Oxygen Depletion in a River

by Giovanna Claiborne

Submitted : Spring 2013

By using separation of variables and the first-order linear form equation, oxygen deficit in a river, with multiple changing variables, can be found at different points of time. A graph plotted between time 0 to 18.5 hours shows the oxygen deficit increasing to unacceptable levels above 4 mg/L and then decreasing back to below 4. In the problem, the stream reaeration rate is higher than the rate at which microorganisms use up dissolved oxygen, although it takes over 65 km for dissolved oxygen levels to be at a habitable level again after organic waste was deposited because the river is only flowing at 1m/s.

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