A magnetite bearing ore is liberated in a milling circuit prior to concentration; the circuit consists

of a ball mill, a discharge sump and a slurry pump followed by a hydro$-$cyclone classifier. Fresh

ore that is fed to the mill has a moisture content of $5\%$ and consists of $85\%$ of class $1($dry basis$)$

which has a representative size of $600$ microns, $10\%$ of class $2($drep $300$ microns$),5\%$ of class $3$

$($drep $75$ microns$),$ which are mass fractions on dry basis and amounting to $180TPH.$ The $\%$ solids

in the mill are set at $75\%$ by addition of water to the mill feed. Water is also added to the sump

feeding a pump so that the feed to the hydrocyclone is set at $45\%$ solids. The hydro cyclone

performance is such that $80\%$ of class $1,40\%$ of class $2,20\%$ of class $3,$ and $15\%$ of the water

entering the cyclone reports to the oversize stream. It may be assumed that milling is a first order

rate process. This means that each size class is milled at a rate, which is proportional to the

amount of that class in the mill. The proportionality constants maybe expressed as a function of

particle size, $d($microns$).$ In this case $si=0\mathrm{.}6$ and $s1=20h_{-1}$ is referred to as the selection function,

$si=a*di.$

The breakage function for class $1$ are $0\mathrm{.}65$ to class $2.$

You are required to:

Draw a fully annotated flowsheet diagram

Calculate the minimum mass of the ore $($dry basis$)$ in the mill which ensures that the amount

of class $1$ in the circuit product is $5\%($dry basis$),$ assuming both a plug flow mill and a perfectly

mixed mill.

Construct a table showing flowrates in tph of each of the classes and water as well as the

percentages of class $1($dry basis$)$ and solids in every stream.