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4. [20] A city of 100,000 people discharges 51,840 m/d of treated wastewater into the Bergelmir River. The treated wastewater has a BOD; of 15 mg/L and a BOD decay constant (i.e., k) of 0.20 day at 20°C. The DO of the wastewater is 1.0 mg/L. Bergelmir River has a flow rate of 2.50 m/s and a velocity of 0.50 m/s. The ultimate BOD and DO in the river are 4.0 and 7.0 mg/L, respectively. Assume complete mixing and that the velocity in the river is the same upstream (i.e., before mixing) and downstream (i.c., after mixing) of the outfall. Given that the river and wastewater temperature is 20 °C. Saturation values of dissolved oxygen can be found in Table A- 2 in Appendix of the textbook. (a) Calculate the initial oxygen deficit and initial ultimate BOD after mixing, (b) The average depth (i.e., H) of the river after mixing is 3.0 m and the bed activity coefficient (i.e., n) is 0.50, calculate the deoxygenation rate constant and reacration rate constant. Based on the calculated rate constants, what is the DO concentration 16 km downstream?
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