Euler number, hydrocyclones

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... 

Whilst with larger hydrocyclones the resistance coefficient called the Euler number, Eu, depends on the Reynolds number, for very small hydrocyclones (such as the one used in this work) it is practically constant. We felt justified, therefore, in using such a combination of Eu with Stk (instead of a straight product of Stk-Eu as derived from first principles, equation 6.12), which would obviate the need to measure flow rates on the rig and, therefore, greatly simplify the testing procedure. 

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. 

Despite the very different approaches and assumptions, the forms of correlations obtained by the equih-brium orbit theory and residence time theory are similar. For specific hydrocyclone designs, both theories provide their respective empirical equations for determining the cut size and pressure drop in terms of three dimensionless groups, the Stokes number at cut size, Stkso, the Euler number, Eu, and the Reynolds number, Re (see discussions in Sec. 5.4 below) ... 

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