The Oxygen Sag Equation: New properties and a linear equation for the critical deficit

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Abstract
In this paper some newly discovered properties of the Streeter‐Phelps oxygen sag equation are examined. The convexity of the critical dissolved oxygen (DO) deficit is established, and it is shown that the critical DO deficit can be represented by a conical surface. By using these properties it is shown how to approximate with a high degree of accuracy the critical deficit as a linear function of initial BOD loading and initial oxygen deficit. The linear approximating equation will find use in mathematical programing formulations of water quality management problems.

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