Calculation of the hydraulic gradient due to the upward flow of a large size particles-water mixture in a swaying vertical pipe is a central problem in the design of systems for deep-sea mining of manganese modules. Here, the problem is investigated experimentally and with a mathematical model. An experimental apparatus that mimics the deep-sea mining system was built to investigate the effects of swaying on the hydraulic gradient. The experimental results reveal that the hydraulic gradient in a swaying vertical pipe is greater than in a fixed vertical pipe (for the same flow and solid-loading conditions) as a result of the instantaneous particle-wall collisions and the solids sliding over the pipe wall. A mathematical model for the mixture flows is suggested based on a Lagrangian simulation technique. The model results offer additional insight into the dynamics of this complex flow and agree well with the new laboratory data.