The wetted-well column shown in Figure 30.4 is used to humidify a pressurized air stream. Bone-dry air (containing no water vapor) at 2.0 atm and 27°C is introduced to the bottom of the column at a volumetric flow rate of 4000 cm³/s. Liquid water is added to the top of the column. The liquid water uniformly coats the inner surface of the tube as a thin liquid film flowing downward. The falling liquid film of water evaporates into the air flowing upward. The wetted-wall column has an inner diameter of 5.0 cm and a length of 6.0 m. The column temperature is maintained at 27°C, and the total system pressure is maintained at 2.0 atm. At 27°C, the kinematic viscosity of air is 0:157 cm²/s and the vapor pressure of liquid water is 0.035 atm. The gas is ideal with R = 82:06 cm³: atm/g mol : K.

a. What is the diffusion coefficient of water vapor in air at 2.0 atm and 27°C?

b. Determine the Sherwood number for the gas phase.

c. Evaluate the gas film coefficient, k_cG, based on the partial pressure driving force.

d. What is the maximum possible concentration of water vapor in the air?

e. Evaluate the concentration of water vapor in the air stream exiting the wetted-wall column. You will need to do a material balance on water vapor within a differential volume element of the column.