Question

A large lake with a volume of 2.0 x 109 ft3 is filled by an inflow stream with a flow rate of 20 ft/s and a non-conservative pollutant concentration of 5 ppm. A sewage outfall also discharges into the large lake with a flow rate of 3.5 ft3/s and a non-conservative pollutant concentration of 30 ppm. A outflow stream leaves the lake with the same flow rate of the inflow stream plus the outfall. The non- conservative pollutant has a decay rate coefficient of 0.20/day. Assume the pollutant is completely mixed in the lake and there is no evaporation or other gains or losses. What would be the steady state concentration in the outflow stream leaving the large lake? 1.

Answer 1

Discharge
`a_(inflow)` =
`20 ft^(3)/s`

Concentration
`c_(inflow)` = 5ppm

Discharge
`a_(outflow)` =
`3.5 ft^(3)/s`

Concentration
`c_(outflow)` = 30ppm

Decay Rate Coefficient = 0.20/day

Steady State Concentration =
`( a_(inflow) * c_(inflow) + a_(outflow) * c_(outflow))/( a_(inflow) + a_(outflow))}`

Steady State Concentration =
`(20 * 5 + 3.5 * 30)/(20 + 3.5)`

Steady State Concentration = 4.702ppm