A 10 X 106 m3 lake is fed by a polluted stream having a flow rate of 5 m3/s and a pollutant concentration of 10 mg/L. There is also a sewage outfall that discharges 0.5 m3/s of wastewater having a pollutant concentration of 100 mg/L. The stream and sewage wastes have a first order decay rate coefficient of 0.2/day. Assuming the pollutant is completely mixed and that the lake volume is constant.
a) Find the steady-state concentration in the lake.
b) The desired concentration in the lake is 1 mg/L. An upstream clean-up effort reduces the stream concentration to 1 mg/L. What would the sewage concentration have to be reduced to in order to achieve the desired concentration?
c) Rather than reducing the sewage concentration, one alternative is to divert another tributary so that the total stream flow is doubled, while the stream concentration would remain at 1.0 mg/L. What would the resulting lake concentration be and is this a viable alternative?
d) If the initial concentration of the lake was 1.0 mg/L, how long would it take to, under conditions in part A, achieve 99% of the steady-state concentration (assuming all loads occur at a constant rate)?