A POTW (a.k.a. waste water plant) 1.0 m^3/s of treated effluent having an ultimate BOD of 30mg/L and DO = 2 mg/L into a stream that has a flow of 8 m^3/s, a BOD = 5.0 mg/L and DO = 9 mg/L. The river and waste mixture has a temperature of 20°C, a deoxygenation constant kd of 0.2 d-1, an average flow speed of 0.3 m/s, and an average depth of 3.0 m. Assume a reaeration constant of 0.6 d^-1.
a. Assuming complete and instantaneous mixing, estimate the ultimate BOD of the river just downstream from the outfall.
b. Assuming complete and instantaneous mixing, estimate the dissolved oxygen deficit just downstream from the outfall.
c. Find the time and distance downstream at which the oxygen deficit is a maximum.
d. Find the minimum value of DO.