Expansion Waves Questions and Answers

Answer: C

The shock relations encode a discontinuous, entropy-generating compression, which is the opposite of what a fan does in every respect. An expansion is handled with the Prandtl-Meyer function and the isentropic relations, and no part of the shock machinery carries over.

Answer: D

The maximum function value is 130.45 degrees, and the flow has already spent \( \nu(2) = 26.38 \) degrees getting to Mach 2, so only about 104 degrees remain. The trap is quoting the maximum as though the flow started from sonic conditions.

Answer: A

Both processes exchange no heat with the surroundings, so both are adiabatic. They part company on reversibility: the shock's steep internal gradients dissipate energy, while the fan's waves are each too weak to do so. Hence the shock destroys stagnation pressure and the fan does not.

Answer: B

Wave drag is present in a purely inviscid supersonic calculation, so the first statement is false. D'Alembert's paradox does not apply here, because the flow field contains shocks and the pressures on forward- and rearward-facing surfaces no longer balance.

Answer: C

Shock diamonds are the signature of a mismatch between exit and ambient pressure. When the two match there is nothing for the waves to correct, so the plume leaves cleanly and the diamonds are absent. The other three are exactly what perfect expansion means.

Answer: D

In a simple wave region the characteristics of one family are straight and carry no change, while those of the other family carry the whole variation. A centred fan is the classic example, and the property is what makes the Prandtl-Meyer solution so compact.

Answer: A

Both processes obey exactly the same conservation laws; nothing in mass, momentum or energy distinguishes them. The asymmetry comes entirely from the entropy condition and from the way the Mach angle varies, which the other three options state.

Answer: B

That angle is the maximum value of the Prandtl-Meyer function for air, reached as the Mach number grows without bound and the static pressure tends to zero. The stagnation pressure is untouched throughout, since the process remains isentropic; it is the static pressure that vanishes.

Answer: C

The area ratio fixes the exit pressure, but the ambient pressure falls steadily as the vehicle climbs, so the two can match at only one altitude. A first stage is therefore overexpanded at sea level and underexpanded high up, and the design altitude is chosen to minimise the total loss over the trajectory.

Answer: D

The method marches the two families of characteristics through the supersonic region and shapes the wall so that each wave generated is cancelled rather than reflected. It is inviscid, needs no shocks, and has no counterpart in steady subsonic flow, where the equations have no real characteristics.