(2) It has a slow rate of convergence, and (3) coding of this method may be harder than other available methods. However, it has several disadvantages to be employed as an adequate hydraulic solvers: (1) It requires an initial guess that conserves continuity equations in the very first iteration in advance of analyzing WDNs. Hardy Cross method, which exploits the Newton-Raphson method, is one of the methods available for this purpose. This analysis is mainly aimed at solving a set of first-order nonlinear differential algebraic equations with iterative methods. Such knowledge is exclusively provided through pipe network analysis. In essence, management and design of WDNs require the knowledge of flow and pressure fields within WDNs. Water distribution networks (WDNs) are a critical infrastructures that affect the daily life of each and everyone who consumes purified water. 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. 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.

Matlab program hardy cross