Water jet technique is widely used in the dredging of rivers and canals, and has significant engineering value. This work develops the sediment dynamic model to build a velocity-based bed load sediment transport model. The process of low-pressure water jet river bed erosion was investigated at various water jet pressures and nozzle outlet diameters, with the Shields Parameter serving as the sediment initiation threshold. The process of developing a flow scour pit is divided into three key stages: particle triggering, quick development, and dynamic equilibrium. A transient simulation of submerged three-dimensional jet erosion was performed using a mixture model in Fluent software, with the laboratory physical model parameters as reference. The numerical simulation findings that the erosion sand pit characteristic parameters agreed with experimental data, and the particle initiation model was also confirmed. An empirical formula was established based on numerical modeling and experimental data to estimate the characteristic size of the scouring pit during jet erosion equilibrium.