Ariver with a flow of 50 m3/s discharges into a lake with a volume of 15,000,000 m3. the river has a background pollutant concentration of 5.6 mg/l. at time zero the concentration in the lake is 5.6 mg/l before an industry begins discharging waste with a flow of 0.7 m3/s also into the lake with a pollutant concentration of 300 mg/l. the decay coefficient for the pollutant in the lake is 0.2 per day. what is concentration leaving the lake one day after the pollutant is added?

Explanation:

The given data is as follows.

       Volume of lake = =

        Concentration of lake = 5.6 mg/l

Total amount of pollutant present in lake =

                                                                    = mg

                                                                    = kg

Flow rate of river is 50

Volume of water in 1 day =

                                          = liter

Concentration of river is calculated as 5.6 mg/l. Total amount of pollutants present in the lake are or

Flow rate of sewage =

Volume of sewage water in 1 day = liter

Concentration of sewage = 300 mg/L

Total amount of pollutants = or

Therefore, total concentration of lake after 1 day =

                                        = 6.8078 mg/l

                  = 0.2 per day

        = 6.8078

Hence, =

              =  

                             = 1.234 mg/l

Hence, the remaining concentration = (6.8078 - 1.234) mg/l

                                                             = 5.6 mg/l

Thus, we can conclude that concentration leaving the lake one day after the pollutant is added is 5.6 mg/l.

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