During a regular cleaning cycle for a cylindrical drinking water storage tank $($diameter $=70$ feet; depth $=12$ feet$),$ a technician accidently overdoses the tank with chlorine. The resulting chlorine concentration in the tank is $18m\frac{g}{L}$ and the EPA limit for chlorine in drinking water is $4\mathrm{.}0m\frac{g}{L}.$ Now, the tank is completely full of water that has a higher chlorine concentration than allowed by law. The operator decides to flush the tank with water from the distribution system which has a chlorine concentration of $1\mathrm{.}8m\frac{g}{L}$ and waste the water to the sewer until the chlorine level reaches the EPA limit$.$ You may assume that for the timeframes considered here that chlorine is conservative $($i$.$e$.,$ non$-$reactive$)$ and the tank is completely mixed. Note that this is an unsteady state system.

a$.$ If the tank is flushed at a rate of $4,000$ gpm$,$ how long $($in hours$)$ will it take to achieve the $4\mathrm{.}0m\frac{g}{L}$ concentration?

b$.$ The operator is impatient and wants to get this done in $30$ minutes. What flushing flowrate $($in gpm and cfs$)$ would be required to achieve the $4\mathrm{.}0m\frac{g}{L}$ concentration?

c$.$ Calculate the volume $($in gallons$)$ of water used $($i$.$e$.,$ wasted$)$ for Part A and Part B$.$ Is there another solution to this problem that you can suggest that might minimize the water usage? Perform some calculations to support your idea.