Incorporating the Modified Orifice Equation into Pipe Network Solvers for More Realistic Leakage Modeling

Abstract

It has been well established in several experimental and modeling studies that leak areas are often not fixed, but vary as linear functions of pressure. Replacing this linear equation into the orifice equation results in a two-part modified orifice leakage equation with head exponents of .5 and 1.5. The purpose of this study was to incorporate the modified orifice equation into the hydraulic network formulation and evaluate its impact on model performance. The conventional and modified software were applied to 6 instances of stochastic leakage distributions in three different pipe networks. It was found that the conventional power leakage equation results in significant leakage volume and flow-rate errors under certain conditions. In addition, a problem of nonconvergence of the conventional global gradient algorithm for leakage exponents greater than 2 was observed and is discussed.