A distillation column is being used to separate methanol and water at atmospheric pressure. The column temperature varies from approximately 65°C at the top to 100°C at the bottom. Liquid enters the top of the column and flows down to the bottom; vapor is generated in a reboiler at the bottom of the column, flows upward, and leaves at the top. The molar flow rate of vapor up the column may be assumed to be constant from top to bottom. The vapor velocity is kept below 5.0 ft/s to keep the vapor from entraining liquid (suspending and carrying away liquid droplets). 

(a) Where in the column is the greatest risk of liquid entrainment? Explain your answer. 

(b) Assuming that the liquid flowing down the column and the column internals (equipment inside the column) occupy a negligible fraction of the column cross-sectional area, estimate the minimum column diameter if the vapor flow rate is 25.0 lb-mole/min. 

(c) Suppose the column is constructed with a diameter 10% greater than that determined in Part (b). What are the vapor velocities at the top and bottom of the column if the vapor molar flow rate in both locations is 25.0 lb-mole/min? How much can the vapor molar flow rate be increased without causing liquid entrainment? 

(d) There is a need to increase process throughput, which would require the vapor molar flow rate to be doubled. It has been suggested that increasing the pressure in the column would allow that to be done without risking excessive liquid entrainment. Again applying a vapor velocity limit of 5 ft/s, what would the new pressure be?