Probability of Pressure Deficit in On-Demand Branched Networks and Incorporation into Design Decisions

Abstract

This technical paper presents analytical expressions to estimate the probability function of head losses in any path of an on-demand branched irrigation network. They are developed for estimating the probability of pressure deficit of a given magnitude at any hydrant. They are also useful for examining the probability of a power deficit at a pumping station designed to guarantee service to a hydrant, as well as the head characteristic curve of the distribution system linked to a definite probability. All this quantified information is useful for decision making on network design and performance. The probabilities calculated with the developed expressions can be taken as complementary or alternative concepts to Clément’s classical design flow method, which is taken here as a benchmark for comparisons. Illustrative examples of network designs are presented to validate the proposed expressions. The least cost design solutions using Clément’s design flows are compared with design solutions here obtained to get the same probability of pressure deficit at the most unfavorable hydrants. The new solutions are less expensive because the flow constraint can be avoided.