Question

Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right. Pressure at location B is observed to be higher than that at an upstream location A. Which among the following options can be the reason?

• A. Since volume flow rate is constant, velocity at B is lower than velocity at A
• B. Normal shock
• C. Viscous effect
• D. Boundary layer separation

Hint:

In supersonic flows, only shock waves can produce a sudden pressure rise. Divergent ducts normally expand and lower pressure unless a shock forms.

Answer 1

The Correct Option is B

We are given supersonic flow entering a divergent channel. In supersonic flows, a divergent duct causes the flow to accelerate and pressure to drop. However, the observation here is that pressure at B is higher than at A, which contradicts the behavior of smooth isentropic supersonic expansion.
Step 1: Identify what can increase pressure in a supersonic flow.
A sudden rise in pressure in a supersonic flow can occur only if there is a shock wave. For a normal shock, the supersonic flow transitions to subsonic flow and large increases in pressure, temperature, and density occur.
Step 2: Evaluate the options.
(A) Constant volume flow rate does not apply here because compressibility is dominant in supersonic flow.
(C) Viscous effects cause small pressure losses, not sudden pressure rise.
(D) Boundary layer separation typically reduces flow momentum but does not create a sharp pressure rise like observed.
Step 3: Conclude the correct mechanism.
The only mechanism capable of causing a large sudden pressure increase in a supersonic flow is a normal shock, which can occur inside a divergent duct. Thus, the higher pressure at B is due to a shock forming between A and B.
Final Answer: Normal shock