(Solved): A railroad tank car is derailed and ruptured. It discharges \( 380 \mathrm{~m}^{3} \) of pesticide ...

A railroad tank car is derailed and ruptured. It discharges \( 380 \mathrm{~m}^{3} \) of pesticide into the Mud Lake drain. As shown in Figure \( \mathrm{P}-2-24 \), the drain flows into Mud Lake which has a liquid volume of \( 40,000 \mathrm{~m}^{3} \). The water in the creek has a flow rate of \( 0.10 \mathrm{~m}^{3} / \mathrm{s} \), a velocity of \( 0.10 \mathrm{~m} / \mathrm{s} \), and the distance from the spill site to the pond is \( 20 \mathrm{~km} \). Assume that the spill is short enough to treat the injection of the pesticide as a pulse, that the pond behaves as a flow balanced CSTR, and that the pesticide is nonreactive. Estimate the time it will take to flush 99 percent of the pesticide from the pond. Now, suppose that instead of being told that the pesticide is nonreactive, you leam that it undergoes destruction in water with a decay rate constant of \( 0.2 \mathrm{~d}^{-1} \). For this one modification of the original problem statement, determine: (i) the "treatment efficiency" of the drain between the derailed car and Mud Lake (in \%); (ii) the time required to flush \( 99 \% \) of the reactive pesticide out of Mud Lake after it has reached the lake (in days).