In Problem 11.8, the critical Mach number for a circular cylinder is given as Mcr = 0.404. This value is based on experimental measurements, and therefore is considered reasonably accurate. Calculate Mcr for a circular cylinder using the incompressible result for Cp and the Prandtl-Glauert compressibility correction, and compare your result with the experimental value. The Prandtl-Glauert rule is based on linear theory assuming small perturbations, and therefore we would not expect that it would be valid for the case of flow over a circular cylinder. Nevertheless, when you use it to make this calculation of Mcr , you will find your calculated result to be within 3.5 percent of the experimental value. Interesting.
Data form Problem 11.8:
For a cylinder: ................ Mcr = 0.404
For a sphere: ................. Mcr = 0.57