1. A pump-around reflux is an internal reflux for a distillation column where the liquid is withdrawn from a lower tray, cooled in a heat exchanger resulting in heat recovery

and then sent back to an upper tray thus reducing the amount of top reflux. In a given distillation tower, the pump-around reflux is withdrawn from the 20th tray and sent to a pump on the ground which is located 20 m below the 20th tray. The pump discharge is cooled in a heat exchanger, and then returned to the 16th tray at the tray level through a control valve. The pump discharge line (including equivalent length of all fittings, bends,etc.) is 50 m long. For a nominal flowrate of 120 m²/h, pressure drop in the cooler is 20 kPa. Assume turbulent flow conditions. Neglect suction line frictional pressure drop. Following information is available:Tray spacing: 0.5 m, Pressure drop per tray: 1 kPa, Discharge pipe diameter = 0.3 m and f (friction factor) = 0.04, Density of Liquid (assume that it is constant) = 800 kg/m³, Tower top pressure: 300 kPa, Pump curve for the pump-around reflux pump is given by: APрump(kPa)=300 – 5v^2 where v is flowrate in m³/min a. For a 50% scale up in the pump-around reflux flow, what would be the minimum discharge pressure of the pump (i.e., under the condition when the pressure drop inа.the control valve is zero)? b. What is the pressure drop in the control valve for the 50% scale up case?