A condensed finite element analysis of microirrigation hydraulics which incorporates pipe components

The hydraulic design of microirrigation systems is a tedious and time-consuming task. It was the goal of this research to simplify the design of microirrigation systems in order to conserve energy and water. Numerical solutions to microirrigation hydraulics are problematic because of the prohibitive number of network nodes which need to be analyzed. In this research, a partial differential equation was developed which incorporates the effect of pipe components at single nodes. The equation further condenses the network matrices by making use of the virtual node concept. The solution converges rapidly, and results are strongly correlated with existing finite element solutions which show strong correlation with empirical data. A large network was solved using the condensed finite element analysis developed in this research; where previous methods would require over 12,000 nodes to solve this network, the method developed here required only 80 nodes. Results correlate strongly to those obtained using the Backstep method.