A wastewater lagoon with a volume of 1200 m3 has been receiving a steady flow of

Question

A wastewater lagoon with a volume of 1200 m3 has been receiving a steady flow of a conservative waste at a rate of 500 m3/d. The waste entering the lagoon has a concentration of 50 mg/L.

a. What is the pollutant concentration in the effluent of the lagoon?

b. If the influent concentration was suddenly increased to 120 mg/L, what would be the effluent concentration

i. 4 days later?

ii. 7 days later?

iii. At steady-state?

c. Repeat part (a) for a non-conservative pollutant with a reaction rate of 0.20 d-1.

d. If the non-conservative pollutant in part (c) was suddenly increased to 120 mg/L, what would be the new steady-state concentration?

e. Develop two graphs. One graph showing influent and effluent concentration from parts (a) and (b) with respect to time and a second graph showing the influent and effluent concentrations from parts (c) and (d) with respect to time.

Explanation / Answer

A.)

a)
In steady flow regime entering volumetric flow rate and effluent flow rate are equal

So rate of change of pollutant is given by:
d(C?V) dt = C_in?Q - C?Q
(C pollutant concentration, V volume of the lagoon, Q volumetric flow rate)
Since V is constant
V?(dC/dt) = Q?(C_in - C)
<=>
(dC/dt) = (Q/V)?(C_in - C)

At steady state conditions
dC/dt = 0
Hence
C = C_in = 50 mg/L

b.)

For this part you need to solve the differential equation from part a)

In difference to part a)) input concentration is 100 mg/l
(dC/dt) = (500 m

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