A 20 °C Brix sucrose solution at 70 °F is being pumped from a large open tank at a rate of 16 gallons/min through a 1 in galvanized steel pipe to an upper level. The pipe is 100 ft long and includes three 90 ° elbows. The liquid level in the tank is 10 ft above the ground and the pipe discharge is 40 ft above the ground. The pressure at the discharge is 5 psi gage. The solution has a r=67.4 lbm/ft3 and a m=0.00128 lbm/ft-s.
a. Calculate the work required of the pump in ft-lbf per lbm of solution.
b. Calculate the theoretical power required of the pump in hp.
c. Comment on the relative amounts of energy comprising the total, required energy of the pump, i.e., observe/comment on the relative energy to overcome friction vs. potential energy vs. kinetic energy, etc.