Compressible Flow Fundamentals Questions and Answers

Answer: C

Mach five is the usual dividing line, chosen because above it several effects that can be ignored at lower supersonic speeds become important together: strong shock layers, viscous interaction, entropy layers and real-gas behaviour such as dissociation. Like the Mach 0.3 threshold, it is a convention rather than a discontinuity.

Answer: D

Accelerating an isentropic flow converts thermal energy into kinetic energy, so the static temperature falls, and with it the pressure and density. The stagnation values stay fixed, so the ratios of stagnation to static properties all increase with Mach number, which is exactly what the isentropic tables tabulate.

Answer: A

In subsonic flow the density changes more slowly than the velocity, so continuity behaves much as it does in incompressible flow: squeezing the duct speeds the flow up and drops the pressure. The behaviour reverses once the flow is supersonic, which is the content of the area-velocity relation.

Answer: B

Above Mach one the density falls faster than the velocity rises, so continuity demands that the area increase for the flow to accelerate further. This inversion is why a supersonic nozzle must diverge, and it is the single most counter-intuitive result in elementary compressible flow.

Answer: C

The area-velocity relation permits a change from subsonic to supersonic flow only where the area is stationary, that is at the throat, and there the Mach number must be exactly one. Once that condition is reached the nozzle is choked and the mass flow cannot be increased by lowering the back pressure further.

Answer: D

Choking occurs when the throat reaches sonic conditions. Below the throat no signal can travel upstream, so lowering the back pressure changes nothing upstream of it and the mass flow is fixed by the stagnation conditions and the throat area alone. Raising the stagnation pressure is then the only way to pass more mass.

Answer: A

The starred quantities are the values the flow would have if it were brought isentropically to Mach one. They give a convenient fixed reference, and the ratio of local area to the critical area is what the isentropic tables use to relate a duct's geometry to the Mach number in it.

Answer: B

The rule divides the incompressible pressure and lift coefficients by the square root of one minus the square of the free-stream Mach number, so the coefficients grow as the flow speeds up. It is a linearised correction and it fails as the critical Mach number is approached and local supersonic flow appears.

Answer: C

As the free stream speeds up, the acceleration over the upper surface makes some point reach Mach one before the free stream does. That free-stream value is the critical Mach number. It is not itself where drag rises sharply; the drag-divergence Mach number lies a little above it.

Answer: D

Once the local supersonic pocket terminates in a shock, entropy losses across the shock appear as wave drag, and the adverse gradient behind it often separates the boundary layer as well. Both effects arrive together at the drag-divergence Mach number and account for the sharp rise in drag.