Normal and Oblique Shock Waves Questions and Answers

Answer: A

A normal shock always takes a supersonic stream to a subsonic one. This follows from the requirement that entropy increase: the alternative branch, taking subsonic flow to supersonic, would demand an entropy decrease and is forbidden by the second law. The stronger the shock, the lower the downstream Mach number.

Answer: B

A shock is a compression, so pressure, temperature and density all jump upward while the flow is sharply decelerated. The abruptness matters too: the whole change happens over a distance of the order of a few mean free paths, which is why a shock is drawn as a discontinuity in any practical calculation.

Answer: C

The conservation equations admit an expansion discontinuity as a formal solution, but evaluating the entropy change across it gives a decrease, which the second law forbids. Expansions in supersonic flow must therefore be gradual, spread through a Prandtl-Meyer fan of Mach waves rather than concentrated into a single front.

Answer: D

A shock is thin enough that treating it as a mathematical discontinuity is an excellent approximation for any engineering purpose. Its structure is set by molecular transport, so it scales with the mean free path, typically well under a micron at sea level. Continuum theory cannot describe the interior, only the jump across it.

Answer: A

Written in terms of the characteristic Mach number, the velocity divided by the critical speed of sound, the Prandtl relation says the product across the shock is exactly one. It is a compact statement of the fact that a shock always carries the flow from one side of sonic conditions to the other.

Answer: B

The component tangential to an oblique shock is unchanged across it, while the normal component behaves exactly as it would through a normal shock. Every normal shock relation can therefore be reused for an oblique shock simply by replacing the Mach number with the Mach number based on the normal component.

Answer: C

Applying the momentum equation in the direction along the shock, where no pressure difference acts, shows the tangential component to be preserved. Only the normal component is reduced. That combination is what turns the flow towards the shock surface and gives the deflection an oblique shock produces.

Answer: D

Because the normal component drops while the tangential component is preserved, the resultant downstream velocity lies closer to the shock surface than the upstream one did. The flow is therefore turned into itself, which is exactly what happens when supersonic flow meets a compression corner or a wedge.

Answer: A

Below the maximum deflection there are two mathematically valid shock angles for each deflection. The weak solution, with the smaller angle, is the one nature almost always selects and it usually leaves the flow supersonic. The strong solution appears only when a high downstream back pressure imposes it.

Answer: B

The weak solution reduces the normal component below sonic speed but leaves the tangential component untouched, so the resultant is generally still supersonic. That is why a supersonic aircraft can carry a series of oblique shocks without the flow ever going subsonic until the designer intends it to.