Question

A city continuously disposes of effluent from a wastewater treatment plant into a river. The minimum flow in the river is 130 m3/s, and the discharge from the treatment plant is 37 m3/s. Upstream from the outfall, the background concentration is 0.69 mg/L. The maximum allowable concentration in the river is 1.1 mg/L. What is the maximum concentration that of the pollutant (in mg/L) that can be safely discharged from the wastewater treatment plant

Answer 1

`2.54\ \text{mg/L}`

Step-by-step explanation:

C = Allowable concentration = 1.1 mg/L

`Q_1` = Flow rate of river =
`130\ \text{m}^/\text{s}`

`Q_2` = Discharge from plant =
`37\ \text{m}^3/\text{s}`

`C_1` = Background concentration = 0.69 mg/L

`C_2` = Maximum concentration that of the pollutant

The concentration of the mixture will be

`C=(Q_1C_1+Q_2C_2)/(Q_1+Q_2)\\\Rightarrow C_2=(C(Q_1+Q_2)-Q_1C_1)/(Q_2)\\\Rightarrow C_2=(1.1(130+37)-130* 0.69)/(37)\\\Rightarrow C_2=2.54\ \text{mg/L}`

The maximum concentration that of the pollutant (in mg/L) that can be safely discharged from the wastewater treatment plant is
`2.54\ \text{mg/L}`.