Characterization of leak flow from pipes under the effect of cavitation in water distribution systems

The leakage flow-pressure relationship in water distribution systems (WDSs) is critical for leakage assessment and management. Few studies to date have addressed the impact of hydraulic factors on the discharge coefficient (C_d). The observed decline of C_d with increasing Reynolds number (Re) contradicts the theoretical stability of turbulent flow at Re>30,000, suggesting cavitation effects. This study employs a combined approach of direct visualization experiments and transient computational fluid dynamics (CFD) simulations to systematically investigate the flow characteristics of low-deformability circular orifices on pipes under pressure heads of 0-70 mH₂O. The occurrence of cavitation was confirmed via visual observation, hydraulic analysis, and CFD simulations. Empirical models were established for post-cavitation C_d -pressure relationships, critical cavitation pressure, and pre-cavitation C_d-t/d correlations. Analysis based on CFD results demonstrates that as t/d increases from 0.5 to 1.2, flow re-expansion after the vena contracta induces a local vacuum, amplifying the effective pressure drop and intensifying cavitation. This study also explains why leakage exponent (N1) values significantly below 0.5 have been observed in some previous experiments, providing a hydraulic basis for accurate leakage prediction and pressure management in WDSs.