The linearized perturbation velocity potential equation for supersonic flow takes form of which of these partial differential equations?

Correct Answer : Option (D) :   θ_c > θ_cmax

Explaination : For a given freestream Mach number M_∞, there exists a maximum cone angle for which if we go beyond that value, the shock wave originating at the cone’s vertex gets detached. Thus, the condition for detached shock wave is θ_c > θ_cmax.

Correct Answer : Option (B) :   (θ_max)_wedge > (θ_max)_cone

Explaination : Due to the three-dimensional relieving effect, for a particular freestream Mach number, the maximum cone angle allowed is larger than the maximum wedge angle before the shock wave becomes detached.

Correct Answer : Option (A) :   Between the oblique shock and the sonic line

Explanation : The incoming flow over a cone is mostly supersonic between the surface of the cone and the oblique shock wave. Except in some cases when the half cone angle is large, flow sometimes becomes subsonic and one of the rays originating the cone’s vertex acts at the sonic line. The flow between the sonic line and the oblique shock thus remains supersonic.