Problems with non conservative

pollutant

Consider a lake having a volume of $10$ million $m^3,$ where there is a steady state of inflow and outflow at

${10}^6\frac{m^3}{?}$ day. The concentration of a chemical $x$ of the lake is $5m\frac{g}{L}.$ Due to an accident in a local

waste$-$water facility, a raw sewage containing the chemical $x$ at a concentration of $5555m\frac{g}{L}$ with daily

flowrate of $0\mathrm{.}1MCD$ was started to be discharged to the lake and continued. The K of the wastewater is

$\frac{0\mathrm{.}1}{?}$ day. Consider instantaneous mixing in the lake as soon as the sewer flow started, the outflow

became $1\mathrm{.}1$ million MCD$.$

$($a$)$ Determine what will be the concentration of $x$ in the lake after $7$ days.

$($b$)$ What will be the steady state concentration of $x.$

$($C$)$ What will be the concentration of $x$ at point $B,$ when the distance from lake to point $B$ is $2$ miles and

water velocity is $0\mathrm{.}2\frac{m}{sec}.$