Ethyl benzene (boiling point 136.2°C) and styrene (boiling point 145.2°C) are separated by continuous distillation in a column operated under a vacuum to keep the temperature under 110°C and to avoid styrene polymerization. The feed is 30,000 kg/h with 54 percent ethyl benzene and 46 percent styrene (weight percent. and the products have 97 percent and 0.2 percent ethyl benzene. The relative volatility is 1.37, and with a reflux ratio of 6.15, about 70 plates are needed. The top of the column operates at 50 mm Hg and 58°C, and the average pressure drop per tray 2,5 mm Hg. 

(a) If the column is designed to have an F factor of 2.8 (m/s)(kg/m³ɣ^0.5 at the top, what diameter column is needed? 

(b) For a uniform diameter column, what would be the F factor at the bottom of the column? 

(c) If the column was built in two sections, with a smaller diameter for the bottom section, what diameter should be used so that F is never greater than 2.8?