Question

A treated wastewater (initial contaminant concentration, flow rate = 5C, 0.2Q) enters a stream (initial concentration, flow rate = 0.01C, Q). Calculate contaminant concentration in stream immediately after mixing of wastewater with stream water?
1. 0.84C
2. 0.04C
3. 1.0Q
4. 1.2Q

Answer 1

Correct Answer - Option 1 : 0.84C

Concept:

Contaminant concentration in stream immediately after mixing wastewater with stream water is given by,

\({C_{mix}} = \frac{{{C_w}{Q_w}\; + \;{C_s}{Q_s}}}{{{Q_w}\; + \;{Q_s}}}\)

Here, C_w = Contaminant concentration of waste water, C_s = Contaminant concentration of stream

Q_w and Q_s are discharges of treated wastewater and stream.

Calculation:

Given,

C_w = 5C, C_s = 0.01C, Q_w = 0.2Q, Q_s = Q

∵ We know that, \({C_{mix}} = \frac{{{C_w}{Q_w}\; + \;{C_s}{Q_s}}}{{{Q_w}\; +\; {Q_s}}}\)

\({C_{mix}} = \frac{{5C\; \times \;0.2Q \;+ \;0.01C\; \times \;Q}}{{0.2Q \;+\; Q}} = \frac{{CQ \;+\; 0.01CQ}}{{1.2Q}}\)

⇒ \({C_{mix}} = \frac{{1.01CQ}}{{1.2Q}} = 0.84C\)