The following data were collected in the laboratory on the filtration of $CaC{O}_3$ sludge through a washing plate and

frame filter press. After assembling the press, the data were taken by noting the time required for the collection of

succeeding $5-1$b batches of filtrate.

a$.$ If the total time required for draining, dumping and reassembling the filter is $15$ minutes each cycle and the

cake is to be washed with volume of water equals to $25\%$ more than the square of the volume of filtrate

collected, determine the volume of filtrate that would be collected every $24$ hours at optimum operating

cycle.

b$.$ If a rotary vacuum filter is suggested for the same sludge. The filter is to consist of a cylindrical

drum $5$ feet in diameter and $5$ feet in width, rotating at $8$ minutes per revolution, and immersed in

an open tank of the sludge at a depth of one$-$third $(\frac{1}{3})$ of the drum diameter. The pressure inside the

drum is $4\mathrm{.}7$ psia. Assuming the resistance of the filter itself to be negligible, how much time will

be required to produce $250f{t}^3$ of filtrate?

c$.$ If a basket centrifugal filter is suggested for the recovery of the same calcium carbonate sludge

using a filtration rate same as the rotary drum filter and other pertinent data given below, determine

the height of the centrifugal basket.

Assume that the cake is incompressible, the filter medium resistance is negligible and the

liquid surface corresponds to the filter cake surface with a cake thickness of $3cm.$