The equation to determine the terminal settling velocity of a particle through a fluid is

$v_s=\frac{({}_p-{}_w)d_p^{2}g}{18}$

where

$v_s=$ velocity of the particle in $\frac{m}{s}$

${}_p=$ density of the particle in $k\frac{g}{m^3}$

${}_w=$ density of the fluid in $k\frac{g}{m^3}$

$d_p=$ diameter of the particle in $m$

$g=$ acceleration due to gravity $\frac{m}{s^2}$

$=$ viscosity of the fluid in $P{a}^{**}$ s

Using the SI system of units, show that the right side of the equation is dimensionally homogenous with the left side equation, where both sides are expressed in $\frac{m}{s}.$

Hint #$1$: $"18"$ in the equation is a constant, and therefore, can be removed for this exercise.

Hint #$2$: You will need to break down the unit Pa into its base units.