At present time the theory of turbulent incompressible and compressible fluids is in whole semi-empirical, and has some extent of untransparency due to complexity of Navier-Stokes equations. Applying of tunnel mathematics allow us to reduce a number of unknown quantities by three at once what is very useful for a hypersonic flow of fluid since the state equation of gas become needless. Solutions obtained by means tunnel mathematics is applicable only in some vicinity of certain z-coordinate but it is very suitable for the area of boundary layer.
This paper is a continuation of tunnel mathematics applying to the problems of fluids entrained by a rotating disk of finite radius in the area of boundary layer. Now we proceed to compressible fluid. The case of incompressible fluid was considered earlier [9]. The principles of application are similar. Especially this concerns to non-slip boundary conditions imposed on a disk surface which remain unchanged. The motion of compressible fluid entrained by a rotating disk of finite radius exhibits complex interaction pattern of main stream and compression and rarefaction simple cylindrical waves propagating in fluid. If the velocity of main stream is subsonic then these simple cylindrical waves propagate in both direction of cylindrical polar r-coordinate, if that is supersonic then they travel only in direction of increasing of r-coordinate. If the velocity of main stream becomes supersonic then forming of a shock wave is possible. Moreover, when the velocity of main stream become comparable with that of sound the considerable heating of the gas and the disk occurs and we then should to deal with the equations of motion in the boundary layer together with the equation of heat transfer in it [1].
We suppose that Reynolds number is large enough and the viscosity has in important effect on the motion of fluid only in a very small region near the disk (Prandtl`s boundary layer). We also suppose that in the subsonic case the fluid and the disk have at beginning approximately the same temperatures and the energy dissipation occurs only by means internal friction.