A new relationship between grain size and fall (settling) velocity in air

Abstract

The fall velocity of natural sand grains is a fundamental attribute of sediment transport in fluid environments where particles may become partially or fully suspended. Several formulae have been proposed to calculate the fall velocity of particles in air, but there is considerable uncertainty about which is the most accurate or appropriate for a given set of environmental conditions. Five experiments that reported observations of fall velocity of different types of particles in air are described, evaluated, and compared. The experiment data were quality-controlled using four criteria: (1) particles had to have sufficient drop heights to attain their terminal fall velocity; (2) particles had to be in the range of sand sizes; (3) data identified as being problematic by the original authors were removed; and (4) particles comprise natural, irregular shaped sediments. The quality-controlled data were aggregated and analyzed using linear regression to obtain a relationship between grain size (d, in mm) and fall velocity (w₀ , in ms^-1): $w_0=4.248d+0.174$ . This is a statistically strong relationship with a coefficient of determination of 0.89 (p < 0.001). This relationship can be regarded as a universal fall velocity model for natural, sand-sized particles falling through a static column of air. In terms of predictive analyses, our heuristic method outperforms alternative formulae and yields a better fit to the experimental data over the full range of sand sizes.