Settling-velocity radius scaling ($W_s\propto r^2\text{or}{r}^{1/2}$)

For spheres with the same density contrast, balance submerged weight, proportional to $r^3$, against Stokes drag law, proportional to $r{W}_s$, to obtain $W_s\propto r^2$. With constant drag coefficient, quadratic drag is proportional to $r^2{W}_s^2$, giving $W_s\propto r^{1/2}$. The two radius laws require their corresponding particle Reynolds number limits.