Input Mach number M.
Input Heat-capacity ratio gamma.
Input Throat area A*.
Input Total pressure P0.
Input Total temperature T0.
Area-Mach relation (isentropic, M=1 at the throat):
$$\frac{A}{A^*}=\frac{1}{M}\left[\frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}$$
Isentropic static pressure and temperature ratios:
$$\frac{P}{P_0}=\left(1+\frac{\gamma-1}{2}M^2\right)^{-\frac{\gamma}{\gamma-1}},\quad \frac{T}{T_0}=\left(1+\frac{\gamma-1}{2}M^2\right)^{-1}$$
Choked (M=1 at throat) maximum mass flow:
$$\dot{m}=A^{*}P_0\sqrt{\frac{\gamma}{R\,T_0}}\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{2(\gamma-1)}}$$
For a given A/A* there are two solutions, subsonic and supersonic (e.g. A/A*=2 → M≈0.31 or M≈2.20). Flow accelerates subsonically in the converging section, reaches M=1 (choked) at the throat, and becomes supersonic in the diverging section. This simplified model assumes isentropic, one-dimensional flow and ignores shocks, boundary layers, and losses.