# Qualification of Hydraulic Analysis Models for Optimal Design of Water Distribution Systems
## 3 Application and Results
### Hydraulic Comparison of Abnormal System Conditions for WDSs  
In this chapter, to derive the characteristic of hydraulic analysis approaches, DDA and PDA, two kinds of abnormal scenarios are generated. The scenarios consist of two cases: fire flow and pipe breakage conditions. The first scenario considers the possibility of a fire flow in one or mode nodes. Due to the unexpected high demand of water in these nodes, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Description**} & \multirow{2}{*}{**Type**} & \multicolumn{6}{c}{**Parameters**} \\ \cline{3-8}  & & \(a\) & \(b\) & \(c\) & \(d\) & \(e\) & \(f\) & \(u\) \\ \hline Base installation & PVC pipe & \(-1.0\) & 0.0008 & 3.59 & 0.011 & 1 & 0.0067 & 150 \\ Trenching and & Sandy gravel soil with 1:1 side & \(-24\) & 0.32 & 0.67 & 16.7 & 0.38 & 0 & 4 \\ excavation & Sandy gravel soil with 1:1 side & 2.9 & 0.0018 & 1.9 & 0.13 & 1.77 & 0 & 4 \\  & slope (>200 mm) & 1.6 & 0.0062 & 1.83 & \(-0.2\) & 1 & 0.07 & 0 \\ Embedment & Ordinary & \(-0.094\) & \(-0.062\) & 0.73 & 0.18 & 2.03 & 0.02 & 4 \\ Backfill and & Sandy gravel soil with 1:1 & \(-0.094\) & \(-0.062\) & 0.73 & 0.18 & 2.03 & 0.02 & 4 \\ compaction & side slope & \(-0.094\) & \(-0.062\) & 0.73 & 0.18 & 2.03 & 0.02 & 4 \\ Valve fitting and & Medium spacing & 9.8 & 0.02 & 1.8 & 0 & 0 & 0 & No \\ hydrant & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters based on the pipe construction cost. the system can considerably change in pressures and demand availability. The second scenario simulates an unexpected break in one or more pipes, depending on the size of the network. To implement these changes, the nodes and pipes are selected randomly, and DDA and PDA are applied to all the scenarios in order to derive the hydraulic conditions in the applied WDSs. To apply Scenario 1 (fire flow condition) in WDSs, node 6 is selected to increase the demand, and Scenario 2 is simulated by a fire flow pipe breakage condition simultaneously with pipe 2 and node 6, as shown in Figure 3. The results for Scenario 1 for the two-loop network are presented in Table 2.  
It is interesting to analyze the pressure results from the DDA method. In node 6, there is a negative pressure, which is considered unrealistic in the water distribution system. On the contrary, the PDA approach shows more realistic positive pressures in all the nodes. It is important to note that in other nodes where the demand has not been affected, the behavior of both approaches is considered consistent, confirming that both methodologies can be applied in a water distribution system for normal conditions. Figure 4 represents the pressure in each node for both approaches, comparing the variable pressures. A similar analysis was performed for Scenario 2, where pipe 2 and node 6 were both selected to simulate an abnormal condition. Table 3 shows the results of DDA and PDA analyses. The difference between the two approaches is noticeable because the negative pressures are replaced with zero values in PDA due to the insufficient nodal pressure. Finally, Figure 5 presents a comparison of nodal pressure results from Scenario 2. The incidence of pipe break can be easily identified because of the high number of nodes with negative pressure.