Answers to Study Questions

1. Under what conditions do the oblique shock relations reduce to the normal shock relations?
   ans:    When wave angle b = p/2.
    
2. Under what conditions do the oblique shock relations reduce to the change in properties across a Mach wave?
   ans:    When the wave angle equals the Mach angle (b = m).
    
3. How will b vary with Mach number for a fixed turning angle (q)? Assume that the weak attached solution prevails.
   ans:    The wave angle b will decrease with Mach number for a fixed turning angle q.
    
4. For a fixed Mach number, how will the shock strength vary with the flow turning angle? Assume that the weak attached solution prevails.
   ans:    The shock strength will increase with turning angle q for a fixed Mach number.
    
5. What is the advantage of using a sequence of oblique shocks to compress a gas as opposed to a single normal shock?
   ans:    A sequence of oblique shocks can compress the gas the same amount (or more) than a normal shock but with much lower losses in total pressure.
    
6. Why is loss in total pressure synonymous with inefficiency?
   ans:    Loss in total pressure equates to an increase in entropy and thus is a direct measure of the degree of irreversibility or efficiency.
    
7. Why are supersonic jet engine inlets almost always designed to operate with oblique shocks?
   ans:    In order to minimize losses in total pressure.
    
8. Is the flow over a cone in supersonic flight two dimensional? Explain your answer.
   ans:    No. The streamlines curve between the shock and the body surface. (This is a direct consequence of the difference in area between the conical shock and the cone surface.)
    
9. Which body produces a stronger shock, a wedge or cone of the same angle? What accounts for the difference?
   ans:    A wedge will produce a stronger shock. The cone has a weaker shock since the flow has the opportunity to adjust between the shock and the cone surface.
    
10. Which body compresses the gas more, a wedge or cone of the same angle? What accounts for the difference?
    ans:    A wedge will compress the gas more. This is because the wedge produces a stronger shock as explained in the previous answer.
     
11. Why will an oblique shock almost always reflect off a solid boundary?
    ans:    In order to change the flow angle so that is is parallel to the boundary downstream of the reflected shock.
     
12. How is the turning angle specified for the reflected shock?
    ans:    The flow must be turned parallel to the boundary.
     
13. What will happen if the turning angle for the reflected shock is greater than q_max?
    ans:    An oblique shock is not possible and a normal shock will form.
     
14. What shock configuration is generated when oblique shocks of opposite families (right- as opposed to left-running) intersect?
    ans:    A refraction where the wave angles and shock strengths change downstream of the intersection point.
     
15. What shock configuration is generated when oblique shocks of the same family intersect?
    ans:    A convergence where the shocks merge together to form a single stronger shock.
     
16. Each streamline passing through a curved bow shock ahead of a blunt object corresponds to a particular point on the b-q curve. Explain how every possible solution on the b-q curve is realized by considering all streamlines from the stagnation streamline to one infinitely far away from the body.
    ans:    The stagnation streamline passes through the shock at a right angle and thus is the solution on the upper left hand corner of the b-q curve. The wave angle then decreases continually until the Mach angle is reached infinitely far away from the body. This continuous change in the wave angle corresponds to moving along the b-q curve from the upper left hand corner to the lower left hand corner.
     
17. When a detached bow shock forms, which oblique shock solution applies in the region close to the stagnation streamline?
    ans:    The strong solution.
     
18. Why is a subsonic region formed near the nose of a blunt body in supersonic flow?
    ans:    Since the wave angle is close to p/2, the strong solution with a subsonic flow downstream is found.
     
19. How will the temperature near the nose of a blunt body in supersonic flow compare with the temperature near the tip of a cone at the same flow conditions? Explain your answer. Assume that the cone leads to an attached shock.
    ans:     Since the flow is stagnant at the nose of both bodies, the temperatures would be the same if the flow is adiabatic ($T_0$=const). At high $M$, radiation from the hot gas behind the bow shock in the case of a blunt body is a source for heat transfer and will result in a drop in stagnation temperature. This will in turn lead to a lower temperature at the stagnation point
     
20. Can you think of any reason why re-entry vehicles are generally quite blunt?
    ans:    in order to create a strong normal shock and thus produce a large amount of drag that is used to slow the object.