Separation by a hydrocyclone of particles that are denser than the fluid

Separation by a hydrocyclone of particles that are denser than the fluid 

As the rotational flow is of vortex type (equation [17.18]), with the circulation given by [17.24], we infer  

The separation condition remains Urp Rc,H) 0 when there is one discharge flow per nozzle, but the flow rates Qj, and need to be known in order to e q)ress the criterion in a form similar to [17.71]. 

Relation [17.71] gives the separation condition for any particle of size d introduced into the hydrocyclone. The equality determines the maximiun size Jmax of the particles so that all of them flow out through the spigot. By comparison with the results obtained for centrifuge decanters (equation [17.52]) and separators (equation [17.59]), it is found that the larger the flow rate is, the more effective the separation performed by a hydrocyclone will be. In the previous two cases, the flow rate should not exceed a certain value. This remarkable result, which seems smprising at first glance, since the residence time diminishes when the flow rate increases, is explained by the fact that the intensity of the vortex increases with the squared flow rate. 

The main benefit of hydrocylones is their simplicity. In mechanical terms, they do not consist of any moving parts. However, these apparatus cause a substantial head loss, since the energy of rotation is lost. Moreover, the separation characteristics of a hydrocyclone are closely dependent on the head losses at the 

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