When a convergent-divergent nozzle operates at an over-expanded condition, the exit pressure P_e is:

(A) Lower than ambient pressure P_a, resulting in oblique shocks at the exit lip

(B) Higher than ambient pressure P_a, resulting in expansion fans

(C) Exactly equal to chamber stagnation pressure P_0

(D) Zero

Answer Key:

A

### Solution: Over-expansion occurs when the nozzle expands gas to a pressure below ambient (P_e < P_a), causing compressive oblique shocks or Mach disks to form at the exit. Correct: A.

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