Matrix Methodology to Study the Probability of Pressure Deficit in On-Demand Branched Irrigation Networks

Abstract

This paper presents a matrix algebraic expression based on the probability of pressure deficit. A set of expressions to calculate the average and the variance of the aggregated head losses in any pathway of the irrigation network is proposed, and the probability law of the aggregated head losses is deduced. A methodology to design and manage on-demand branched irrigation networks based on the probability of pressure deficit is developed. The proposed methodology corrects some weak points detected in previous methods related to the probability of pressure deficit concerning certain sections with large head losses. The methodology is tested in two networks (one simulated and one real network belonging to the Canal de Estremera Irrigation District). The resulting data show the capability of the methodology to model the simulations. The results also show that when designing the network with the proposed methodology, the total cost of the project decreases and management of the network becomes more efficient compared with certain traditional methods for irrigation network design.