A wastewater is discharged through an outfall to a freshwater stream of mean velocity 0.1 m/s. The DO upstream of the outfall is 8.5 mg/L. The saturation (maximum) DO for the river water is 9.2 mg/L. After the wastewater mixes with the stream flow, the ultimate BOD of the mixed flow at the point of discharge is 25 mg/L. Assuming the deoxygenation rate k1 = 0.25 d-1 and the reaeration rate k2 = 0.4 d^-1. Determine:
a. The time (tc) and distance downstream (xc) where DO is a minimum.
b. The minimum DO.