Question

A lake is fed by a polluted stream and a sewage outfall. The stream and sewage wastes have a decay rate coefficient (k) of 0.5/day (1st order units). Assuming complete mixing and no other water losses or gains, what is the steady-state pollutant concentration as mg/L in the lake? Incoming Stream: C = 10 mg/L, Q = 40 m^3/s Sewage Outfall: C = 100 ppm, Q = 0.5 m^3/s Lake: V= 200 m^3

Answer 1

Solution :

Given :

k = 0.5 per day

$C_s = 10 \ mg/L \ ; \ \ Q_s= 40 \ m^3/s$

$C_{sw} = 100 \ ppm \ ; \ \ Q_{sw}= 0.5 \ m^3/s$

Volume, V $= 200 \ m^3$

Now, input rate = output rate + KCV ------------- (1)

Input rate  $= Q_s C_s + Q_{sw}C_{sw}$

                $=(40 \times 10) + (0.5\times 100)$

                $= 2 \times 10^5 \ mg/s$

The output rate $= Q_m C_{m}$

                          = ( 40 + 0.5 ) x C x 1000

                          $=40.5 \times 10^3 \ C \ mg/s$

Decay rate = KCV

∴$KCV =\frac{0.5/d \times C \ \times 200 \times 1000}{24 \times 3600}$

            = 1.16 C mg/s

Substituting all values in (1)

$2 \times 10^5 = 40.5 \times 10^3 \ C+ 1.16 C$

C = 4.93 mg/L