Settling velocities of particulate systems, 3. Power series expansion for the drag coefficient of a sphere and prediction of the settling velocity

The following equation has been previously developed for the drag coefficient of a sphere.

$\text{C}{}_{\mathrm{D}}\text{= C}{}_0\text{[1 + (σ}{}_0\text{/Re}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)]}{}^2$

In this work the authors propose a power series expansion for C₀ in terms of the Reynolds number:

$\text{C}{}_0\text{= 0 284153}\text{Σ}\text{α=0}\text{n}\text{B}{}_{\mathrm{\alpha }}\text{Re}{}^{\mathrm{\alpha }}$

A fifth-order polynomial permits obtaining the drag coefficient and the settling velocity of a sphere, up to a Reynolds number of 3 × 10⁵, with an average relative error of about 2%.