Title: Characterising the pressure-leakage response of pipe networks using the FAVAD equations
This study investigated the feasibility of characterising the pressure-leakage response of water distribution systems using the FAVAD (Fixed and Variable Area Discharges) equation, instead of the conventional N1 power equation. The study was based on 300 network models with randomly distributed leaks and 35 networks generated through a sensitivity analysis. It was found that the leakage rate and average zone pressure head (AZP) before and after pressure reduction may be used in conjunction with the FAVAD equation to estimate the initial leakage area (A0S) and head-area slope (mS) of any system. In addition, A0S and ms were shown to provide good estimates respectively of the sum of the initial areas and head-area slopes of all the individual leaks in the system. The study found that a dimensionless leakage number may be calculated for any system and used to characterise the pressure-leakage response. Finally, the study showed that it is possible to convert between N1 and the leakage number using a simple equation.
Title: Incorporating the Modified Orifice Equation into Pipe Networks Solvers for More Realistic Leakage Modeling
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 0.5 and 1.5 respectively. 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 600 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 non-convergence of the conventional global gradient algorithm for leakage exponents greater than two was observed and is discussed.
Title: Predicting the Head-Area Slopes of Circular Holes in Water PipeH
Leak openings in water distribution system pipes are not static, but vary with pressure. These changes in area affect the way that leaks respond to changes in pressure, and are thus important for municipal engineers to understand. In this study, the behavior of round holes in pressurized pipes was investigated using finite element analysis (FEA), under the assumption of linear elastic behavior. It was found that the areas of the round holes vary as linear functions of pressure in the pipe. A sensitivity analysis was then carried out to investigate parameters that influence the head-area slope. The elastic modulus, internal pipe diameter and pipe wall thickness were found to be the most important parameters. Solid mechanics theory was used to develop an equation to predict the head-area slope m of round holes in pipes. Finally, the results were compared to the findings of an experimental study. The comparison showed that the head-area slopes for both the equation and the FEA were within or close to the 95 % confidence intervals of the experimental study
Title: Characterising Leakage in a Real Transmission Main by Means of a Pipe Condition Assessment Equipment:
In this paper the performance of a Pipe Condition Assessment Equipment (PCAE) device, developed at the University of Cape Town is verified. The condition of a real transmission main in South Africa is tested using the PCAE. The physical characteristics of the detected leaks on the main are determined using the modified orifice leakage model. The overall results of the test are discussed in terms of the effectiveness of the PCAE to detect leakage and the ability of the modified orifice equation to characterise leaks in real transmission mains.