BOD and Oxygen Relationships in Streams

The equations of Streeter and Phelps for the BOD and dissolved-oxygen profiles along a natural stream are extended to take into account the effects of longitudinal dispersion, removal of BOD by sedimentation, addition of BOD along the path of flow, removal of oxygen by plant respiration and by the oxygen demand of benthal deposits, and the addition of oxygen by photosynthesis. Methods by which various coefficients in the equations might be evaluated from theory or from field measurements are examined. The effect of longitudinal dispersion on the BOD and dissolved-oxygen profiles is shown to be negligible in most fresh water streams. A theory of reaeration, based on the random replacement of the interfacial liquid-film, is presented. It is proposed that the micro-scale portion of the turbulent energy spectrum principally is responsible for the film replacement on which reaeration depends. Theoretical values of the reaeration coefficient are in good agreement with values reported in the literature.