An Analytical Solution for the Hydraulics of Looped Pipe Networks

This study introduces an analytical solution for the hydraulic analysis of looped water distribution networks (WDNs). Conventional approaches to solving ∆Q equations for looped water discharge correction entail iterative hydraulic analysis to compute the system pipe flows, velocities, and nodal pressures. In contrast, using the proposed analytical approach, the ∆Q equation is solved with the exact flow directions determined, consolidating known flow directions into a single unknown variable (∆Q) for each loop. Comparative analyses prove that this approach can precisely compute the hydraulic properties of WDNs. Finally, a Z-test hypothesis test is applied to assess the efficacy of the modified shortest-path algorithm. The results show that this algorithm attains an average accuracy of 90% in predicting exact flow directions, with a confidence level of 99%.