A waste material from pollution control, containing copper oxide, underwent a leaching process with sulfuric acid, resulting in a slurry with a pulp density of $2\mathrm{.}20$ and mass fraction of solid equal to $61\mathrm{.}54\%.$ The concentration of $CuS{O}_4$ in the solution phase of the slurry was measured to be $0\mathrm{.}160.$ This slurry underwent counter$-$current washing in three stages as shown in Figure $1$ with water. The volume fraction of liquid in the slurry remained consistent throughout the process. The volumetric flow rate of the liquid used for washing was equal to the volume of wash water. How much wash water is required to ensure that the discharge slurry contains only $1\mathrm{.}0\%$ of the original copper content? The solids in the slurry have a density of $5\mathrm{.}0k\frac{g}{m^3}.$

Based on your findings complete the table provided below and draw a graph showing the effect of the water flow rate on number of stages and the recovery of $CuS{O}_4.($You need to draw a graph in which $y$ axis represents the flow rate of the wash water $($or concentration of $CuS{O}_4$ in slurry$)$ and $x$ axis shows the number of stages.

Data. The approximate specific gravity of $CuS{O}_4$ solutions is: $Sp.Gr$ of $CuS{O}_4$ solution$==1+w_{\text{C}\text{u}\text{S}\text{O}}$ where $w$ is the mass fraction of $CuS{O}_4.$

Hint: use $1000L$ of feed slurry as your basis.

Figure $1.$ Flowsheet for washing leached $CuS{O}_4$ from insoluble residue. Double arrows refer to slurry flow, and single arrows to solution flow.

Table $1.$ Mass balance for $CuS{O}_4$ washing circuit $(kg)$

$\backslash$table$[[,$M$/$S I,M$/$S II$,$M$/$S III$],[$mass fraction of CuSO $4,,,],[$mass of wash liquid out,,,$],[$mass of CuSO $4$ in wash liquid,,,$],[$mass of slurry liquid out,,,$],[$mass of CuSO $4$ in slurry liquid,,,$],[$mass fraction of CuSO $4,,,]]$