Question

Which one of the following statements is not true for a supersonic flow?

• A. Over a gradual expansion, entropy remains constant
• B. Over a sharp expansion corner, entropy increases
• C. Over a gradual compression, entropy remains constant
• D. Over a sharp compression corner, entropy increases

Hint:

Entropy increases across shock waves and non-isentropic expansions.

Answer 1

The Correct Option is A

In the realm of aerospace engineering, understanding the characteristics of supersonic flow is crucial. Supersonic flow refers to the movement of a gas at a velocity greater than the speed of sound in that gas. To evaluate which statement is not true for supersonic flow concerning entropy changes, consider the following insights based on fluid dynamics:

• Entropy and Expansion: In a supersonic flow, expansion can be either gradual or sharp. For a gradual expansion, an isentropic process (where entropy remains constant) is typically applicable when there is no shock wave. However, real-world gradual expansions are often slightly irreversible, which may lead to a minimal increase in entropy.
• Entropy and Compression: For a gradual compression, the process is generally not isentropic because even small compressive shocks or boundary layer effects cause an increase in entropy.
• Sharp Expansion and Compression Corners: Sharp changes, whether expansion or compression, usually involve shock waves or rapid changes in flow direction, leading to a definite increase in entropy due to their highly irreversible nature.

Given this understanding, the statement "Over a gradual expansion, entropy remains constant" is not entirely true as even slight irreversibility in practical scenarios results in an increase in entropy. By comparison, the other statements accurately reflect the behavior of entropy under sharp expansions and compressions.

Scenario	Entropy Change
Gradual Expansion	May slightly increase (not always constant)
Sharp Expansion Corner	Increases
Gradual Compression	Generally increases
Sharp Compression Corner	Increases

Therefore, the correct choice that is not entirely true for supersonic flow is: "Over a gradual expansion, entropy remains constant".