## Eq

and the total coarse efficiency as:

so that Ef + Ec = 1. The total efficiency has no value in determining the effectiveness of a classification process, because it only defines how much of the feed ends up in one or other of the two outlet streams, not how much of the desired material ends up in the correct outlet stream. To discover this, it is necessary to determine the grade efficiency, which is independent of the feed, provided that the classifier is not overloaded:

Grade efficiency at si-iex =

Amount of desired material Ln product of size x Amount of desired material in feed of size x

Coarse grade efficiency, <7<.(.i), at sizex =

Amount of coarse product of size x Amount of feed of size x

Similarly, the fine grade efficiency is defined as:

These equations can be used to evaluate the grade efficiency of a classifier, provided that the total efficiency and the size distribution of two of the streams are known. Results are usually plotted as grade efficiency curves of Gc(x) or Gfx) against x. The classifier separates on the basis of Stokes diameter, so it is preferable to carry out the size determinations on the same basis.

The grade efficiency curve is best determined by plotting Fc(x) against F(x) and differentiating (Fig. 8b), because this allows experimental errors to be smoothed out. The tangent at Fc(x) = 100% in Fig. 8(b) has a slope of dFc(x)/dF(x) = 100/60; hence, Ec = 60/100. Because this tangent merges with the curve at x = 58 /'m. all particles coarser than 58 /'m are collected with the coarse fraction. Differentiating this curve at selected values of F(x) and multiplying by 60 gives Gc(x), the relevant diameters being determined from size distribution data. The 50% size on the grade efficiency curve is called the equiprobable size because particles of this size have an equal chance of being in either the coarse or the fine stream. Figure 8(a) shows how the feed is split between the coarse and fine fractions, i.e., Ffx) + Fc(x) = F(x).

The grade efficiency is often expressed as a single number. This number is known as the sharpness index, and is a measure of the slope of the grade efficiency curve:

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