$(55)3.$ A wet ball milling operation is used to grind crude ore into smaller particles of a desired size classification. As shown in the diagram below a slurry of crude ore and water $($Stream $1)$ is fed into a ball mill along with a recycle stream $($Stream $2).$ The mill product $($Stream $3)$ is sent to a mechanical classifier where additional water $($Stream $4)$ is added. Smaller particles remain suspended in the water and exit the classifier as a fine product $($Stream $5),$ while larger particles settle out and are taken from the bottom of the classifier to be recycled back to the mill for additional grinding. The liquid$-$to$-$solid mass ratio is $1\mathrm{.}3(1\mathrm{.}3$ tons water for each $1\mathrm{.}0$ ton of ore$)$ for the feed slurry, $0\mathrm{.}5$ for the recycle, $0\mathrm{.}7$ for the mill product, and $3\mathrm{.}1$ for the fine product. If the mill receives $250$ tons of dry crude ore per day, calculate:

a$)$ the daily fresh water requirement $($mass flowrate of stream $4)$

b$)$ the mass flowrate of the recycle stream

c$)$ the component mass flowrate of ore in the mill product stream

Stream $4$:

Fresh Water

Stream $1$: