Problem $1(25$ points$)$

A catalyst developer is trying to determine the length of edge of a cube for a catalyst made

from the exact same material of a spherical catalyst they use. The spherical catalyst has a

density of $2500k\frac{g}{m^3}$ that has a terminal velocity of $0\mathrm{.}15\frac{m}{s}$ in a fluid of density ${70}_k\frac{g}{m^3}$

and viscosity of $0\mathrm{.}0005Pa*s.$ Determine the diameter of the spherical particle? What is the

edge length of a similarly designed cube catalyst with the same terminal velocity in the same

type of fluid $($i$.$e$.$ particle and fluid densities$/$viscosities are the same in both cases$)?$

Hint: You need to know how to relate particle diameter of sphere to that of the length of the

cube.