Settling-velocity radius scaling
= Settling-velocity radius scaling
{title2=$W_s\propto r^2\ \text{or}\ r^{1/2}$}
For spheres with the same density contrast, balance submerged weight, proportional to $r^3$, against <Stokes drag law>, proportional to $rW_s$, to obtain $W_s\propto r^2$. With constant <drag coefficient>, <quadratic drag> is proportional to $r^2W_s^2$, giving $W_s\propto r^{1/2}$. The two radius laws require their corresponding <particle Reynolds number> limits.