Channel Flow of a Compressible Fluid Gas driven through an hourglass-shaped nozzle. In the narrowing part it speeds up; at the throat it can just reach the speed of sound; then in the widening part — uniquely for a supersonic gas — it keeps accelerating. Lower the pressure downstream and a standing shock wave appears in the diverging cone, snapping the flow abruptly back to subsonic; lower it further and the shock marches out of the nozzle into a diamond-patterned jet. The journey: mass conservation plus the isentropic relations give one equation, A/A* = f(M), with a subsonic and a supersonic root. Which root, and where the normal shock sits, is fixed entirely by the back-pressure ratio p_b/p₀.