

where:

\ q_c is now impact pressure measured behind a normal shock.