Consider a wedge with a half-angle of 10° flying at Mach 2. The oblique shock wave angle \beta is 38.4 10 41.5 39.3
The Correct Answer and Explanation is:
Correct Answer: 39.3°
Explanation:
In compressible flow, when a supersonic flow encounters a wedge, an oblique shock wave forms ahead of the wedge. The angle this shock makes with the incoming flow is called the shock wave angle (β). The wedge deflects the flow through a certain angle, called the deflection angle (θ). For this problem:
- Mach number (M) = 2.0
- Wedge half-angle (θ) = 10°
- We are to find the corresponding shock wave angle (β)
To solve this, we use the θ–β–M relation from oblique shock theory. This relation is complex and usually solved numerically or with charts or computational tools, but general trends and approximations help us identify the correct answer from multiple choices.
The θ–β–M relation shows that for a given Mach number and deflection angle, there is a unique shock angle for the weak shock solution, which is the physically realistic case (strong shocks are rare in external flows). For Mach 2 and a deflection angle of 10°, the oblique shock angle typically falls in the high 30s.
Let’s test the options:
- 38.4°: Slightly low for a 10° wedge at Mach 2
- 10°: This is the wedge angle, not the shock angle
- 41.5°: Slightly high
- 39.3°: Most accurate
Using standard oblique shock tables or computational methods, the shock angle β for M = 2 and θ = 10° is approximately 39.3°, which matches the weak oblique shock solution.
Therefore, the correct shock wave angle is 39.3°. This ensures the flow turns appropriately to follow the wedge surface after the shock, maintaining physical realism and flow continuity in supersonic conditions.
