Toward an analytical solution for looped pipe network hydraulics

Hydraulic analysis of looped Water Distribution Networks (WDNs) requires solving continuity and energy equations to determine nodal pressure heads and pipe flow discharges. Traditional loop-based (∆Q) methods, such as the Hardy-Cross method, rely on iterative procedures. This study introduces a critical flow path detection algorithm to predict pipe flow directions as prior knowledge, enabling the development of an analytical solution based on the ∆Q equation. Validation on single-loop, benchmark, and randomly generated WDNs shows that the proposed method achieves an average accuracy of 90% in detecting flow directions, as confirmed by a z-test with a 99% confidence interval. Moreover, coupling the algorithm with the global gradient method enhances computational efficiency by 100% (doubling convergence speed) compared to the traditional approach. These findings demonstrate that the developed methodology substantially improves both the accuracy and efficiency of hydraulic analysis in WDNs.