Formulation and analysis of transient flows in fluid pipelines with distributed leakage

For health monitoring and condition assessment in water pipelines, most of the current transient-based leak detection studies simulate a practical leakage as a discrete point via the orifice equation. However, a solid evidence is yet to illustrate the validity of this simplification. Therefore, this study aims to fill this gap, by relaxing the assumption of leaks as dicrete points, and considering longitudinal crack-shaped leakages of various size. The analytical solutions based on the Fourier series in a typical reservoir-pipeline-reservoir are developed to analyze the time-domain pressure signals in transient operation. The proposed analytical solutions are numerically validated against the method of characteristics for different leaky scenarios including the leak ratio and longitudinal-crack length. Good agreement between the two methods demonstrates the effectiveness and accuracy of the derived analytical solution. For the distributed outflow along the entire pipe manifold, the numerical validation of the proposed analytical solution is provided by extracting data from the literature. The comparison among the time-domain signals of discrete and distributed leakage revealed that a longitudinal crack can slightly smoothen the pressure peaks with minor changes in amplitudes.