A wastewater stream with flow rate 2 m$^3$/s and ultimate BOD 90 mg/L joins a small river with flow rate 12 m$^3$/s and ultimate BOD 5 mg/L. Both streams mix instantaneously. The cross-sectional area of the river is 50 m$^2$. Assuming the deoxygenation rate constant $k = 0.25$/day,

Question

A wastewater stream with flow rate 2 m$^3$/s and ultimate BOD 90 mg/L joins a small river with flow rate 12 m$^3$/s and ultimate BOD 5 mg/L. Both streams mix instantaneously. The cross-sectional area of the river is 50 m$^2$. Assuming the deoxygenation rate constant $k = 0.25$/day, the BOD (in mg/L) of the river water 10 km downstream of the mixing point is

Accepted Answer

15.46. After instantaneous mixing, the ultimate BOD becomes $(2\times 90 + 12\times 5)/(2+12)=17.14$ mg/L. The mixed flow is 14 m$^3$/s, so velocity = 14/50 = 0.28 m/s, and 10 km takes about 0.413 day. Applying first-order decay, BOD = 17.14$e^{-0.25\times 0.413}$ \approx 15.46 mg/L.

Solution

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