$[30$ points$]$ Consider an outfall that is discharging raw sewage at a $4\frac{m^3}{s}.$ The

sewage is going into a river which is $20$ m wide, $15$ m deep and flowing at a rate of

an ultimate BOD of $5m\frac{g}{L}.$ The water in both the river and the outfall can hold $10$

$m\frac{g}{L}$ of $O_2$ at saturation, but the actual $O_2$ just downstream of the outfall is $9m\frac{g}{L}.$

The deoxygenation constant $(k_d)$ is determined to be $0\mathrm{.}25$ day $,$ and the reaeration

constant $(k_r)$ is $0\mathrm{.}60da{y}^{-1}*kr$

Sketch a plot of the dissolved $O_2$ concentration using distance from the outfall as the

x $-$axis. Be as quantitative as possible. Calculate and indicate on your graph the

following values:

$D_0$

$[O_2{]}^s$

Distance to the critical point downstream

$O_2$ at the critical point