Abstract
The effect of the pipe material plays a preeminent role in the overall water leakage behaviour of cracks, and specifically of longitudinal cracks for pipes composing Water Distribution Systems. Due to pipe material properties, a longitudinal crack on a pipe exhibits expansion behaviour under internal pressure increases, taken up by hoop stresses, which cause high stress concentration around the crack, provoking the expansion of cracked areas. With the aim of assessing the increment of water leakages through longitudinal cracks, caused by pressure increase, in this paper results from experimental tests of a longitudinal crack on a pipe wall were analysed and discussed. This is achieved by subjecting several plates with different length of cracks to tension and monitoring the opening of the cracks. A mathematical model for longitudinal crack opening is derived using the orifice equation, as a function of pressure, pipe material properties, pipe geometry and fluid properties for uni-axial stress state. Subsequently, an equation describing the increase of the leakage flow rate as function of the increase of the crack area in uni-axial stress state is determined. The derived model (Ilunga’s Equation) contradicts the Torricelli’s orifice equation which assumed that the orifice area is fixed, but variable with the change in pressure due to pipe material properties.