$5\mathrm{.}3$ A continuous rotary drum filter, $3$ m long and $1\mathrm{.}5$ m in diameter, is used to filter a slurry containing $640$ kg of zinc sulphide $($ZnS$,$ type B$)$ per m$3$ of water. The drum operates at a fixed internal pressure of $20$kPa, a rotational speed of $6$ revolutions per hour and with $30$ per cent of the drum surface submerged in the slurry. The internal liquor level is constant at $0\mathrm{.}5$ m$.$ The filter cake is compressible and its specific cake resistance is shown in the attached graph. The filter medium resistance may be neglected.

Calculate

a$.$ the filtration pressure drop;

b$.$ the average specific cake resistance;

c$.$ the average thickness of the filter cake produced per cycle;

d$.$ the average filtration rate;

e$.$ the filter capacity based on solids collected.

Data: Solids density: $3800$ kg$/$m$3$ Filtrate density: $1000$ kg$/$m$3$

Average cake voidage: $0\mathrm{.}6$ Filtrate viscosity: $1$ cp

Atmospheric pressure: $101\mathrm{.}3$ kPa