Choked flow

Remarks

The bound comes from writing $\dot m = \rho u A$ in terms of the local Mach number $M$ with the isentropic relations: the mass flux $\rho u$ is largest at $M = 1$. Example: air, $\gamma = 1.4$, flows from a tank through a converging nozzle. The flow chokes when the outside pressure falls to $p^* = p_0 \left(\frac{2}{\gamma + 1}\right)^{\gamma/(\gamma - 1)} \approx 0.528\, p_0$, and below that pressure $\dot m$ stays equal to $\dot m_{\max}$. Non-example: with outside pressure $0.8\, p_0$, the exit flow is subsonic, its Mach number is below $1$, and $\dot m < \dot m_{\max}$. More generally, a steady compressible flow in a duct is called choked when it reaches $M = 1$ at a section. It then carries the largest mass flow allowed by the upstream state. Friction and heat addition in a constant-area duct can also cause choking.