Experiments on the pressure drop created by a sphere settling in a viscous liquid. Part 2. Reynolds numbers from 0·2 to 21,000

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Abstract
The pressure drop ΔP created by the motion of a ‘small’ spherical particle settling along the axis of a large-diameter circular cylinder filled with a quiescent liquid was measured in the particle Reynolds number range (based on diameter) from Re = 0·2 to 21,000. For Re < 125 it was found that ΔPA/D = 2·0 (A = cylinder cross-sectional area; D = particle drag), in agreement with existing theory in the Stokes and Oseen regimes. Beyond Re = 125 a fairly abrupt transition occurs, the ΔPA/D ratio decreasing asymptotically towards 1·0, the limiting value predicted by elementary momentum principles for an ‘unbounded’ fluid, with increasing Re. At Re ≈ 6000 the transition is essentially complete.

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