Waste gas (left(mathrm{CO}_{2} ight)) is vented to outer space from a spacecraft through a circular pipe (0.2

Waste gas \(\left(\mathrm{CO}_{2}\right)\) is vented to outer space from a spacecraft through a circular pipe \(0.2 \mathrm{~m}\) long. The pressure and temperature in the spacecraft are \(35 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). The gas must be vented at the rate of \(0.01 \mathrm{~kg} / \mathrm{s}\). The friction factor for the flow in the pipe is given by

\[ \begin{gathered} f=64 / \operatorname{Re}, \quad \operatorname{Re}<5000 \\ f=0.013, \quad \operatorname{Re}>5000, \quad \operatorname{Re}=\frac{4 \dot{m}}{\pi \mu D} \end{gathered} \]

The viscosity \((\mu)\) is \(4 \times 10^{-4} \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\). Determine the required pipe diameter.