## 4 Discussion
Research indicates that under a random water use system, the random water supply mode can effectively distribute the flow across branch pipes, provided that the total flow of the pipeline network meets the overall water demand. The number of nodes with a pressure head of \(H_{min}\) at the inlets of branch pipes exceeds that of the uniform water supply mode. The pressure head fluctuations between branch pipes are comparable to those in the uniform water supply mode, with extreme pressure head variations mostly occurring between adjacent branch pipes that experience significant flow changes. The reliability of node pressure head in the pipeline network surpasses that of the first two modes. Although the actual flow velocity of some branch pipes deviates from the economic flow velocity, the deviation is minimal; overall, the hydraulic reliability of the pipeline network lies between that of the first two modes. To ensure system stability, it is essential to monitor pipeline sections with significant fluctuations in water supply flow, particularly at nodes located in lower terrain areas. Gradual operation of valves should be implemented to avoid sudden pressure head changes. Furthermore, the installation of pressure head sensors at nodes prone to fluctuations is recommended to enable real-time monitoring of system pressure head and flow, allowing for prompt adjustments to the number of open branch pipes. The design of the pipeline network must account for water distribution uniformity, system operability, and safety. Determining the appropriate hydraulic evaluation indicators for assessing the safety of the pipeline network is crucial [44]. The hydraulic reliability of large-scale irrigation pipe networks is influenced by factors such as water supply uniformity, pressure head reliability, and flow velocity deviation. These indicators often serve as key constraints in the optimization of pipeline network design [45]. This study demonstrates that, among these three indicators, pressure head reliability carries the greatest weight, followed by water supply uniformity, with flow velocity deviation having the lowest weight. Under the uniform water supply mode, the pipeline network system exhibits the highest hydraulic reliability, along with the best performance in water supply uniformity and minimal flow velocity deviation. In the random water supply mode, the hydraulic reliability of the pipeline network is intermediate, falling between the segmented and uniform water supply modes, with the highest node being pressure head reliability. In contrast, the hydraulic reliability of the pipeline network is the lowest under the segmented water supply mode. In summary, for large-scale irrigation pipeline networks, the traditional centralized water supply model reduces the hydraulic reliability of the system. Adopting a pressure head-reducing uniform water supply mode improves hydraulic reliability, although it does not fully ensure pressure head stability across the network. By implementing a random water supply mode, node pressure head reliability is enhanced. In practical applications, it is crucial to carefully control the proportion and location of open branch pipes. Additionally, in areas with uneven terrain, special attention must be given to managing the pressure head at nodes located at lower elevations.