The objective of this work is to apply the Finite Element Methodology (F.E.M.) to several piping systems, using an incompressible working fluid, in order to calculate the volumetric flow on each element and the piezometric load on each node of the network. To accomplish this goal a computational code was designed using Fortran Computational Language. Such a code consists of a main program and six subroutines. The input variables are general data of the network including the number of pipes, the number of nodes, the piezometric load values on nodes where they are constant (tanks for example), demanding flows in those nodes where the fluid is removed from the system, a connectivity table indicating the assumed flow direction in each pipe, and the number of pumps with respective parabolic curve coefficients. Program data also included both the maximum number of iterations and tolerance allowed. Fluid properties such as kinematic viscosity, density and pipe features such as length, diameter and absolute rugosity are also required. The output data include pipe volumetric flows and piezometric load on variable static pressure nodes.
In this work, three different network systems were analyzed: 51-, 63- and 65-element networks. All were examples taken from the bibliography. The Finite Element Methodology results were first validated with real data, and then compared with the other results coming from the Hardy-Cross, Newton-Raphson and Linear Methods. The comparison was based on convergence speed and numerical stability. It is concluded that the methodology called Finite Element Methodology requires a smaller number of iterations than the Hardy-Cross, Linear and Newton-Raphson Methods. Another advantage of the Finite Element Methodology is that there is no need to assign the flow initial values that satisfy the Continuity Equation on each node of the piping network before running the program. Also, no loops establishing is needed. In addition, the designed code permits calculations for networks that present both booster and feed pumps. The importance of this work rests on the fact that nowadays it is necessary for piping network flow analysis to use computational simulation in order to design systems more efficiently and economically. Furthermore, this work is important for network construction as well as the satisfaction of consumer demand on a local community level, taking into account prevailing normative requirements. This paper, consequently, aims to contribute to progress in these areas.