The effect of shape and density on the free settling of particles at high Reynolds numbers

Terminal velocity drag coefficients C D were determined for cylinders, prisms, disks, and spheres in air and water at N Re from 1,000 to 300,000, the regime where particles rotate and/or oscillate. These and other similar data show that C D is a function of particle and fluid densities ρ p and ρ f , as well as shape and N Re . By considering C D a function of particle moment of inertia and the rotational moment generated by circulation (or alternatively the field force and the lift), one can deduce that {article}{empty}{document}CD = f(ρ pρ p\, or\,ρ p - ρ fρ f,a length ratio, N_ RE ){document} . This relationship correlates the data for ρ p = 1.2 to 8.3 and ρ f = 0.1 to 1.3 g./cc. to within ± 10%.