Template:Model theory (Text, Hydrocyclone, Partition Metrics)

Several metrics are provided to characterise the partition curve.

The $d_{50}$, also known as the cut or separation size, is defined as the size of a particle which has an even (50%) chance of appearing in either the underflow or overflow stream. The $d_{50}$ size is estimated via a log-linear interpolation of geometric mean size ($\ln {\bar {d}}$) against the uncorrected partition to underflow of all solids in the feed.

The Ecart Probable, or $E_{\rm {p}}$, is a measure of the deviation of a partition curve from a perfect separation, and is typically defined for size classification as:

$E_{\rm {p}}={\dfrac {d_{75}-d_{25}}{2}}$

where $d_{75}$ and $d_{25}$ are the sizes of particles which have a 75% and 25% probability, respectively, of appearing in the underflow stream. The $d_{75}$ and $d_{25}$ sizes are estimated by log-linear interpolation of geometric mean size against the uncorrected partition to underflow of all solids in the feed.

The Imperfection, $I$, is a normalised measure of the sharpness of separation, which is suggested to be independent of the magnitude of the $d_{50}$, and is typically defined for size classification as:

$I={\dfrac {E_{\rm {p}}}{d_{50}}}={\dfrac {d_{75}-d_{25}}{2d_{50}}}$