GATE 2022 ME (ME2) – Question 24
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?
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Correct answer: (B) Normal shock
Explanation
In a **diverging** duct the area increases with distance.
**Isentropic flow.** For supersonic flow ($M>1$) the area-velocity relation is
$$\frac{dA}{A}=(M^2-1)\frac{dV}{V},$$
so increasing area gives increasing velocity and, by Bernoulli-type reasoning, **falling pressure**. A pressure rise from A to B therefore cannot come from smooth supersonic flow.
**A normal shock** is the one mechanism that raises static pressure: the flow suddenly drops to subsonic speed and the pressure and temperature rise.
- Option A is wrong, because a velocity drop with constant volume flow does not describe supersonic flow in a diverging duct (and the area changes).
- Viscous effects and separation can raise the pressure only in thin regions near the wall and are not the fundamental reason.
Answer: **normal shock** (B).