Compressible Flow Fundamentals Questions and Answers

Answer: A

For a perfect gas the speed of sound is the square root of the specific heat ratio times the gas constant times the absolute temperature. Pressure and density appear only through their ratio, which the equation of state ties to temperature, so temperature is the only independent variable that matters.

Answer: B

Mach number compares the local flow speed with the local speed of sound, both evaluated at the same point. Because the speed of sound falls as the gas cools, the Mach number can change along a streamline even where the speed is constant, which is why it must always be treated as a local quantity.

Answer: C

Below about Mach 0.3 the density change across the flow field is under five per cent, small enough that treating the air as incompressible introduces little error. The figure is a convention rather than a physical threshold, and the choice of five per cent is what fixes it at roughly 0.3.

Answer: D

Stagnation temperature is defined by an adiabatic deceleration to rest, so it measures the total energy of the flow per unit mass. It does not require the process to be reversible, which is why stagnation temperature is conserved across a shock wave while stagnation pressure is not.

Answer: A

The energy equation for steady adiabatic flow without work reduces to the statement that the sum of the enthalpy and the kinetic energy per unit mass is constant, and for a perfect gas that sum is proportional to the stagnation temperature. It therefore holds whether the flow is reversible or not.

Answer: B

Stagnation pressure survives only when there is no entropy rise, so the flow must be both adiabatic and reversible. Any irreversibility, whether a shock wave, friction or mixing, reduces it. Stagnation temperature, by contrast, needs only the adiabatic condition.

Answer: C

A shock is adiabatic, so the total energy and with it the stagnation temperature are unchanged. It is strongly irreversible, however, so entropy rises and stagnation pressure drops. That loss of stagnation pressure is the real cost of a shock and the reason supersonic intakes are designed to avoid strong ones.

Answer: D

Disturbances travel outward at the speed of sound while being swept downstream at the flow speed, so the envelope they form makes an angle whose sine is the ratio of the two, that is the reciprocal of the Mach number. The angle narrows as the Mach number rises, and it is undefined below Mach one.

Answer: A

A body moving supersonically cannot send any signal ahead of its Mach cone, so the fluid outside the cone is entirely unaware of its approach and is called the zone of silence. Inside the cone, the zone of action, disturbances have arrived. In subsonic flow there is no such division, since signals reach everywhere.

Answer: B

Transonic flow is the awkward mixed regime, typically between about Mach 0.8 and 1.2 in the free stream, in which the flow accelerates past sonic speed somewhere on the body while remaining subsonic elsewhere. The mixed character is what makes it so hard to compute and why shock-induced separation appears there.