In a convergent-divergent supersonic nozzle with sonic throat, if the receiver back pressure is lowered below the design exit pressure, the nozzle operates as:

(A) Under-expanded, with expansion fans forming at the nozzle exit lip

(B) Over-expanded, with oblique shock waves forming at the exit

(C) Subsonic diffuser with normal shock in the diverging section

(D) Choked with detached normal shock upstream of the throat

Answer Key:

A

### Solution: When back pressure is lower than design exit pressure ($p_b < p_e$), the gas must expand further outside the nozzle, creating Prandtl-Meyer expansion fans at the lip. This is under-expanded. Correct: A.

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