Expansion Waves Questions and Answers

Answer: A

The first two are correct and are what make the method of characteristics possible. The third is false for steady flow: the governing equations are elliptic below Mach one and have no real characteristics, which is precisely why subsonic flow feels a disturbance everywhere at once.

Answer: B

An expansion is the mirror image of a shock in the static quantities: the Mach number rises while pressure, temperature and density all fall. The difference lies in the stagnation properties and the entropy, both of which survive because every wave in the fan is vanishingly weak.

Answer: C

The rule is worth memorising in one line: a solid wall reflects a wave in kind, a constant-pressure boundary reflects it with the sense reversed. The second half of that rule is what drives the alternating pattern of shock diamonds in an imperfectly expanded plume.

Answer: D

These four values are the ones worth carrying, since almost every textbook problem is built from them. Note how the increments shrink: the first half-unit of Mach number costs about twelve degrees, while the step from Mach 2 to Mach 3 costs about twenty-three for twice the Mach number gain.

Answer: A

The exit pressure relative to ambient settles which case applies. Too high and the gas keeps expanding through fans; too low and shocks recompress it; matched and the plume simply leaves. Severe overexpansion drives the shock inside, and the resulting separation and side loads are a real launch hazard.

Answer: B

Whether the surface turns away from the flow or into it settles expansion against compression, and whether the turn is sharp or gradual settles centred against distributed. The asymmetry between the last two rows is the important one: compressions coalesce, expansions never do.

Answer: C

Correct answer: The Mach number

An expansion accelerates the flow, so the Mach number rises. Everything else falls: the static pressure, temperature and density all decrease as the gas expands, and it does so isentropically, without the losses a shock imposes. That is why a Prandtl-Meyer expansion is reversible in principle while a compression through a shock is not.

Answer: D

Each wave in the fan is vanishingly weak, and entropy rise goes as the cube of wave strength, so the total is negligible. That is exactly why the isentropic relations may be carried straight through a fan while they must never be carried through a shock.

Answer: A

A shock reflecting from a solid wall gives another shock: flow tangency has to be restored by a turn in the same sense, which means a further compression. The rule is that a wall reflects in kind and a constant-pressure boundary reverses the sense.

Answer: B

Correct answer: The Mach angle

The Mach angle is \( \arcsin(1/M) \), so it *decreases* as the flow accelerates - the expansion fan spreads while each individual Mach line lies closer to the flow direction. The Prandtl-Meyer function, the Mach number and the velocity all increase, which is what turning through a convex corner means.