In this paper we propose a mathematical description of the processes of nucleation and growth of particles from a supersaturated solution of fluid and supercooled droplet -based theory of the expanding near the critical point in a channel of constant cross section and a free jet of fluid including the neighborhood of Mach disc . To account for the effect of fluctuations on the processes of hydrodynamics, mass transfer , phase equilibria and nucleation Used crossover equation of state Kiselyov. To find the fields of temperature , pressure, density and velocity of the flow system used by the Navier - Stokes equations, which is solved by a software package Ansys Fluent. Fluid flow is assumed two-dimensional , axially symmetric , stationary , viscous and compressible .