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The area-Mach number relation for isentropic flow gives, for each area ratio above one,

  • A.No solution at all
  • B.Two possible Mach numbers, one subsonic and one supersonic
  • C.A single Mach number, always subsonic
  • D.A single Mach number, always supersonic

Answer: B

For any area larger than the critical area there are two isentropic solutions, one on each side of Mach one. Which one a real nozzle achieves is settled by the back pressure: a low enough back pressure gives the supersonic branch, a high one the subsonic branch, and intermediate values put a shock in the divergent section.

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