The tangential velocity in the hydrocyclone

Based on the Navier-Stokes equation, the paper presents the derivation of the tangential flow velocity formula in a hydrocyclone. The derivation coincides with the solution of the vorte3x filament diffusion problem. The formula reflects the influence on the tangential velocity of the geometric and energy parameters of the hydrocyclone. The graphs showing the change in speed along the height of the device are given. A graph of the effect of velocity of the viscosity of the separated medium is given. In a conical hydrocyclone with a vortex circulation ring, the tangential velocity above the ring is increased by adding the velocity component of the vortex ring. At the level of the plane of the ring is reduced considerably, below the plane in this ring it might have the opposite direction, then peripheral sped curves, when approaching the low in the axial part, are significantly increased, taking the additional effect of vortex flow. In a cylindrical hydrocyclone with axial discharge, in with the radial velocities at the wall of the apparatus equal zero, the tangential velocity at the top of the hydrocyclone is almost constant. The increase and surge in velocity is observed only at the lower discharge opening due to the impact of the vortex funnel of the drain. In a flowing cylindrical hydrocyclone near the discharge holes, the radial velocities have different directions, and the tangential velocity near them may also have a reverse direction. To eliminate this phenomenon, the absolute value of the exponential exponent must be used in the tangential velocity formula. If there are several discharge holes, the same tangential velocity near these holes will be equal if the flow through these holes is equal.