Influence of Radial Change in Gas Density on Nonlinear Hydrodynamic Effects in Its Flow Over a Rotating Disk

A laminar boundary layer in a gas flow near a disk rotating at a constant angular velocity under the conditions of a significant radial redistribution of the gas density is investigated. The analysis is performed on the basis of a self-similar transformation for the gas density varying according to a power law in the radial direction. Calculation of the boundary layer characteristics in the gas flow was made by the Slezkin–Targ method. The dependence of the resistance forces acting on the disk on the gas compressibility is investigated. It is shown that an increase in the radial gradient of the gas density leads to a noticeable increase in azimuthal friction forces in the boundary layer near the disk. The results obtained for an extended disk are used to estimate the intensity of the circulation flow in a rotating cylinder of finite dimensions at a small ratio of the height of the cylinder to its radius. As follows from the calculation results, an increase in the gas compressibility parameter leads to an increase in its circulation rate.