A stream of waste water having COD of 30 ppm discharges water at the rate of 100 L/s into another stream with a flow rate of 600 L/s and COD of 10 ppm

Question

A stream of waste water having COD of 30 ppm discharges water at the rate of 100 L/s into another stream with a flow rate of 600 L/s and COD of 10 ppm. Assuming instantaneous and complete mixing, what is the resultant COD just downstream from the point of discharge?

20 ppm

12.85 ppm

5.71 ppm

0.15 ppm

Solution

Correct option is B

The correct answer is (b).

Introduction

This is a classic mass balance calculation used in environmental engineering to determine the mixed concentration of a pollutant (COD) when two continuous streams merge.

Assuming complete mixing, the law of conservation of mass applies to calculate the resultant downstream concentration.

Information Booster

The fundamental mass balance equation is: C_{mix} = rac{(Q_1 imes C_1) + (Q_2 imes C_2)}{Q_1 + Q_2} .
Where Q represents the flow rate and C represents the concentration of the respective streams.
For the wastewater stream: Q1 = 100 L/s, C1 = 30 ppm.
For the receiving stream: Q2 = 600 L/s, C2 = 10 ppm.
Total mass loading = (100 imes 30) + (600 imes 10) = 3000 + 6000 = 9000 mg/s.
Total combined flow = 100 + 600 = 700 L/s.
Resultant COD = rac{9000}{700} = 12.85 ppm.

Additional Knowledge

Option A (20 ppm) is a simple, incorrect arithmetic average of the two concentrations without accounting for their vastly different flow rates.
Option C (5.71 ppm) is a mathematical distractor resulting from incorrect manipulation of the fractions.
Chemical Oxygen Demand (COD) is a crucial metric that measures the amount of oxygen required to chemically oxidize organic and inorganic matter in water, serving as an indicator of pollution.
Historically, the adoption of strict mathematical modeling for watershed management became imperative following catastrophic river pollution events in the mid-20th century, prompting authorities to mandate precise effluent discharge limits.