Problem No$.1(30$ points$)$

An activated sludge process is treating wastewater with the average daily flow of $2$ MGD $.$ The volume of aeration basin is $750,000$ gallons. The influent wastewater entering the aeration basin has an average $BO{D}_5$ of $180m\frac{g}{L},$ and the activated sludge process is designed to remove $95\%$ of $BO{D}_5.$ There are $20m\frac{g}{L}$ of biomass in the effluent, $2000m\frac{g}{L}$ of biomass in the aeration basin, and $8000m\frac{g}{L}$ of biomass in the recycle stream. The biomass has a yield coefficient of $0\mathrm{.}5$ g biomass $\frac{?}{gBO{D}_5}$ and a decay constant of $0\mathrm{.}02da{y}^{-1}.$

$($a$)$ Determine the mean cell residence time $($MCRT$)$ of the process $($in days$)$

$($b$)$ Calculate the wasting flow rate $(Q_w)$ needed to maintain the calculated MCRT $($in MGD$).$

$($c$)$ Calculate the mass of "wasted" activated sludge disposed of each day $($in lb$/$day$)$