A pitot tube is used to measure the Mach number $left(M_{1} ight)$ of a supersonic flow as

A pitot tube is used to measure the Mach number $\left(M_{1}\right)$ of a supersonic flow as shown in the figure.

Although a curved shock stands ahead of the probe, it is fairly accurate to assume that the fluid in the stream tube captured by the probe has passed through a normal shock wave. It is also reasonable to assume that the probe measures the stagnation pressure downstream of the shock wave $\left(P_{0,2}\right)$. If the static pressure upstream of the shock wave $\left(P_{1}\right)$ is also measured, then the Mach number $M_{1}$ can be evaluated. Derive the relation connecting $P_{0,2} / P_{1}$ and $M_{1}$ (this is called the Rayleigh pitot formula).

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