Equilibrium-orbit Models the Model of Barth

The model of Barth (1956) (see also Muschelknautz (1972)) is the original equilibrium-orbit model. 

We are neglecting the gas density in comparison to the solid density in the centrifugal force term (Chap. 2). Equating these forces to find the cut size 0 50 gives  

Once we have the cut size, we can fit a grade-efficiency curve through it. Barth determined a universal curve by experiment, and gave it graphically in his paper. Dirgo and Leith (1985) have fitted a functional form to this curve (see also Overcamp and Mantha (1998)) to obtain  

Equation (5.2.2) represents one functional form for representing the grade-efficiency curve (GEC). The writers own analysis on numerous commercial and laboratory cyclones reveals that the form of Eq. (5.2.2) describes some cyclone geometries quite well, especially smooth, well-designed laboratory cyclones. The exponent 6.4 is, however, a little larger than the values t3q i-cally observed in some large-scale, refractory-lined, commercial cyclones and in some poorly designed small-scale cyclones. In these latter cases, the exponent typically lies between 2 and 4. 

If one has generated GEC data on a given cyclone type, one can then plot versus In( ) using linear coordinates or simply ( — 1) versus 

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