Abstract
The empirical biochemical oxygen demand (BOD) equation is expressed as a multiorder reaction equation of order n, then is combined with the dissolved oxygen mass balance equation to give the differential form of an oxygen sag equation for small rivers and streams for which dispersion can be neglected. The value of n in the BOD reaction is restricted to values that are larger than one (first order). The dissolved oxygen sag equation is verified with two published dissolved oxygen sag models by setting n equal to 3/2 (three-halves order BOD reaction), and n equal to 2 (second order BOD reaction). The proposed dissolved oxygen sag equation may be applied to test the BOD and dissolved oxygen models in large, complex numerical models, such as models used in developing total maximum daily load recommendations. Examples show how the BOD reaction order affects the dissolved oxygen sag characteristics of a river.
Published Version
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