A treated wastewater (with a flow of 0.415 m^3 /s, an ultimate BOD of 40 mg/L and the DO of 1.3 mg/L) is discharged into a stream flowing at 0.835 m^3 /s. Just upstream from the discharge point, the stream itself has an ultimate BOD of 1.8 mg/L and the DO of 6.8 mg/L. The deoxygenation constant Kd is 0.20/day and the reaction rate constant Kr is 0.28/day. The saturated value of DO in river is 8.38 mg/L.
Required:
a. Assuming complete and instantaneous mixing, find the ultimate BOD of the mixture of waste and river just downstream from the outfall.
b. Assuming a constant cross-sectional area for the stream equal to 55 m2, what ultimate BOD would you expect to find at a point 10,000 m downstream?