Template:Model theory (Text, Reid-Plitt Efficiency Curve)

The Reid-Plitt expression for corrected partition to underflow, $E_{\rm {uc}}$ (frac), is:

$E_{\rm {uc}}({\bar {d}}_{i})=1-\exp \left[-\ln 2\left({\dfrac {{\bar {d}}_{i}}{d_{50{\rm {c}}}}}\right)^{m}\right]$

where:

• $i$ is the index of the size interval, $i=\{1,2,\dots ,n\}$, $n$ is the number of size intervals
• ${\bar {d}}_{i}$ is the geometric mean size of particles in size interval $i$ (mm)
• $d_{\rm {50c}}$ is the corrected size at which 50% of the particle mass reports to underflow and 50% to overflow (mm)
• $m$ is the sharpness parameter that determines the steepness of the partition curve (-)

The actual partition to underflow , $E_{\rm {ua}}$ (frac), is computed as:

$E_{\rm {ua}}({\bar {d}}_{i})=E_{\rm {uc}}({\bar {d}}_{i})+R_{\rm {f}}(1-E_{\rm {uc}}({\bar {d}}_{i}))$

where $R_{\rm {f}}$ is the fraction of fines and/or feed liquids split to the underflow (frac).