Vertical tubes 100 mm in diameter and 6 m long are used to concentrate a dilute aqueous solution in a once-through falling-film evaporator. The flow rate per tube is 3,000 kg/h, and the viscosity of the solution at the initial boiling point is 2.5 cP 

(a) What would be the average residence time of the liquid in the tube if no evaporation occurred? 

(b) What fraction of the water would be evaporated if the overall ΔT were 90°C and the overall heat-transfer coefficient were 3,500 W/m². °C? 

(c) If the same fraction evaporated could be achieved in an upflow evaporator of the same size. what would be the average residence time? (Assume the fluid in the tube is two-thirds liquid and one-third vapor.)