A lagoon with a volume of 1200 m^3 has been receiving a steady flow of a conserv

Question

A lagoon with a volume of 1200 m^3 has been receiving a steady flow of a conservative waste at a rate of 100m^3/day for a long enough time to assume that steady-state conditions apply. The waste entering the lagoon has a concentration of 10mg/L. For a nonconservative pollutant with a rate constant k=0.2/day,

a) What would be the concentration of pollutant in the effluent leaving the Lagoon?

b) If the input waste concentrationsuddenly increased to 100 mg/L, what would the concentrationin the effuent be 7 days later?

Explanation / Answer

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 = 10 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) = (100 m

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