A $500 \mathrm{~m}$ long water distribution pipeline $\text{P}$ with diameter $1.0 \mathrm{~m}$, is used to convey $0.1 \mathrm{~m}^{3} / \mathrm{s}$ of flow. A new pipeline $\text{Q}$, with the same length and flow rate, is to replace $\text{P}$. The friction factors for $\text{P}$ and $\text{Q}$ are $0.04$ and $0.01$, respectively. The diameter of the pipeline $\text{Q}$ (in meters) is $\_\_\_\_\_\_$ (rounded off to $2$ decimal places).