Some further observations on the hindered settling velocity of spheres in the inertial how regime

Recently, it has been shown that the expression for the wall correction factor, due to Newton, for the terminal velocity of a sphere settling in the high Reynolds number region correlates most of the literature data: k = (1 - A s/A) (1 - A s/A) 0.5 The objectives of this communication are threefold: firstly, to show that more recent data obtained in the free falling mode in cylindrical tubes, due to Bougas and Stamatoudis, up to d/D = 0.7 and 1350 ≤ Re ≤ 77,000, and due to Uhlherr and Chhabra up to d/D = 0.95 and Re ≤ 20,000, are also in line with the predictions of eq.(1) Secondly, the wall correction results for spheres obtained in wind tunnels of square cross-section up to As/A = 0.3 are also well correlated by eq.(1). These data thus extend the range of applicability of Newton's equation to the case of hindered settling in vessels of square cross-section. Eq.(1) represents the wall correction equally well irrespective of whether the sphere settles at its terminal velocity in a quiescent medium. Lastly and more importantly, it would be useful to know a priori the limiting values of the sphere Reynolds number beyond which one can use eq.(1).