Abstract
Many attempts to date have been directed to develop a relationship for the prediction of the hydraulic gradient im in heterogeneous flow of settling slurry having coarse solid particles. This fact indicates clearly that existing correlations lack the universality, and often provide poor im prediction results due to the great diversity of flow conditions.In this paper a heterogeneous suspentions model was developed for the flow simulation and scale-up of slurry pipelines in the deposit regime. Our analytical work has two main steps: In the first part, the modified O'Brien's equation for distribution of suspended particles above the bed was derived, and solved mathematically. Secondly, the mean velocity-hydraulic gradient correlation was determined in theory.The predictions for the concentration distributions and the hydraulic gradient from the model were in good agreement with experimental results taken from the published literature for a variety of flow conditions of slurries. Based on the above analyses, we also discussed specific energy, Batchelor's dimensionless number, and Durand-Condolios equation.As a result, it was confirmed that in the design of slurry pipelines for the commercial transportation of any materials our study made possible to predict the hydraulic gradients precisely in the deposit regime without laboratory flow loon tests.
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