### Gladkov S. Bogdanova S.

## On the distribution of pressures at the frontal surface of rotating disks with different angular velocity in the gas

### Reporter: Gladkov S.

In this communication the disk was considered and both the frontal surfaces of it rotate at different, but constant angular velocities in opposite directions, in a gas continuum. Under condition of gas compressibility it was found the common decision of system of both the continuity equation and Navier-Stokes equation. Also, it was calculated the distribution of all three components of velocity as the function of radial and axial coordinates. It was solved the stationary problem for the constant - property flotation on both sides of the two halves of the plane of the disk, the angular speed of which omega_{1} and omega_{2} . It was calculated the distribution of pressures on both sides of the disk and was shown some difference of pressures, which can lift or drop the disk. It was shown that the tangent velocity to surface of the disk depends on the coordinates as a function of superposition of the Bessel’s function and the both frequency of rotating like as a velocity of components v_{z} and v_{r} . This decision was find due to the solvation of nonlinear differential system of equations, where we have to account the dependence of the density gas from coordinates. Using the formulas of transition, it was calculated the distribution of pressures on both sides of the rotating surface and was shown its difference. Note, that in classical paper by T. Karman the problem of distribution of velocities and pressures of the rotating disk was solved, but only for the incompressible liquid. See [1] more for learning details.

Reference

[1]. L. D. Landau, E. M. Lifshitz. Hydrodynamics. V. 6. М.: Nauka. 1988, p. 112.

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