I read the book Mechanic of fluids shames and I find this relationship:
$\frac{1+kM_1^2}{1+kM_2^2} =\frac{M_1}{M_2} \left ( \frac{1+\dfrac{(k-1)}{2}M_1^2}{1+\dfrac{(k-1)}{2}M_2^2} \right )^{0.5}$
where $M_1$ is the Mach number of supersonic flow and $M_2$ is the Mach number for subsonic flow.
How can I find $M_2$ as a function of $M_1$, say $M_2 = f(M_1)$?
Sorry for my English.