Please rather than giving instructions on how to solve the problem actually solve it$.$

$($a$)$ Using the following batch flux plot data, graphically determine the limiting feed

concentration for a thickener of area $300m^2$ handling a feed rate of $0\mathrm{.}03\frac{m^3}{s}$ and with

an underflow rate of $0\mathrm{.}015\frac{m^3}{s}.$ Determine the underflow concentration and overflow

concentration under these conditions. Sketch a possible concentration profile in the

thickener clearly indicating the positions of the overflow launder, the feed well and the

point of underflow withdrawal $($neglect the conical base of the thickener$).$

$($b$)$ Under the same flow conditions as above, the concentration in the feed increases to

$110\%$ of the limiting value. Estimate the solids concentration in the overflow, in the

underflow, in the section of the thickener above the feed well and in the section below

the feed well.