Dry air, flowing at a velocity of \( 1.5 \mathrm{~m} / \mathrm{s} \), enters a 6 -m-long, 0.15 -m-diameter tube at \( 310 \mathrm{~K} \) and \( 1.013 \times 105 \mathrm{~Pa} \). The inner surface of the tube is lined with a felt material (diameter-to-roughness ratio, \( D / \varepsilon \), of 10,000 ) that is continuously saturated with water at \( 290 \mathrm{~K} \). Assuming constant temperature of the air and the pipe wall, determine the exit concentration of water in the exit gas stream.
Diffusivity of water in air at \( 300 \mathrm{~K}=2.6 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s} \)
Kinematic viscosity of air at \( 300 \mathrm{~K}=1.569 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s} \)
The vapor pressure of water at \( 290 \mathrm{~K}=17.5 \mathrm{~mm} \mathrm{Hg} \)
The gas constant \( =0.08206 \mathrm{~L} \cdot \mathrm{atm} / \mathrm{mol} \cdot \mathrm{K} \)
The Fanning friction factor is given by: \( f=0.00791 R e^{0.12} \)