$(30)$ An $8$ mgd $($average flow$)$ wastewater treatment plant has a cylindrical primary clarifier that treats a wastewater with an influent solids $(x)$ concentration of $800m\frac{g}{L}$ of TSS and influent $5$day BOD$(BO{D}_5)$ of $340m\frac{g}{L}.$ The clarifier has an average solids $($TSS$)$ removal efficiency $()$ of $65\%,$ a tank diameter of $80$ feet, and a hydraulic retention time $($HRT$,t,t_D)$ of $1\mathrm{.}6$ hours. The sludge at the bottom of the tank has a solids concentration of $3\%$ TSS$.$

a$.$ Find the effluent solids concentration from the clarifier $($in $q,$ mg$/$L TSS$).$

b$.$ If the influent ultimate BOD$(L_o,BO{D}_u)$ is $425m\frac{g}{L},$ what is the BOD rate constant $($in $d^{-1})?$

c$.$ What is the overflow rate $($OR$)$ for the clarifier $($in $gp\frac{d}{f}{t}^2)?$ Is this acceptable? Justify your response based on design criteria $($last page$).$

$\backslash$table$[[k=,d^{-1}$