A catalyst having spherical particles with $d_{p}=50 \mu \mathrm{m}$ and $ho_{s}=1.65 \mathrm{~g} / \mathrm{cm}^{3}$ is used to contact a hydrocarbon vapor in a fluidized reactor at $900^{\circ} \mathrm{F}, 1 \mathrm{~atm}$. At operating conditions, the fluid viscosity is $0.02 \mathrm{cP}$ and its density is $0.21 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$. Determine the range of fluidized bed operation, that is, calculate

(a) Minimum fluidization velocity for $\varepsilon_{m f}=0.42$

(b) The particle terminal velocity