## 3 Results
### Comparison of Hydraulic Reliability of Pipeline Network Under Different Water Supply Modes  
The hydraulic reliability of the pipeline network under different water supply modes was calculated using Formulas (3)-(13), based on the flow rate, pressure head, and velocity values at the nodes simulated by EPANET. The calculated hydraulic reliability values for various regions and pipeline systems are presented in Table 6.  
The results presented in Table 6 indicate a clear pattern in the hydraulic reliability of different water supply modes and individual branch pipes. Except for the areas controlled by the II and III main pipes in the segmented water supply mode, the reliability follows the order from high to low: water supply uniformity reliability, flow velocity reliability, and node pressure head reliability. This pattern primarily arises because the calculation is based on flow distribution, while the pressure head values are derived from the model. Among the different water supply modes, the hydraulic reliability of the uniform water supply mode is generally the highest, followed by the random water supply mode, with the segmented water supply mode exhibiting the lowest hydraulic reliability. In the segmented water supply mode, the water supply uniformity reliability and node pressure head reliability in the area controlled by the III main pipe are the highest, while its flow velocity reliability is the lowest. This is attributed to the low elevation of the III main pipe, which increases the pressure head difference within this area of the self-pressurized system. Additionally, the weight assigned to node pressure head reliability is relatively high, such that higher pressure head results in greater flow velocity. In all areas, except for that controlled by the I main pipe, the reliability of water supply uniformity is the highest, the reliability of flow rate is the lowest, and the reliability of pressure head is intermediate. Therefore, in a self-pressurized water supply system, if the segmented water supply mode is adopted, the impact of terrain elevation differences should be prioritized, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Water Supply Mode**} & \multirow{2}{*}{**Region**} & \multicolumn{5}{c}{**Reliability**} \\ \cline{3-6}  & & \(S_{1}\) & \(S_{2}\) & \(S_{3}\) & \(S\) \\ \hline \multirow{4}{*}{Segmented} & I main pipe & 4.04 b & 0.46 d & 2.04 b & 1.88 c \\  & II main pipe & 3.79 b & 1.00 c & 0.36 c & 1.74 c \\  & III main pipe & 4.29 ab & 1.11 c & 0.20 c & 1.91 c \\  & The entire network & 4.04 b & 0.84 cd & 0.64 c & 1.79 c \\ \hline \multirow{4}{*}{Uniform} & I main pipe & 4.8 a & 0.61 d & 4.33 a & 2.65 b \\  & II main pipe & 4.75 a & 1.62 b & 4.39 a & 3.14 a \\  & III main pipe & 4.80 a & 0.89 c & 4.26 a & 2.78 a \\  & The entire network & 4.76 a & 0.94 c & 4.49 a & 2.83 a \\ \hline \multirow{4}{*}{Random} & I main pipe & 3.73 b & 2.04 a & 2.67 b & 2.69 ab \\  & II main pipe & 4.16 a & 1.95 a & 2.53 b & 2.75 a \\ \cline{1-1}  & III main pipe & 4.10 b & 0.71 d & 2.41 b & 2.41 b \\ \cline{1-1}  & The entire network & 3.99 a & 1.54 bc & 2.50 b & 2.49 b \\ \hline \hline \end{tabular} Note: Different lowercase letters in the vertical columns of the table indicate that there are significant differences in reliability between different regions and water supply modes (\(p<0.05\)).  
\end{table} 
Table 6: Hydraulic reliability of pipeline network under different water supply modes. and attention should be given to controlling the water flow velocity in the pipeline to improve the hydraulic reliability of the pipeline network. Under the uniform water supply mode, the hydraulic reliability of the pipeline network in each region is generally higher than that in the segmented water supply mode. The difference in hydraulic reliability between the main pipes is minimal, with the reliability of water supply uniformity being comparable to that of flow velocity, both of which are higher than those observed in the segmented water supply mode.