Alake has a volume of 500,000 m3 with the average surface area being 50,000 m2 and average depth 10m. it is bordered by many wastewater treatment plants which use ozone for wastewater disinfectant before the treated effuluent is released into the lake. there is a single outflow with a flowrate of 1.5m3/sec, which maintains the lake at constant level. bromate is formed as a disinfectant by product of the ozonation process which is put in at a constant average rate of 3,800 kg/yr. the lake is in steady state and can be assumed to be fully mixed.
a. what is the average hydraulic residence time in the lake?
b. what is the concentration of bromate in the lake? assuming the bromate is is a conserved, non-reacting, dissovled constituent.
c. if the input of bromate into the lake could be stopped instantaneously, calculate the time in years required for the average bromate in the lake to decline to 0.02 mg/l. assume the hydraulic throughput continues as before and that the is the only phenomena driving the decline in bromate.