$(12$ points$)$ On January $9,2014,$ crude $4-$Methylcyclohexanemethanol $($MCHM$),$ a coal processing chemical, leaked from holding tanks owned by Freedom Industries into the Elk River near Charleston, WV$,$ which was flowing at $3,000f\frac{t^3}{s}.$ The river at this flow

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CE $/$ ENVE $347-$ Fall $2024$

rate averages $5$ feet in depth and $60$ feet in width $($assume a rectangular channel$).$ Approximately $3,500$ gallons of MCHM at a concentration of $90,000ppm$ entered the river each hour for the duration of the spill. The Kanawha Valley Water Treatment Plant, which provides water to over $300,000$ people, is located $1\mathrm{.}5$ miles downstream from the site of the spill and was continuously withdrawing water from the Elk River on the day of the spill to treat for drinking water.

a$.$ Assuming the river quickly became well mixed, what was the concentration of MCHM in the Elk River just downstream from the site of the spill $($in ppm$)?$

b$.$ From the time the MCHM first entered the Elk River, how long did it take to reach the intake for the Kanawha Valley Water Treatment Plant?

c$.$ If MCHM degrades at a rate of $3\mathrm{.}93{10}^{-5}mg{L}^{-1}mi{n}^{-1},$ what was the concentration at the intake for the treatment plant? Does substantial degradation of the contaminant occur as it travels from the site of the spill to the treatment plant intake?