Mathematical modeling for dissolved oxygen sag analysis in river

In this paper, we consider the general mass conservation equation, which averaged over the cross section of the stream. We apply this concept for a continuous discharge of wastewater into a river, so which is applicable to the BOD, which also undergoes a first-order decay process. For dissolved oxygen, the one-dimensional mass conservation equation is easily deducted, The time derivative term is removed because steady-state concentrations are sought, and the dispersion term is also removed because of negligible effects for a continuous discharge and appropriate source and sink terms are added and the maximum dissolved-oxygen deficit is obtained. We also discussed zero order kinetics model, derived on the basis of assumptions that the concentration of bacteria is relatively constant and that the rate of substrate utilization is zero order. We find for the dissolved oxygen deficit at the transition when the substrate is all utilized. For times greater than there is no longer any substrate and thus k₀ =0.