Analysis of Liquid Flow-Induced Motion of a Discrete Solid in a Partially Filled Pipe

An analysis is presented for the liquid flow-induced motion of a solid in partially filled pipes. A general equation of the flow-induced motion of a solid is developed. Two alternate force models, one (F ) based on free stream velocity and another (F ) based on free stream momentum flux, are formulated to simplify the general equation. The equation of motion is solved for the motion of a cylindrical solid with steady-uniform liquid flows and the effects of relevant variables on the motion of a solid are predicted. The variables considered include: volume rate of liquid flow, Q; pipe diameter, D; Manning coefficient, n; and slope, S; solid diameter, d; length, L; specific gravity, σ; coefficient of friction between a solid and the pipe wall, η; and the two force functions, F and F . The flow rate, Q required to initiate the motion of a solid increases with an increase in D, n, d, L, σ, and η _s, and decreases with an increase in S. The force function F predicts a lower value of Q than does the force function F The velocities of a solid increase with an increase in Q and S and decrease with an increase in D, n, d, L, σ, and η. The force function F predicts higher values of the velocity of a solid than does the force function F . The effects of the variables Q _o, D, S, d, L, and η _s, on the velocities of a solid are qualitatively consistent with the available experimental data. The qualitative agreement between the predicted results and experimental data demonstrate the validity of the analysis presented.