Sonic density of a polytropic nozzle
= Sonic density of a polytropic nozzle
{title2=$\rho_*=[\dot M/(A_*\sqrt{\gamma K})]^{2/(\gamma+1)}$}
For steady <polytropic flow> with $p=K\rho^\gamma$, $K>0$, $\gamma>1$, a sonic section has $u_*=c_*=(\gamma K\rho_*^{\gamma-1})^{1/2}$. Substitution in <mass conservation> $\dot M=A_*\rho_*u_*$ gives the displayed density. These conditions fix the sonic state for a prescribed flux and throat area, subject to compatible reservoir and downstream <boundary conditions>.