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A lagoon receiving a steady flow of a conservative waste

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A lagoon with volume 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. Assuming completely mixed conditions,
a) what would be the concentration of pollutant in the effluent leaving the lagoon?
b) If the input waste concentration suddenly increased to 100mg/L, what would the concentration in the effluent be 7 days later?

2. repeat problem 1 for a nonconservative pollutant with reaction rate K = 0.20/d

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The solution provides detailed explanations (including illustrations) on the concept of Continuous stirred tank reactor and step-by-step instruction on solving the problem in 10 pages of Word documents.

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Let C1 be the concentration (mg/L) of the stream coming in the lagoon.
Let C be the concentration (mg/L) of the stream coming out of the lagoon.

Let V1 be the volumetric flowrate (m3/s) of the stream coming in the lagoon.
Let V2 be the volumetric flowrate (m3/s) of the stream coming out of the lagoon.

We have
Volume of lagoon VL = 1200 (m3) = 1.2*106 (L)
V1 = 100 (m3/day) = 105 (L/day)
C1 = 10 (mg/L)

Part 1: No reaction
Perform material balance for the lagoon
Rate of change of material = Rate of mass in - Rate of ...

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