The ULS (underwater launch system) driven by piston pump exhibits complex hydrodynamic phenomena during launch process, leading to significant challenges in accurately predicting internal ballistic trajectories. Accurate and efficient prediction, however, not only enhances ballistic control precision but also reduces R&D costs and development cycles. Therefore, establishing a streamlined, efficient, and accurate analytical model for internal ballistic trajectory prediction is crucial for the design, optimization, and control of ULS. This study investigates the coupling mechanism between the piston movement, equipment movement, fluid velocity, flow rate and pressure in a ULS driven by a piston pump. First, the hydrodynamic characteristics of the ULS during launch operations were analyzed. Based on these characteristics, simplified assumptions and definitions were established to develop the analytical model. Next, the governing flow equations were developed using mass and energy conservation principles, explicitly accounting for clearance leakage between the piston and equipment caused by pressure differentials and motion-induced effects. Subsequently, CFD-based analysis was conducted to investigate localized pressure losses and spatial pressure distribution during the launch process. Based on these findings, a pressure equations incorporating both localized losses and pressure gradients was developed for the analytical model. Finally, the model's accuracy is validated through multi-operational condition experiments, which show that the maximum motion speed errors for the piston and equipment are 5.4 % and 6.9 %, respectively.
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