Hydrocyclones pressure loss

The Euler number, which is a pressure loss factor, is defined as the limit of the maximum characteristic velocity v obtained by a certain pressure drop AP across the hydrocyclone. It can be expressed as... 

Due to the vortex flow in the hydrocyclone, the static pressure in the flow increases radially outward. This centrifugal static head is primarily determined by the distribution of both, the tangential fluid velocities and the suspension densities, within the flow and it constitutes the major contribution to the total pressure loss across an operating hydrocyclone. 

When describing the pressure loss in an operating hydrocyclone, it is common practice to relate pressure drop and flow rate in the same way as for any other flow devices, using a dimensionless pressure loss coefficient. This is defined later in this chapter (equation 6.9) as the Euler number, Eu, and, for the reasons indicated above, it must not be seen as an equivalent of the friction factor in pipes because it has very little to do with friction. 

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