$[20$ points$]$ E$-$B Problem $3\mathrm{.}5$

An industry has a two$-$stage treatment for its wastewater. The first stage is a chemostat with $=1d.$ The

second stage is a lagoon, which can be approximated as a chemostat with a detention time of $10d.$ The

kinetic parameters are

$Y=0\mathrm{.}7gVS\frac{S_a}{g}$

hat$(q)=18\frac{g}{g}VS{S}^{-d}$

$K=10$mgBO$\frac{D_L}{l}$

$b=\frac{0\mathrm{.}25}{d}$

$f_d=0\mathrm{.}9$

Assume that the SMP formation can be ignored completely. The total flow rate is $3,785m\frac{3}{d},$ and

$S^0=1,000$mgBO$\frac{D_L}{l}.$

If $x_v^0=40m\frac{g}{l},x_a^0=0,$ and all input COD and VSS are biodegradable, estimate the effluent

quality $($COD$,$ BOD $L_L,VSS)$ from the whole system. Compute the required $N$ and $P$ supplies; express

the answer in $m\frac{g}{l}$ of wastewater flow.