Compressible Flow Fundamentals Questions and Answers

Answer: A

To a first approximation the section responds to the component of the free stream normal to the leading edge, which is smaller than the free-stream speed by the cosine of the sweep angle. The section therefore behaves as though it were flying more slowly, and the onset of local supersonic flow is delayed.

Answer: B

For any area larger than the critical area there are two isentropic solutions, one on each side of Mach one. Which one a real nozzle achieves is settled by the back pressure: a low enough back pressure gives the supersonic branch, a high one the subsonic branch, and intermediate values put a shock in the divergent section.

Answer: C

Air is predominantly diatomic, and 1.4 follows from the translational and rotational degrees of freedom being active while the vibrational ones are largely frozen out at ordinary temperatures. Monatomic gases give 1.67, and the value for air falls below 1.4 at high temperature as vibration is excited.

Answer: D

The specific gas constant for air is the universal constant divided by the molar mass of air, giving 287 J per kg per K. The value 8.314 is the universal constant in molar units, while 1005 and 718 are the specific heats at constant pressure and constant volume, whose difference is the gas constant itself.

Answer: A

A pressure disturbance moves relative to the gas at the speed of sound, but the gas itself is moving faster than that, so the net motion of every disturbance is downstream. This is why a supersonic flow cannot be influenced by anything happening behind it, and why choked nozzles behave as they do.

Answer: B

At supersonic speed a detached bow shock forms ahead of the probe, and the entropy rise across it reduces the stagnation pressure that the probe then measures. The Rayleigh pitot formula accounts for this. Stagnation temperature is unaffected, since a shock is adiabatic.

Answer: C

The Prandtl-Glauert factor divides the incompressible coefficient by the square root of one minus the square of the Mach number, and that factor is less than one, so the compressible coefficient is the larger. Physically, compressibility exaggerates the pressure peaks over the surface.

Answer: D

The pressure difference drives a shock into the low-pressure driven gas, compressing and heating it, while a centred expansion fan runs back into the high-pressure driver gas. The region between them is the uniform test gas, and it is what makes the shock tube such a useful short-duration facility.

Answer: A

Continuity requires the product of density, velocity and area to stay constant. Above Mach one the fractional fall in density outpaces the fractional rise in velocity, so the area must increase to keep the product fixed. Below Mach one the balance is the other way round and a converging duct accelerates the flow.

Answer: B

Every isentropic ratio -- stagnation to static temperature, pressure and density, and the area ratio relative to the critical area -- is a function of Mach number and the specific heat ratio alone. Tabulating against Mach number therefore captures the whole of isentropic flow for a given gas.