Problem $1(10$pt$)$: A wastewater treatment plant has a flow of $30$ mgd or $1\mathrm{.}31\frac{m^3}{s}.$ The influent BOD is $220m\frac{g}{L}.$ Assume that $25\%$ of the BOD is removed in the primary clarifiers. The plant is designed to carry $3,000m\frac{g}{L}$ of bacteria in the aeration basin.

a$)$ What is the BOD after the primary clarifiers? $($This is also the BOD concentration going into the aeration basin.$)$ Find the volume of the aeration basin in $m^3$ to meet an $\frac{F}{M}$ ratio of $0\mathrm{.}35$ mg BOD per mg of biomass per day. $($You can think of the F$/$M ratio as $0\mathrm{.}35$ day ${?}^{-1}).$

b$)$ What is the wastage rate in $k\frac{g}{?}$ day to meet a solids residence time $({}_c)$ of $8$ days?

Problem $2(10$pt$)$: Construction and demolition $($C&D$)$ debris is a significant portion of municipal solid waste. Roughly, the construction of a typical $2,200$ square foot $(194m^2)$ residential home generates $2,900$ pounds $(1,320kg)$ of wood waste and $690$ pounds $(313$ kg $)$ of cardboard waste.

a$)$ From Table $1,$ calculate the lower heating value $($LHV$)$ of wood and cardboard in $k\frac{J}{k}g.$

Table $1$: Thermodynamic Properties of Some Components of C&D Waste

$\backslash$table$[[,$HHV $(k\frac{J}{k}g),$Moisture $(\%),\%H($dry mass$)],[$Wood$,16,500,8\mathrm{.}1,5\mathrm{.}9],[$Cardboard$,15,500,12\mathrm{.}3,5\mathrm{.}5]]$

b$)$ Assume that $30\%$ of the C&D debris is recycled, and $70\%$ is incinerated to generate energy. What is the total amount of energy that can be produced from the incinerated C&D debris? Assume the waste$-$toenergy facility is $24\%$ efficient $($i$.$e$.,24\%$ of the fuel energy is converted to usable energy out$).$ For the heat value of wood$/$carboard$,$ use the average of their respective HHV and LHV$.$