DATA and assumptions:

$Q_R=20m^{3}h{r}^{-1}$

$Q_w=1m^{3}h{r}^{-1}$

$V=400m^3$

Steady state $B{D}_w=20mg{L}^{-1}$

BOD concentration in river upstream of the lake is negligible.

DO concentrations are near saturation and do not change over time or space

BOD in the river and lake decays according to the typical first order reaction:

BOD$+DO$ products $,R=k[BOD]$ where $k=0\mathrm{.}12da{y}^{-1}$

$($a$)$ Calculate the steady state BOD concentration in the lake

$($b$)$ The wastewater treatment plant operators make a

change in the treatment process and the plant effluent

BOD concentration increases as shown in the graph at

right, and reaches a new steady state concentration of

$150mg{L}^{-1}.$ Derive an equation for the BOD

concentration in the lake as a function of time, after

the process modification was made.

$($c$)$ Graph the BOD concentration in the lake, as a function of time. Please also indicate important

values that define the shape of the graph, such as the concentration at $t=0,$ the new steady state

value, and the characteristic time to reach that new steady state. Label your axes and provide

units for the values on the axes.