The wastewater treatment pond in the below figure is slowly
accumulating a chemical X entering in the influent. a) write a differential equation for
the accumulation of X in the pond, assuming the system is completely mixed,
evaporation can be described in terms of a mass transfer coefficient (specify the
dimension of the coefficient), and the pond is leaking water and chemical at a rate
proportional to bC, where b is a dimensionless coefficient between 0 and 1 and C is
the bulk concentration of X in water. The pond volume is considered variable. b)
Assume that the evaporation rate is small, and that inflow is interrupted for a period of
time but the leakage continues from the bottom. Derive an equation that describes the
concentration of X in the pond.