Expansion Waves Questions and Answers

Answer: C

A conical nozzle leaves the flow spreading radially, so only the axial component contributes to thrust and a divergence loss results. A contoured bell shaped by characteristics turns the flow back parallel to the axis before it leaves, recovering most of that loss for a modest gain in weight.

Answer: D

A well-designed nozzle contour absorbs each characteristic rather than reflecting it, so the test section receives uniform parallel flow at the design Mach number. Residual waves show up directly as Mach number non-uniformity across the model and are a principal measure of tunnel quality.

Answer: A

The shock dissipates energy, so it reaches a hotter, higher-entropy state for the same pressure rise and destroys stagnation pressure doing it. An isentropic compression achieves the same pressure more efficiently, which is why intake designers approach it as closely as they can with a series of weak waves.

Answer: B

A gently concave surface generates a distributed compression rather than a single shock, and so long as the characteristics do not coalesce the process is nearly isentropic. In practice they do eventually coalesce, and the boundary layer complicates matters, so such intakes are usually mixed designs.

Answer: C

That single question, whether the wall turns into the oncoming flow or away from it, settles everything else: compression and a shock in the first case, expansion and a fan in the second. Sharpness affects only whether the waves are centred, and neither case needs viscosity.

Answer: D

A sharp corner introduces no length scale, so every characteristic emanates from that one point and the solution is self-similar. Rounding the corner spreads the origins of the waves along the surface, giving a distributed rather than a centred expansion, though the downstream state is the same.

Answer: A

The waves now spring from many points along the curve rather than from one corner, so the near field differs. Because the process remains isentropic and the total turning is the same, the downstream Mach number and pressure are identical to the sharp-corner case.

Answer: B

The expansion is isentropic and costs nothing, but the shock raises entropy and destroys stagnation pressure irreversibly. The round trip therefore ends below where it began. This asymmetry is the whole reason supersonic intake design is difficult: expanding is free, compressing is not.

Answer: C

Both are true and the second explains the first. No length scale enters the problem, so the geometry of how the turn is distributed affects only the near field. The downstream state follows from the total angle turned through, whether that happens at one corner or over a curve.

Answer: D

All three are correct. Neither process exchanges heat, so both are adiabatic and both conserve stagnation temperature. They part company only on reversibility, and it is the shock's entropy rise that destroys stagnation pressure while the fan leaves it intact.