Normal and Oblique Shock Waves Questions and Answers

Answer: A

All three are correct. A higher Mach number narrows the Mach cone and, on the weak branch, reduces the shock angle for the same turning, wrapping the shock in towards the surface. It also raises the maximum deflection, which is why a wedge that detaches its shock at one speed may hold it attached at a higher one.

Answer: B

Static pressure jumps up, the Mach number is always taken below one, stagnation temperature survives because the shock is adiabatic, and stagnation pressure falls because it is irreversible. Keeping these four straight is most of what is needed to answer any normal shock question.

Answer: C

These four cover the whole range of shock strengths. A Mach wave is the vanishing limit, the weak and strong branches are the two roots of the theta-beta-Mach relation, and the detached bow shock is what forms once the deflection asked for exceeds anything an attached shock can supply.

Answer: D

These four numbers are worth memorising together, since Mach 2 is the standard worked example. The pressure has more than quadrupled, the density has not quite tripled, the flow has been taken well subsonic, and more than a quarter of the stagnation pressure has been destroyed.

Answer: A

The shock angle and the deflection angle are the two variables the theta-beta-Mach relation connects for a given upstream Mach number. The Mach angle is the lower limit of the shock angle, and the detachment angle is the upper limit of the deflection, beyond which the shock stands off.

Answer: B

The distinction between adiabatic and isentropic is the one this table is built to sharpen. A shock is adiabatic yet raises entropy; an ideal nozzle is both adiabatic and reversible; a heated duct with friction is neither; and a Mach wave is so weak that its entropy rise, being cubic in strength, may be neglected entirely.

Answer: C

The Mach number always falls across a normal shock, and indeed falls below one. Pressure, temperature, density and entropy all rise. The velocity falls as well, so any option suggesting the flow speeds up through a shock can be discarded immediately.

Answer: D

Mass is conserved perfectly well across a hypothetical expansion discontinuity; the conservation equations alone do not rule it out. What rules it out is the entropy condition, which the other three options all state in different words.

Answer: A

The tangential component passes through unchanged, since no pressure gradient acts along the shock. That fact, combined with the reduction of the normal component, is exactly what produces the deflection. The other three statements are all correct.

Answer: B

The pressure ratio, like the temperature ratio, grows without limit as the shock strengthens. The density ratio saturates at six for air, the downstream Mach number approaches 0.378, and the velocity ratio approaches one sixth, the reciprocal of the limiting density ratio.