Estimation of leak area-pressure relationship for cracks on water pipes using models based on linear-elastic fracture mechanics

Abstract

The assessment and control of the real losses from water distribution systems require the accurate estimation of the flow rate from an individual leak as a function of the internal pressure. The lack of analytical models able to accurately describe the relationship between the area of the leak and the pressure head is the key problem. This paper utilized the linear-elastic fracture mechanics (LEFM) theory for thin shells to derive models for both longitudinal and circumferential cracks. The models were validated by both finite element (FE) simulations and laboratory experiments under varying crack and pipe parameters. Both fluid-structure interaction (FSI) and traditional FE simulations were performed, and the results were compared to quantify the effect of leakage hydraulics on leak area. In the laboratory experiments, an image analysis technology was utilized to measure the leak area and flow rate simultaneously, so that the effect of the discharge coefficient could be excluded. In addition, the leak area was systematically measured under the effect of different parameters. The results revealed that the values predicted by the derived models were in good agreement with the experimental and FE simulation values for both types of cracks. The LEFM theory and the phenomena observed in this study can improve our understanding of the leak behavior and enable the development of effective pressure management strategies for water distribution systems.