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The entropy rise across a weak oblique shock varies, to leading order, as

  • A.The shock strength itself
  • B.The square of the shock strength
  • C.The fourth power of the shock strength
  • D.The cube of the shock strength

Answer: D

Expanding the entropy change for a weak shock shows the first and second order terms vanish, leaving a cubic dependence on the strength. This is why a vanishingly weak wave may be treated as isentropic, and why splitting a compression into several weak shocks is so much cheaper than doing it with one strong one.

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