Part I

Prove that for a discrete type I spherical particle of diameter $($d$)$ settling in a grit chamber of a wastewater treatment plant the terminal settling velocity is given by the following Stokes Law equation:

$V_S=\frac{g{d}_p^2({}_p-{}_w)}{18}$

Where: $V_s=$ terminal settling velocity, $g=$ gravitational constant $=9\mathrm{.}81\frac{m}{se{c}^2},$

$(d_p)$ particle diameter in $m,=$ dynamic viscosity $(k\frac{g}{m}-sec)$

${}_p=$ particle density $k\frac{g}{m^3},{}_w=$ water density $k\frac{g}{m^3},$

Part II