Catalyst pellets $5mm$ in diameter are to be fluidized with $45000k\frac{g}{h}$ of air of density $1k\frac{g}{m^3}$ and viscosity $0\mathrm{.}0002$ poise at $1$atm and $80C$ in a vertical cylindrical vessel. The density of the catalyst particles is $960k\frac{g}{m^3}$; their sphericity is $0\mathrm{.}86.$ If the given quantity of air is just sufficient to fluidize the solids with the voidage at minimum fluidizing condition being $0\mathrm{.}45,$ what is the vertical cylindrical vessel diameter? Use Ergun equation.