For which of these flows do we need a divergent duct to increase the velocity of the flow?

Correct Answer : Option (C) :   s₁ < s₂

Explaination : The flow diffuses to a slower velocity when the flow interacts with the oblique shock waves inside the diffuser. This causes the diffuser to have a normal shock wave at the end. The entropy of the exit is therefore higher than the entropy of the inlet segment.

Correct Answer : Option (A) :   η_D > 1

Explaination : The diffuser efficiency is given by the ratio of actual total pressure ratio across the diffuser to the total pressure ratio of a hypothetical normal shock wave at test section Mach number. For a supersonic test section Mach number, the diffusers perform better than the normal shock, thus the numerator of the ratio is greater than the denominator, hence η_D > 1.

Correct Answer : Option (B) :   Rise in entropy within diffuser

Explanation : In a supersonic wind tunnel, there are two throats present. One is that of the nozzle which is known as the first throat which has sonic speed with corresponding area as A*. The second throat is that of the diffuser which is always greater than the first throat because there’s an increase in entropy due to the presence of shock waves.