Question

Please show work & justify any assumptions made.The concepts here fall under the umbrella of Fluid Mechanics as well.

Question 1 4 pts You are to design a system to pump 1.0 x 104 kg/h of water/ethanol mixture at 114C and 1.1 atm absolute pressure from the first distillation column to a second distillation column to finish the purification. If the friction loss in the line between the first distillation boiler is 7.1 kN/m2 and the specific gravity of the mixture is 0.866 how far above the pump must the liquid level be to give a net positive suction head of 1.9 m? Assume the vapor pressure is 1.1 atm at 114C. Give the answer in meters with 2 significant figures. Question 2 4 pts Calculate the power require to drive the pump in problem 1 if the pump is to elevate the water/ethanol mixture 11.0 m to the second distillation unit. Assume the pressure in the second unit is atmospheric, the pump the friction loss in the pump discharge line is 35 kN/m2, the efficiency is 70.0%, and the velocity in the discharge line is 2.0 m/s. Provide the answer in Watts with 2 significant figures.

Answer 1

1.) Absolute pressure P = 1.1 atm

Head due to absolute pressure h = P/rho*g = 1.1*101325/(866*9.8) = 13.13m

Frictional loss in line which goes to distillation column ΔPf = 7.1KN/m2 = 7100 N/m2

Head due to friction loss hf = ΔPf/rho*g = 7100/866*9.8 = 0.836 m

Vapor pressure of mixture Pv = 1.1 atm

Head due to vapor pressure hv = 13.13 m

Let us assume z m above the pump is installed .

NPSH = 1.9m

(h+z) - hv - hf = 1.9 m

z - 0.836 = 1.9

z = 2.736 m

2)

friction loss in pump discharge ΔPf = 35 kN/m2

head due to friction hf = ΔPf/rho*g = 35*1000/866*9.81 = 4.12m

velocity of discharge line v = 2 m/s

efficiency = 70%

P2 - P1 = 1.1 - 1= 0.1 atm = 10132.5 N/m2

head due to pressure difference h1 = 10132.5/rho*g = 10132.5/866*9.8 = 1.19 m

elevation height h = 11 m

head due to velocity h = v^2/2g = 4/2*9.81 = 0.203 m

total head required H = 4.12 + 1.19 + 11 + 0.203 = 16.51 m

total delivered power to fluid Pf= m*g*H

m = mass flow rate = 10^4 kg/h = 2.77 kg/s

P = 2.77*9.81*16.51 = 448.63 W

Power required for pump with 70% efficiency P = Pf/0.7 = 448.63/0.7 = 640.91 W