A dairy processing plant is planning to discharge wastewater at a rate of 5 m³/s into a river that has a 7Q10 discharge of 30 m³/s. Available data indicate that the river has a bottom width of 20 m, side slopes of 2:1 (H:V), depth of flow of 3 m at a discharge of 35 m³/s, average roughness height of 1.5 cm, DO concentration of 8.5 mg/L, 5-day BOD of 5 mg/L, temperature of 22°C, and average annual wind speed over the river of 5 m/s. The milk processing waste will have negligible DO and be at approximately the same temperature as the river. Laboratory tests on the combined river water and wastewater indicate that the BOD decay factor of the mixed water is 0.15 d?¹ at 22°C, and BOD removal due to sedimentation is negligible. The dairy plant is to be located in a state where the DO in the stream is required by law to be greater than or equal to 5.0 mg/L, and the boundary of the mixing zone is located 800 m downstream of the wastewater discharge.
(a) Calculate the required length of the diffuser such that complete cross-sectional mixing occurs at approximately 100 m downstream of the diffuser. Does significant decay in BOD occur during cross-sectional mixing?
(b) Using the calculated diffuser length, estimate the DO in the river 100 m downstream of the diffuser, and find the maximum 5-day BOD of the dairy wastewater that will cause the river to meet the DO criteria on the boundary of the mixing zone.
