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Modeling an unsteady flow is an important problem in pressurized pipeline systems. Depending on the dimensions and properties of the fluid and pipeline material, the generation of hydraulic transient issues and their spatiotemporal variation patterns can be different. To address the water hammer problem without scale issues in pipeline systems, this study developed a dimensionless impedance method (DIM). The existing partial differential equations of mass, momentum, and energy conservation were converted into corresponding dimensionless equations. The solutions of proposed equations were analytically developed in terms of several operators in the dimensionless frequency domain. A dimensionless water hammer number was introduced to address the similarity in hydraulic transients between different systems. Both numerical and experimental comparisons showed that the DIM well matched the existing methods. Based on comprehensive simulations of water hammer phenomena for ranges of water hammer numbers, a vectorized chart was formulated for a reservoir pipeline valve system. Both simulations and calibrations of the experimental hydraulic transients achieved well-matched results between the DIM computations and chart interpolation results. The proposed DIM method can provide substantial efficiency for both simulation and calibration, as well as generality in transient solutions for pipeline systems.

Dimensionless impedance method for the transient response of pressurized pipeline system