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An expansion shock, across which pressure would fall discontinuously, is impossible because it would

  • A.Violate conservation of mass
  • B.Require the flow to be viscous
  • C.Require the entropy of the gas to decrease
  • D.Require the stagnation temperature to rise

Answer: C

The conservation equations admit an expansion discontinuity as a formal solution, but evaluating the entropy change across it gives a decrease, which the second law forbids. Expansions in supersonic flow must therefore be gradual, spread through a Prandtl-Meyer fan of Mach waves rather than concentrated into a single front.

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