Solid Particles Falling Through Fluids

Abstract

The forces acting on a sphere falling through a fluid (call it gas for convenience) are as follows:

$$ \left|\left(\begin{array}{c}\hfill \mathrm{Force}\;\mathrm{causing}\hfill \\ {}\hfill \mathrm{particle}\;\mathrm{t}\mathrm{o}\hfill \\ {}\hfill \mathrm{accelerate}\hfill \end{array}\right)\right|=\left|\left(\begin{array}{c}\hfill \mathrm{n}\mathrm{e}\mathrm{t}\;\mathrm{weight}\hfill \\ {}\hfill \mathrm{of}\;\mathrm{particle}\hfill \end{array}\right)\right|-\left|\left(\begin{array}{c}\hfill \mathrm{drag}\hfill \\ {}\hfill \mathrm{force}\hfill \end{array}\right)\right|\kern2em \left[\frac{\mathrm{kg}\cdot \mathrm{m}}{{\mathrm{s}}^2}\right] $$