Abstract: Reservoir fluid mud is defined as a layer of highly sandy water that exists at the bottom of the reservoir, with strong mobility. The study of its movement law is of great significance for the realization of optimized scheduling of siltation reduction in reservoirs. In order to gain a more accurate understanding of the transport law of fluid mud, it is essential to not only comprehend the distribution characteristics of flow velocity within the fluid mud but also to elucidate the impact of various factors on the alteration of flow velocity and thickness during the movement of the fluid mud. In this paper, the power law model is selected as the rheological model of fluid mud based on the Navier-Stokes (N-S) equations. The motion model of fluid mud, constructed by the perturbation method, is simplified using the finite volume method with staggered mesh in space and the second-order Runge-Kutta method in time. During the numerical solution process, the parameters of the flow velocity distribution are introduced. And the parameters are corrected using Newton's iterative method, thereby ensuring that the model accurately reflects the flow velocity distribution pattern within the fluid mud. To validate the model, the flow test of fluid mud on gentle slope was conducted. The results demonstrated that the established model can effectively portray the movement process of fluid mud. Furthermore, the analysis of the bottom slope, fluid mud density, viscosity coefficient, and other parameters revealed the influence of these factors on the flow characteristics of fluid mud. The findings indicate that an augmentation in the density of fluid mud will curtail its mobility and diminish the thickness alteration along the way. An elevation in the incline of the bottom surface will markedly augment the flow velocity of the fluid mud and markedly transform the thickness distribution pattern. An augmentation in the viscosity coefficient will result in a reduction in the flow velocity of the fluid mud and a contraction in the duration of the movement, while also impairing the mobility of the fluid mud.