Chapter 11, Problem 11.8P

Consider the flow over a circular cylinder; the incompressible flow over such a cylinder is discussed in Section 3.13. Consider also the flow over a sphere; the incompressible flow over a sphere is described in Section 6.4. The subsonic compressible flow over both the cylinder and the sphere is qualitatively similar but quantitatively different from their incompressible counterparts. Indeed, because of the “bluntness” of these bodies, their critical Mach numbers are relatively low. In particular:

For a cylinder: $M_{cr}=0.404$

For a sphere: $M_{cr}=0.57$

Explain on a physical basis why the sphere has a higher $M_{cr}$, than the cylinder.