The mean velocity of slightly buoyant and heavy particles in turbulent flow in a pipe

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Abstract
A large number of small spheres of the same size were injected successively into a horizontal pipe conveying water at constant mean velocity, and their times of transit were measured. The mean velocity of the spheres that were either somewhat heavier or lighter than water was less than that of those of neutral density; for those having a terminal velocity in water within ± 1% of the mean velocity of the water in the pipe, the discrepancy was only about 0.1%. The dispersion of the times of transit of the spheres was almost independent of their density. A theory is developed to show how the mean velocity of the spheres depends upon their relative density and size.

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