Air can be humidified by passing through a long tube whose inside diameter is lined with a wick saturated with liquid water. The device is shown below. In the process, air containing 1.0 mol % water vapor at 40°C and 1 atm total pressure enters a 3.0 cm inside diameter tube at a velocity of 3 m/s. Water evaporates from the wick as the air passes over it. Water adsorbent liner with 1.0 mm thick 0.6 g water/cubic cm liner. Gas stream velocity of 3 m/s, 1 atm and 40C D=3.0 cm L=8m There is no diffusion resistance of water vapor through the wick itself. The entire process is maintained at 40°C where the saturated vapor pressure of water is 55.4 mmHg. The viscosity of air under these conditions is 1.91 x 104_8_ and the density of air is 1.13 x 10-38. The cm-S diffusivity is 0.28
(i) Using a shell balance, develop a differential equation to predict the concentration of water vapor exiting the tube.
(ii) Integrate the equation you developed in (a) with the appropriate boundary conditions (or limits) to obtain the final form of the equation to predict the concentration of water vapor exiting the tube.
(iii) If the thickness of the wick lining the inner surface of the tube is 1.0 mm and it initially contains 0.6 g of water per cm'. If the tube is 8.0 m long and humidification occurs at 40°C and 1.0 atm pressure, determine the concentration of water vapor in the outlet air.
(iv) Determine how long the process can operate before the liquid water is depleted.