The ultimate BOD of a river at the confluence of the river and a sewage outfall is 50 mg/L and the DO is at the saturation value of 9.0 mg/L after mixing. The deoxygenation (or decay) rate coefficient (Kd) is 0.3 d-1 and the reaeration rate coefficient (Kr) is 0.9 d-1. The river is flowing at a velocity of 48 miles/day and the only source of BOD is from the sewage discharge. Required:
a. Find the critical distance downstream (in miles) at which DO is a minimum.
b. Find the minimum DO (in mg/L)
c. If a wastewater treatment plant is to be built, what fraction of the BOD would have to be removed from the sewage to assure a minimum of 5.0 mg/L everywhere downstream?