In the hydraulic system depicted in the figure, the main water tank is buried underground, and the overflow valve is open to the atmosphere. 40,000 liters of water per hour is supplied from this tank to two separate lines, A and B, located at different heights. Line A is equipped with a valve, heater, and expansion tank, while line B has a filter, valve, and expansion tank. The main line uses DN100 stainless steel pipes, DN60 pipes for line A, and DN40 pipes for line B. With this configuration: e(toughness)=0.002 mm, La=45 m, Lb=35 m, dynamic viscosity of water=0.00112, g=9.81 m/s,

a) Determine the head losses for lines A and B. b) Find the head produced by the pump used. c) Calculate the power of the pump used.