View source for Template:Model theory (Text, Whiten-Beta Efficiency Curve)

:<math>E_{{\rm oa}i} = C \left [ \dfrac{ \left (1 + \beta \beta^*  \dfrac{\bar d_i}{d_{\rm 50c}} \right )(\exp (\alpha) - 1)}{\exp \left ( \alpha \beta^* \dfrac{\bar d_i}{d_{\rm 50c}} \right ) + \exp (\alpha) - 2} \right ]</math>

where:
* <math>i</math> is the index of the size interval, <math>i = \{1,2,\dots,n\}</math>, <math>n</math> is the number of size intervals
* <math>E_{{\rm oa}i}</math> is the fraction of particles of size interval <math>i</math> in the feed reporting to the overflow stream (frac), <math>0 \leq E_{{\rm oa}i} \leq 1</math>
* <math>\bar d_{i}</math> is the [[Conversions|geometric mean size]] of particles in size interval <math>i</math> (mm)
* <math>d_{\rm 50c}</math> is the ''corrected'' size at which 50% of the particle mass reports to underflow and 50% to overflow (mm)
* <math>C</math> is the fraction of feed liquids split to overflow (frac)
* <math>\alpha</math> is a parameter representing the sharpness of separation
* <math>\beta</math> is a term introduced to accommodate the so-called ''fish-hook'' effect, and controls the initial rise in the efficiency curve at finer sizes
* <math>\beta^*</math> is computed to ensure the Whiten-Beta function preserves the definition of <math>d_{\rm 50c}</math> in the presence of the fish-hook, i.e. <math>E = 0.5 C</math> at <math>d_{\rm 50c}</math>