## 5 Results and Discussion
### Assessment of Pipe Deterioration  
The second part of this study is the application of the HS algorithm to find the critical pipes in terms of the roughness coefficient \(C\). For this purpose, the HS was implemented in the same manner as for the optimal pipe diameter, but the \(C\) value was used as the objective function. In this case, by loading the original Cheongna WDN model into the EPANET-MATLAB Toolkit, the optimal values of the roughness coefficient that must be maintained to provide the original level of serviceability were determined. In this manner, it is possible to identify the conduits that exhibit higher values of \(C\), and are thus considered to be the ones that are most sensitive to pipe aging. In this case, the range of values for the HS objective function was set between 70 and 100, based on the assumption that ductile iron tends to increase its roughness coefficient by decreasing the Hazen-Williams value of \(C\) by 10 every ten years [2]. Table 7 lists the different values as pipes age.  
Figures 6 and 7 show the outcomes of this approach, in which the optimal distribution of the roughness coefficient for the entire network can be observed. Those conduits that maintain a value of \(C\) = 100 are considered as critical pipes and should be repaired or replaced in the first term as the WDN ages. Thus, this approach can provide a useful tool for determining the repair or replacement of deteriorated pipes.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Min.** & **O** & **Max.** & **O** & **Average** & **Min. Hydraulic** & **Max. Hydraulic** & **Min. Flow** & **Max. Flow** & **Average Flow** \\
**(mm)** & **(mm)** & **O** (mm) & **Head (m)** & **Head (m)** & **Velocity (m/s)** & **Velocity (m/s)** & **Velocity (m/s)** \\ \hline
80 & 800 & 186.9 & 17.46 & 39.06 & 0.05 & 2.42 & 0.54 \\ \hline \end{tabular}
\end{table}
Table 6: Outcomes of the Cheongna WDN optimization after applying the HS algorithm.  
Figure 5: EPANET model of the Cheongna WDN, highlighting the head pressure in the nodes after applying the optimal pipe diameters.  
Then, as explained before, as the Hazen-Williams \(C\) value of ductile iron decreases by ten every 10 years, it is relatively simple to identify from the obtained results the service life of the conduits according to the required level of serviceability of the system, which in this case was set by the constraints in the nodal head pressure. In this manner, the main objective of this second part of the study is achieved by simulating a scenario in which the original set of pipe diameters is used in order to analyze the consequences of the system aging and to identify those conduits that are more sensitive to this aging. Thus, decision makers have a tool for operation management in terms of repairing or replacement of deteriorated pipes by WDN aging.  
Figure 6: EPANET model of the Cheongna WDN, highlighting the optimal Hazen–Williams roughness coefficient \(C\) value distribution determined by the HS algorithm based on the original set of pipe diameters.  
Figure 7: EPANET model of the Cheongna WDN, highlighting the head pressure in the nodes based on the optimal Hazen–Williams roughness coefficient \(C\) value distribution.