A city of 200,000 people deposits 37 cubic feet per second (cfs) of sewage having a BOD of 28.0 mg/L and 1.8 mg/L of DO into a river that has a flow rate of 250 cfs and a flow speed of 1.2 ft/s. Just upstream of the release point, the river has a BOD of 3.6 mg/L and a DO of 7.6 mg/L. The saturation value of DO is 8.5 mg/L. The deoxygenation coefficient kd is 0.61/day, and the reaeration coefficient kx is 0.76/day. Assume complete and instantaneous mixing of the sewage and river.

Structural Analysis
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A city of 200,000 people deposits 37 cubic feet per second (cfs) of sewage having a BOD of 28.0 mg/L
and 1.8 mg/L of DO into a river that has a flow rate of 250 cfs and a flow speed of 1.2 ft/s. Just upstream of the release point, the river has a BOD of 3.6 mg/L and a DO of 7.6 mg/L. The saturation value of DO is
8.5 mg/L. The deoxygenation coefficient kd is 0.61/day, and the reaeration coefficient kx is 0.76/day.
Assume complete and instantaneous mixing of the sewage and river.
(a) Find the initial oxygen deficit and ultimate BOD just downstream of the outfall.
(b) Find the time and distance to reach the minimum DO.
(c) Find the minimum DO.
(d) Find the DO that could be expected 10 miles downstream.
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