A hydrocyclone with diameter of $0\mathrm{.}900m$ is used to classify a minerals slurry at a feed flow rate of $75\mathrm{.}6m^3$ per hour and the volumetric split $S$ is $0\mathrm{.}74.$ The Plitt model was used to evaluate the performance of the hydrocyclone. The simplified equations for the Plitt model are among the equations given in the formulae sheet.

$($Note: The flow rate for the Plitt model is in litres$/$min and the cyclone diameter is in $cm).$ The size distribution of the feed is given Table $1$ and if required assume the specific gravity of solids to be $3\mathrm{.}2$ and that of slurry $($pulp$)$ to be $1\mathrm{.}455.$ The sharpness of separation for of the cyclone $m=2\mathrm{.}5.$

Using the Plitt model and feed size distribution data determine $($show sample calculations for the row involving $53$ micrometres size data$)$:

a$)$ the $d_{50c}$ and $R_f$ for the cyclone

$4$

b$)$ the actual, corrected, and reduced partition numbers for the cyclone

$9$

c$)$ If the two feed size distributions labelled $($A$)$ and $($B$)$ are used what difference would you expect in the $d_{50c}$ from Plitt model and why?

$3$

d$)$ Name four ways in which you could improve the efficiency of the hydrocyclone.

$4$

Table $1$: Design data set for $0\mathrm{.}900m$ cyclone

$\backslash$table$[[\backslash$table$[[$Size$,],[$Micrometers$]],\backslash$table$[[$Feed size distribution,$],[\%$ retained $($A$)]],\backslash$table$[[$Feed size distribution,$],[\%$ retained $($B$)]]],[212,2,1\mathrm{.}4],[150,12\mathrm{.}4,6\mathrm{.}8],[106,22\mathrm{.}3,13\mathrm{.}8],[75,25,28\mathrm{.}5],[53,16\mathrm{.}1,21\mathrm{.}1],[38,10\mathrm{.}6,12\mathrm{.}6],[25,5\mathrm{.}5,7\mathrm{.}5],[0,6\mathrm{.}1,8\mathrm{.}3]]$