Discussion
Shock structures for flow at three different Mach numbers over a given wedge are shown in the figure below. Assuming that only the weak shock solutions are possible for the attached oblique shocks, which one of the following options is TRUE?
Answer: D
The correct order is \(M_{3} \lt M_{1} \lt M_{2}\).
For a fixed wedge angle, the weak oblique shock lies closer to the wedge surface (a smaller shock angle) as the Mach number rises, because the shock angle approaches the Mach angle, which shrinks with \(M\). As the Mach number falls, the shock angle grows until, below a certain Mach number, no attached shock can turn the flow through the wedge angle and the shock detaches into a curved bow shock standing ahead of the wedge.
In the figure, the flow at \(M_{3}\) has a detached shock, so \(M_{3}\) is the lowest. The shock at \(M_{2}\) hugs the wedge more closely than the shock at \(M_{1}\), so \(M_{2}\) is the highest. Any order that puts \(M_{3}\) above \(M_{1}\) or \(M_{1}\) above \(M_{2}\) contradicts these shapes.
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