Dimensionless Scale-up of Equipment

In the Stokes number relationship x is the particle relaxation time defined as 

In Equations 10.114 through 10.116 the components have already been defined, that is, v is the characteristic velocity of flow in the separator, D is 

In gravity settling tanks, assuming low feed solids concentration and plug flow through a vessel of plan area A, the following relationship for its grade efficiency can be derived  

Equation 10.119 represents the very best performance of a settling tank. Such performance should be considered theoretical or ideal, and so it may not be totally applicable due to nonideal distribution of the flow, end effects, turbulence, and some others effects. However, it can be used as a preliminary approach to select the minimum area of the tank required to obtain a given cut size. 

When Equation 10.120 holds, the cut size and the overall separation efficiency, in both cases, should be the same. Equation 10.120 can be used for sizing centrifuges from laboratory tests, or for predicting capacities of existing machines. 

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