Location of supersonic flow in a steam nozzle:\nIn a properly operating convergent–divergent (De Laval) nozzle, where is the steam flow supersonic?

Introduction / Context:
Compressible-flow behavior in nozzles depends on area changes and pressure ratios. The De Laval nozzle accelerates subsonic flow to sonic at the throat and then to supersonic speeds in the diverging section when the back pressure is low enough to choke the flow.

Given Data / Assumptions:

• Adequate pressure ratio to achieve choking at the throat.
• Adiabatic, frictionless approximation for basic explanation.
• Steam as the working fluid (concept applies to gases generally).

Concept / Approach:
Area–Mach number relations state that subsonic flows accelerate in converging passages; sonic Mach number M = 1 occurs at the minimum area (throat) when choked; supersonic flows accelerate in diverging passages. Thus, in a C–D nozzle with sufficient pressure ratio, the divergent section supports M > 1 flow.

Step-by-Step Solution:

Verification / Alternative check:
Measured pressures and temperatures along instrumented nozzles match isentropic C–D predictions when properly expanded, confirming supersonic flow in the diverging section.

Why Other Options Are Wrong:

• Entrance/convergent portion: Flow is typically subsonic there.
• Throat: At best sonic (M = 1), not supersonic.

Common Pitfalls:
Assuming supersonic flow can occur in a purely convergent nozzle; without a diverging section, maximum Mach is 1 at the exit when choked.

Final Answer:
in the divergent portion of the nozzle