A circular sewer pipe, having Manning's coefficient $(n)$ of $0.01$, is laid at a bed slope of $1: 100$. If it is flowing $80 \%$ full for a discharge of $2 \mathrm{~m}^{3} / \mathrm{s}$, then its diameter is $\_\_\_\_\_\_ \: \mathrm{m}$. (rounded off to three decimal places)
