Q$2.$ A river is merged with an effluent flow of a wastewater treatment plant. Conditions are given below.

A wastewater treatment plant designed for a community of $30,000$ people has a flow of $100ga\frac{l}{?}$ person$/$day and a BOD of $0\mathrm{.}2lb\frac{s}{?}$ person$/$day$.$ The upstream characteristics of the receiving waters are as follows:

Flow $=15cfs$

$D.0.=8\mathrm{.}3m\frac{g}{L}$

Temperature $=20C$

$()s()-1()-1$

The treated effluent has a D$.$O$.$ of $5m\frac{g}{L},$ a temperature of $20C,$ and no ammonia.

The minimum stream D$.$O$.$ occurs $2\mathrm{.}88$ days after the effluent wastewater is discharged.

Assume that saturation DO at $20C$ is $9\mathrm{.}2m\frac{g}{L}.$

Determine the followings: $70$ Points

$($a$)$ Determine the percentage reduction of the $5-$day BOD by the plant.

$($b$)$ Determine the minimum dissolved $O_2$ in the stream.

Hint for procedures:

$BO{D}_5$ to the plant: please calculate. If correct, around $240m\frac{g}{L}.$

$BO{D}_5$ treatment $=BO{D}_5$ reduction in treatment plant $=$ unknown removal$\%($goal$)$

$BO{D}_5$ from the plant $=BO{D}_5$ in effluent $=BO{D}_5$ discharged $=$ unknown $m\frac{g}{L}($goal$)$

Mixing two streams $($river and plant$)$

$BO{D}_5^{\text{'}}$ after mixing $($a$)BO{D}_5$ of river flow $($known$)$ and $($b$)BO{D}_5$ from the plant $($unknown$)$

Then flow over time and river: time $\text{'}$ and $($:$BO{D}^{\text{'}}{?}^{\text{'}}\}$ day as $t^{**}$ From the $t^{**}$ equation, determine $Li=BO{D}_u^{\text{'}}$; then from BOD decomposition equation, determine $BO{D}_5\text{'}.$

From $BO{D}_5$ mass balance at the mixing point, determine $BO{D}_5$ from the plant In Plant: $BO{D}_5$ from $240$ to $xxm\frac{g}{L}$dots.$YY\%BO{D}_5$ removal.

If you calculate correctly, answer for $($a$)$ is around $85\%BO{D}_5$ reduction in the plant.