A packed distillation column, with vapor having an average molecular weight of $45 \mathrm{~kg} \cdot \mathrm{kmol}^{-1}$, density of $2 \mathrm{~kg} \cdot \mathrm{m}^{-3}$ and a molar flow rate of $0.1 \mathrm{~kmol}^{-1}$, has a flooding velocity of $0.15 \mathrm{~m} \cdot \mathrm{s}^{-1}$. The column is designed to operate at $60 \%$ of the flooding velocity. Which one of the following is the $\text{CORRECT}$ value for the column diameter (in $\mathrm{m})$?
- $\frac{5}{\sqrt{\pi}}$
- $5 \sqrt{\pi}$
- $4 \pi$
- $\frac{10}{\sqrt{\pi}}$