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 \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm C}_{\rm D} = {\rm f}\left({\frac{{\rho {\rm p}}}{{\rho {\rm p}}}\,{\rm or}\,\frac{{\rho {\rm p} - \rho {\rm f}}}{{\rho {\rm f}}},\hbox{a length ratio, N}_{{\rm RE}}} \right) $\end{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%.