Natural organic matter in a lake causes consumption of dissolved oxygen at a rat

Question

Natural organic matter in a lake causes consumption of dissolved oxygen at a rate of 2 mg per day per L. Water entering the lake is saturated with oxygen at a temperature of 20 deg C. The lake has the following properties (based on Lake Greifensee in Switzerland): volumetric flow rate = 0.34x106 m3/day; volume = 150x106 m3; surface area = 8.6x106 m2. If the reaeration rate constant is 0.5 per day, what is the steady state concentration of dissolved oxygen in the lake? Enter your value in units of mg/L with two significant digits.

Explanation / Answer

volof lake = 150*106 m3

vol flow rate = 0.30*106 m3 /day = .34*106*1000 = 36040 L /day   ( because 1 m3 = 1000L)

consumption of dissolved O2 = 2 mg /day/L

Steady conc of dissolved O2 in lake    =   vol flow rate *k *2mg

                                                        = 36040*0.5*2 = 36040 mg/day

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