Is the leak head-discharge relationship in polyethylene pipes a bijective function?

Traditional characterization of the leak head-discharge relationship in pipeline systems relies on the use of power law functions to explain the increase in leakage rate with pressure when network and laboratory data are analysed. However, recent studies addressed that the leak behaviour is complex and influenced by pipe material and leak geometry. The experimental tests, carried out at Water Engineering Laboratory of the University of Perugia (WEL), Italy, show that the leak head-discharge relationship on polyethylene pipes is not a bijective function since it gives rise to different discharge values with respect to one value of the pressure. To explore this issue, two viscoelastic models of a leak in a polyethylene pipe are introduced and compared with other leakage models. The results show that the viscoelastic behaviour reflects the leak head-discharge relationship, and care should be taken in the use of bijective relationships.