Problem $1$: $(25$ points$)$ A water park has a $2\mathrm{.}0{10}^{4}L$ water tank with two pipes $($A and B$)$ supplying water in$,$ and two pipes $(C$ and $D)$ carrying water out. Pipe $A$ is the chlorine supply, providing $1\mathrm{.}0{10}^3\frac{L}{m}in$ at a chlorine concentration of $6\mathrm{.}0m\frac{g}{L}.$ Pipe $B$ comes from one of the waterslides at $2\mathrm{.}0{10}^3\frac{L}{m}in$ flow, but a degraded chlorine concentration of $2\mathrm{.}0m\frac{g}{L}.$ Pipes C and D evenly split the flow out to two other water slides. The chlorine decays via a first$-$order reaction with $k=\frac{0\mathrm{.}10}{h}r.$

Assuming the tank is at steady state, there is no source of chlorine within the pool, it is completely mixed, and conservative with respect to flow, calculate the chlorine concentration in pipes C and D $[$mg$/$L$].$

a$.(8$ points$)$ Draw a conceptual diagram showing the control volume, flows, concentrations, and any other requisite data.

b$.(15$ points$)$ Solve. List all equations and assumptions. Show all work.c$.(2$ points$)$ What can the water park operators do to ensure that the concentration in the the two waterslides is exactly $4m\frac{g}{L}?$ Briefly explain one approach.

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Answer each question $($Parts a$,$ b$,$ and c$)$ and show full work. This is a mass balance equation for environmental science.