Exact relation for determining the pressure distribution on a sphere at an arbitrary mach number in a supersonic incoming flow

In order to solve stationary problems of a supersonic flow over blunted bodies by the time-dependent setting method, it is necessary to assign the initial data. The closer the initial data to the sought solution, the quicker this solution can be obtained. In many cases the rule of local spheres is used: the initial pressure on a blunted body of an arbitrary shape is taken to be the same as the pressure on a sphere with the identical angle of inclination of corresponding elements of these surfaces to an incoming flow. In this work, a simple analytical relation that allows one to determine the almost exact pressure distribution on a sphere for the whole range of Mach numbers in a supersonic incoming flow is obtained. © 2015, Pleiades Publishing, Ltd.