Nozzle area-Mach number relation
= Nozzle area-Mach number relation
{title2=$A/A_*$}
For a calorically <perfect gas> on a steady isentropic <nozzle> branch,
$$
\frac A{A_*}=\frac1M\left[\frac2{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right)\right]^{(\gamma+1)/(2(\gamma-1))}.
$$
Here $A_*$ is the sonic area. An area ratio greater than one generally admits a subsonic and a supersonic root; <boundary conditions> choose the physical branch. Numerical inversion must retain that branch information.