Question

A lagoon is to be designed to accommodate an input flow of 0.30 m3/s of nonconservative pollutant with concentration 33.0 mg L and reaction rate constant 0.4/day. The effluent from the lagoon must have pollutant concentration of less than 12.0 mg/l. Assuming complete mixing, how long must the lagoon be?

Answer 1

Answer:

The lagoon must be at least 65552 m3

Step-by-step explanation:

First its we have to know the detention time that its needed for the pollutant to reduce its concentration up to 12 mg/l.

We use the formula of decay:

$C=C_{0}*exp^{-k*t}$

We can calculte the time as

$t = -\frac{1}{k}*ln(\frac{C}{C_{0}})=  -\frac{1}{0.4}*ln(\frac{12}{33})=2,529 days$

The flow of the pollutant is 0.3 m3/s, so the daily flow is

$0.3\frac{m^{3}}{s} *86400\frac{s}{day} =25920 \frac{m^{3}}{day}$

The lagoon has to be at least this volume:

$2.529 days * 25920 \frac{m^{3}}{day} = 65552 m^{3}$