## 3 Results  
### Hydraulic Analysis of Pipeline Network Under Different Water Supply Modes  
#### 3.1.1 Segmented Water Supply  
An irrigation cycle should be maintained within 5 to 7 days to meet the water demand of the entire pipeline network during peak usage periods. When designing the rotational irrigation groups, it is essential to consider the average water consumption of each branch pipe. For efficiency, a configuration of four rotational irrigation groups is used as an example. Each group comprises 12 branch pipes and 36 branch valves operating simultaneously, with a water supply duration of 1.5 days per cycle, resulting in a 6-day rotational irrigation cycle. The specific grouping is presented in Table 5.  
Taking the second group as an example, the designed water supply flow rate for the system was calculated to be 13,700 L/s using Formula (1). According to the principles of rotational irrigation grouping, if the flow rate is evenly distributed among the branch pipes, the average design flow rate for each branch pipe is 380.96 L/s. This design flow rate was used as the initial value for node water output in EPANET; however, a warning message appeared, stating \"Negative pressure head occurred at 00:00:00 h, analysis terminated.\" The results showed that negative pressure head occurred \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Error (\%)**} & \multicolumn{3}{c}{**Error (\%)**} & \multicolumn{3}{c}{**Error (\%)**} \\ \cline{2-10}
**Node** & \multicolumn{2}{c}{**Pressure Head**} & \multicolumn{1}{c}{**Flow**} & \multicolumn{1}{c}{**Node**} & \multicolumn{1}{c}{**Pressure Head**} & \multicolumn{1}{c}{**Flow**} & \multicolumn{1}{c}{**Node**} & \multicolumn{1}{c}{**Pressure Head**} & \multicolumn{1}{c}{**Flow**} \\ \hline I-a & 3.73 & 0.40 & II-a & 2.94 & 0.51 & III-a & 4.44 & 0.14 \\ I-b & 3.05 & 0.59 & II-b & 3.29 & 0.08 & III-b & 2.50 & 1.52 \\ I-c & 4.28 & 0.98 & II-c & 4.48 & 0.00 & III-c & 0.57 & 0.00 \\ I-d & 3.43 & 0.46 & II-d & / & 0.78 & III-d & 4.66 & 0.54 \\ I-e & 4.76 & 0.00 & II-e & 4.00 & 0.42 & III-e & 3.95 & 0.27 \\ I-f & 1.07 & 0.37 & II-f & 4.42 & 0.33 & III-f & 1.81 & 0.87 \\ I-g & 6.52 & 0.25 & II-g & 5.00 & 0.72 & III-g & 3.92 & 0.55 \\ I-h & 4.34 & 0.30 & II-h & 7.27 & 0.24 & III-h & 7.45 & 0.37 \\ I-i & 4.88 & 0.21 & II-i & 2.08 & 0.12 & III-i & 3.92 & 0.00 \\ I-j & / & / & II-j & 6.12 & 0.39 & III-j & / & 1.64 \\ I-k & 1.80 & 0.21 & II-k & / & / & III-k & 4.08 & 0.26 \\ I-l & 3.25 & 0.50 & II-l & 4.60 & 0.26 & III-l & 1.88 & 1.66 \\ I-m & 2.78 & 0.68 & II-m & 1.56 & 1.24 & III-m & 1.36 & 0.91 \\ I-n & 4.17 & 0.26 & II-n & 1.90 & 0.46 & III-o & / & 1.21 \\ I-o & 1.47 & 0.01 & II-o & 7.45 & 0.15 & III-q & 4.58 & 0.26 \\ I-p & 4.00 & 0.00 & II-p & 1.81 & 0.01 & & & \\  & & II-s & 0.65 & 0.12 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Error of Flow and Pressure head at Each Node. at multiple nodes within the pipeline network, as illustrated in Figure 2a-c. The maximum negative pressure head approached \(-200\) m, indicating that the pipeline network could not function as intended. In practice, the network was unable to achieve the desired water flow rate. To resolve this, the water supply flow rate to the branch pipes was reduced. Through iterative calculations, the flow rate was adjusted until the pressure head at each node became positive, allowing EPANET to run successfully. The pressure head and flow distribution at each branch valve are presented in Figure 2d-f.  
As shown in Figure 2, in the segmented water supply mode, when the system is divided into 4 groups, each group simultaneously operates 72 branch pipes, causing the network to malfunction. After reducing the water flow rate to the branch pipes, the pipeline  
Figure 2: Flow and pressure head at the inlet of each branch pipe in the second group under segmented water supply conditions. (**a**) the hydraulic performance of the main pipe I under conditions of malfunction. (**b**) the hydraulic performance of the main pipe II under conditions of malfunction.