On determining conditions and suitable locations for fish survival by using the solution of the two coupled pollution and aeration equations

The coupled equations of pollution and aeration for flow in a river were studied under generalized assumptions in terms of parameter dependency on space and time, as well as general boundary constraints. An analytical solution was obtained in the steady-state case. Also, the system was solved in its unsteady state numerically in a dimensionless form using the finite difference scheme. The effect of different parameters controlling the flow (such as the velocity, Peclet number, injected pollutants, and so on…) was studied. Investigations indicate that the special cases of the proposed model (i.e., uniform distribution of pollutant and Dissolved Oxygen concentrations, and zero injected pollutants along the river) give results that agree with the previous studies. This simple model helps in understanding the behavior of the pollution-aeration process and its relation to the injected pollution along a river and its effect on fish survival. A simple procedure was discussed in this study to help in regulating farming, industrial, and urban practices and impose restrictions if necessary. This study determines with accuracy the intervals of the river at which fish can survive at a given time, as well as the maximum amount of pollutants allowed to be injected along the river for fish survival.