# State Analysis of the Water Quality in Rivers in Consideration of Diffusion Phenomenon
## 3 Results and Discussion
The value of the concentration at the same moment in time taking into account the self-cleaning process at a rate of \(V=0.005\) is \(BOD=6.96\) (see Figure 16), without taking into account self-cleaning of the river the value is higher and takes the value of \(BOD=7.73\). The detailed BOD values are summarised in Table 6.  
A different approach to analysis of changes in BOD distribution is shown in Figure 17. The flow rate of the river was taken into account here, but the occurrence of diffusion and the self-cleaning process were neglected. We observe here what was introduced of a tenacious pollutant, introduced over a period of time excluding the diffusion phenomenon leads to prolonged dangerous conditions in the river. Only after a certain time and length does the spread of contamination occur. In this situation, the key influence on the distribution of pollutants is the velocity of water movement and the diffusion occurring within them. Figure 18 shows the distribution of BOD pollutants at different velocities, excluding and including the diffusion mechanism. The omission of diffusion when maintaining the introduced pollutant for an appropriate time results in a state of prolonged hazardous conditions in the river, while the action of diffusion results in the faster dispersement of the introduced pollutant. \begin{table}
\begin{tabular}{c c c} \hline \hline \(V\) [m/h] & \
\begin{tabular}{c} \(BOD\) [mg/L] \\ **Figure** 14 \\ \end{tabular} &
\begin{tabular}{c} **Figure** 16 \\ \end{tabular} \\ \hline
0 & 6.26 & 5.64 \\
0.01 & 8.66 & 7.79 \\
0.001 & 6.60 & 5.95 \\
0.005 & 7.73 & 6.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: BOD values including river self-cleaning process for different water flow rates. Figure 16: BOD distribution at different velocities in the same time steps. Comparing Figures 11 and 18, we can observe the dynamics of the changes in BOD concentration, which is affected by the persistence of the pollutant for a given moment. During the persistence of the introduced pollutant in the water, the value of BOD concentration at the same velocities is higher. A constant flow of pollutants results in higher concentrations. A summary of the values obtained is shown in Table 7.  
Figure 19 shows the effect of velocity on the distribution of pollutants with and without diffusion and self-cleaning, respectively. It can be seen here that at higher velocities of flowing water the distribution of pollutants, including and excluding diffusion effect, takes \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{BOD}\)} & \multicolumn{2}{c}{\(V=\mathbf{0.01}\)} & \multicolumn{2}{c}{\(V=\mathbf{0.001}\)} \\  & \(\mathbf{D=0}\) & \(\mathbf{D=3600\times 5\times 10^{-9}}\) & \(\mathbf{D=0}\) & \(\mathbf{D=3600\times 5\times 10^{-9}}\) \\ \hline Figure 18 & 10 & 8.66 & 10 & 6.60 \\ Figure 11 & 10 & 7.71 & 10 & 5.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: BOD values at initial moments of time for different velocities. Figure 17: BOD distribution excluding diffusion and no self-cleaning process for \(V=0.001\). Figure 18: BOD distribution for different velocities including and excluding diffusion. on similar values. At lower velocities (see Figure 18), it can be seen that the diffusion phenomenon has a strong influence on the distribution of pollutants. The omission of the diffusion phenomenon regarding the self-cleaning process and different river velocities is shown in Figure 20. Higher water flow velocity causes the introduced pollutants to be \"carried away\" by the river resulting in a distribution along the entire length of the river. Conducting simulation experiments without considering diffusion at different velocities with respect to the self-cleaning process, it can be seen that BOD concentration values are high, within the persistence of the pollution, for a long while, and then, they decrease with time and length (Figure 21).