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

Answer:

$2.54\ \text{mg/L}$

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

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

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