Finally, the achieved results demonstrate that the equation selected for computing Darcy–Weisbach friction factor has an inevitable impact not only on the accuracy but also on the convergence of pipe network analysis.
#BENTLEY WATERGEMS PIPE LIBRARY PROFESSIONAL#
Moreover, as many scenarios outperform those of the outdated explicit equation used for the same purpose in professional hydraulic solvers such as EPANET and WaterGEMS, it was recommended they be replaced with one of the explicit equations with higher accuracy. Moreover, 15 explicit equations, which were successfully performed in analyzing all sample networks with the closest results to that of the benchmark solution, were introduced as the most accurate ones. According to the obtained results, 15 explicit relations face the convergence problems which were identified as unreliable equations. In each scenario, one of these explicit relations was considered in the process of analyzing water networks. In the numerical experiment, these pipe networks were solved using three different h-based methods including h-based Newton–Raphson method, finite element method, and the gradient algorithm. In this study, 56 explicit relations available in the literature were implemented in the analysis of four water distribution networks while the benchmark solution is computed considering the implicit C–W formula. This obviously indicates that the modified schemes, particularly the three-step methods, improve the performance of the original loop corrector method by taking lower number of iterations with the compensation of relatively more computational efforts.Īlthough many explicit correlations have already been presented as alternatives to implicit Colebrook–White (C–W) formula, performances of C–W-based relations in pipe network analysis have not been investigated. The results show that the one-step methods improve the rate of convergence of the Hardy Cross method in 10 out of 24 cases (41%), while this improvement was found to be 39 out of 56 cases (69.64%) and 5 out of 8 cases (62.5%) for the two-step and three-step methods, respectively. The performances of these new methods and Hardy Cross method were compared by solving a sample pipe network considering four different scenarios (92 cases). The presented methods were classified into one-step, two-step and three-step schemes based on the number of hypothetical discharges utilized in solving pipe networks. In this study, twenty two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis.