The calculation of the hydraulic gradient due to the upward flow of a large size particles—water mixture in a vertical pipe is a central problem in the design of systems for deep-sea mining of manganese nodules. Here, the problem is investigated experimentally and with a new calculation method. An experimental apparatus that mimics the deep-sea mining system was built to measure the hydraulic gradient due to the mixture upward flow, the settling velocity of a single manganese nodule, and to explore the relationship between the concentration of fluidized manganese nodules and the solid slip velocity. Experimental relations are found. Also, a formula to compute the total hydraulic gradient of the mixture flow under different flow and solid-loading conditions is developed; the formula accounts for the hydraulic gradients produced by the liquid phase, the solid phase, and the inter-particle collisions. The predictions obtained with the derived equation are compared with experimental data readily available and with the newly acquired laboratory data; these predictions agree very well with the empirical data and demonstrate the value of the model as a design tool.

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