Abstract

The relationship between the fall velocity and orthogonal axis ratios of differently shaped grains with stable settling patterns is examined. Contrary to what is generally supposed, the ratio of the intermediate to the long diameter Di/Dl, which is related to the maximum projection area normal to the direction of settling, appears to have the least influence. The best correlation is shown by the ratio of the short to the long diameter Ds/Dl, with Ds/Di giving less accurate results. A modified hydrodynamic shape index given by [1 − (Ds/Dl)]x is proposed, which yields an improved, simplified settling equation applicable to spheroids, prolate and oblate spheroids, discs, cylinders, and ellipsoids. There appears to be a unique value of x for different grain shapes settling within specific ranges of Reynolds numbers. Based on the results of this study, a hydrodynamic classification of grain shapes is proposed.

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