Energetics of centrifugal separation

It is not easy to accnrately calculate the energy consumption of centrifugal separation. The general idea is that the energy of the rotational flow, which is the sum of the kinetic energy and the pressure energy, is lost in the apparatus. These are substantial energy consumptions. 

The total energy integrated over the hquid volume, which is lost at each operation, is  

It is proportional to the maximum velocity of rotation and the volume of liquid. 

In a hydrocyclone, the flow is of the vortex type. The rotational velocity (equation [17.18]) and pressure (equation [17.20]) in the irrotational zone enable the calculation of the rotational energy of a partiole sitnated at radial distance r from the rotation axis  

This quantity is independent of the radius r. It is necessary to know the pressure po at the center of the vortex in the hydrocyclone in order to calcnlate the power of the dissipated rotational energy  

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