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A completely mixed lake with a single inflow and a single outflow stream has the following characteristics:
Mean depth = 5 mSurface area = 11 * 106 m2Residence time = 4.6 yr
An industrial plant presently discharges a chemical (W=2000 * 106 gr/yr) to the lake. In addition, the inflow stream also contains the same chemical at a concentration of 15 mg/L. Note that the volumetric inflow and outflow are equal. Assume that a first-order decay reaction can be used to characterize its removal by chemical oxidation. The reaction constant is k=0.1 yr-1.
a) Write a mass balance equation for this chemical b) If the lake is at steady-state, compute the in-lake concentration of the chemical c) If the lake is at steady-state, what industrial plant loading rate must be maintained to lower the lake's concentration to 30 ppm? Express your result as a percent reduction d) Evaluate each of the following engineering options to determine which is the most effective for lowering the steady-state in-lake concentration of the chemical:
i) Reduce the present loading rate of the industrial plant by building a waste treatment facility that will remove 50% of the chemical from the plant's effluentii) Double the lake's depth by dredgingiii) Double the lake's outflow rate by diverting a chemical-free water as the second inflowing stream to the lake
e) Determine the 95% response times for each of the alternative options given in part (d).
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