Simple Beam Model to Estimate Leakage in Longitudinally Cracked Pressurized Pipes

Losses from water distribution systems are reaching alarming levels in many cities throughout the world. Leakage is often the principal cause of water loss due to aging and deterioration of these systems and pressure has been verified to assume a key-role in water loss management. This paper presents a simple analytical model based on a beam with elastic constraints to estimate the leak area (from which the leakage is then estimated) in longitudinally cracked pressurized pipes and to evaluate the effect of pressure on the opening area of the crack. The model is calibrated on the results of a three-dimensional finite element analysis and then validated by experimental results. The validation has been carried out for a wide range of pipes made of different materials (PVC, cast iron, asbestos-cement, and steel) with radii ranging from 27.5 mm to 110 mm and thicknesses from 1.5 mm to 12 mm and crack lengths from 50 mm to 200 mm. The beam model, notwithstanding its simplicity, provides reliable leakage evaluations in longitudinally cracked pressurized pipes.