Shape entropy and settling velocity of natural grains

The shape of sedimentary particles has been quantified by many different form indices, which have been utilized mainly in determining grain hydrodynamic behavior. Although the orthogonal axis dimensions required for calculating shape indices are easily measured in the case of grains larger than 2 mm, this is impractical for sand and silt. Different data sets of the settling velocity of natural quartz grains varying in size between 0.0001 and 1 cm are used in this paper to determine their mean Hofmann shape factor, which defines a polynomial curve. In the grain-size range from clay to medium-size pebbles, sand exhibits the highest sphericity, culminating with coarse to very coarse sand. The two polynomial equations describing the curve are employed to determine the settling velocity of natural grains, with a mean accuracy of 95.1 (+/-4.5) %. The latter is similar to that obtained for both smooth ellipsoids and angular grains, which suggests that grain roundness does not play a major role in the settling velocity of particles up to a Reynolds number of at least 4,200.