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


  • Mansur Arbabi,

  • Jack Elzinga,

  • Charles ReVelle


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.