You have obtained the following flux results for sludge thickening:

$\%$ solids Solids Flux, kg$/$m$2/$day

$0\mathrm{.}5290$

$1\mathrm{.}0250$

$1\mathrm{.}5150$

$2\mathrm{.}070$

$2\mathrm{.}545$

$3\mathrm{.}035$

$3\mathrm{.}525$

$4\mathrm{.}020$

$4\mathrm{.}515$

$5\mathrm{.}012$

a$.)$ Plot the flux curve

b$.)$ Calculate the Limiting Flux $($kg$/$m$2/$d$)$ and the underflow velocity $($m$/$d$)$ for an underflow concentration of $4\%$

c$.)$ What is the required surface area if the total load is $1000$ kg$/$d$?$