$4.$ A batch settling column analysis is performed on a surface water sample containing an initial SS concentration of $\backslash (597\backslash$mathrm$\{$mg$\}/\backslash$mathrm$\{$L$\}\backslash ).$ The settling column is $125$ mm in diameter, $3\mathrm{.}0$ meters tall and has sampling ports located at $\backslash (0\mathrm{.}5,1\mathrm{.}0,1\mathrm{.}5,2\mathrm{.}0\backslash ),$ and $2\mathrm{.}5$ meters from the water surface. SS concentrations at various sampling times are listed in the table below. Make a plot of overall $\backslash \%$SS removal versus overflow rate and find the design overflow rate for $\backslash \%$ suspended solids removal.

$\backslash$begin$\{$tabular$\}\{$cccccc$\}$

$\backslash$hline & $\backslash$multicolumn$\{5\}\{$c$\}\{$ Suspended Solids Remaining, mg$/$L $\}\backslash \backslash$

$\backslash$cline $\{2-6\}$ Depth, $\backslash (\backslash$mathbf$\{$m$\}\backslash )$ & $\backslash (\backslash$mathbf$\{10\}\backslash$mathbf$\{$~ m i n$\}\backslash )$ & $\backslash (\backslash$mathbf$\{20\}\backslash$mathbf$\{$~ m i n$\}\backslash )$ & $\backslash (\backslash$mathbf$\{30\}\backslash$mathbf$\{$~ m i n$\}\backslash )$ & $\backslash (\backslash$mathbf$\{40\}\backslash$mathbf$\{$~ m i n$\}\backslash )$ & $\backslash (\backslash$mathbf$\{50\}\backslash$mathbf$\{$~ m i n$\}\backslash )\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{0.5\}\backslash )$ & $394$ & $298$ & $227$ & $179$ & $119\backslash \backslash$

$\backslash (\backslash$mathbf$\{1.0\}\backslash )$ & $465$ & $358$ & $299$ & $239$ & $179\backslash \backslash$

$\backslash (\backslash$mathbf$\{1.5\}\backslash )$ & $490$ & $400$ & $340$ & $281$ & $221\backslash \backslash$

$\backslash (\backslash$mathbf$\{2.0\}\backslash )$ & $507$ & $418$ & $358$ & $316$ & $263\backslash \backslash$

$\backslash (\backslash$mathbf$\{2.5\}\backslash )$ & $513$ & $436$ & $376$ & $376$ & $287$

$\backslash$end$\{$tabular$\}$