Approximate Analytical Solution for Lowest Water Level of One-Way Surge Tank in Long-Distance Pipeline System during Hydraulic Transients

A one-way surge tank (OWST) is a critical facility for balancing water hammer pressures in long-distance pipeline systems, and its cross-sectional area is determined by the lowest water level (LWL) during the hydraulic transient process. Currently, LWL estimation relies primarily on numerical simulations and lacks theoretical or formulaic references. To address this gap, this study first analyzed the propagation law of pressure wave in a pipeline system featuring an OWST and quantified their influence on the OWST discharge using the Joukowski law. Subsequently, an improved mathematical model describing the surge characteristics of the pipeline system was derived. Finally, by incorporating the impact of pressure wave on OWST discharge, an explicit expression for water level oscillations was deduced based on the Krylov–Bogoliubov–Mitropolsky method, resulting in an approximate analytical solution for the LWL. The numerical validation tests revealed that OWST discharge exhibited a step-like change under the influence of a pressure wave, and the LWL closely aligned with the proposed method. In conclusion, these findings contribute to a deeper understanding of water hammer mitigation in OWST, demonstrating significant engineering relevance for their safe and efficient operation.