Velocity profiles for the isotropic turbulent flow of a viscous-linear incompressible fluid were obtained for a cylindrical flat-bottomed hydrocyclone by solving the Navier-Stokes equations. The flow is assumed axially symmetric and steady and the inflow to the hydrocyclone is assumed to occur through a ring in the upper portion of the cylinder. An asymptotic expansion of the stream function and the circulation in terms of the Rossby number is used. The Rossby number is proportional to the square of the ratio of radial flow per unit volume and the circulation in the outer radius of the cyclone. A perturbation series for small Rossby number is inserted into the motion equations. When the leading order term is considered, the solution gives a radial and tangential velocity depending on the radial coordinate only and the axial velocity as function of the radius and depending linearly on the axial coordinate. In addition to the leading term, when the first order term is considered, the solution gives a radial, tangential and axial velocity depending on the radial and axial coordinates. Predicted velocity profiles compare well with measurements with laser Doppler velocimetry on a 100 mm diameter cylindrical fiat-bottomed hydrocyclone.
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