Question $3(12$ marks$)$

A hydrocyclone is fed with slurry and at steady state the operating conditions:

Feed solid mass flow rate: $495\frac{t}{h}$

Feed solid weight fraction: $40\%$

Underflow solid mass flow rate: $366\frac{t}{h}$

Underflow solid weight fraction: $68\mathrm{.}26\%$

The size analysis of samples from each stream are given in Table below.

$($a$)$ Calculate partition coefficient for each size.

$($b$)$ Calculate corrected partition coefficient for each size.

$($c$)$ Plot partition curve and corrected partition curve, determine $d_{50},d_{50c},$ and sharpness of cut I

$($based on the corrected curve$).$