Question

A pump takes water at 60°F from a large reservoir and delivers it to the bottom of an open elevated tank 25 ft above the reservoir surface through a 3 inch ID pipe. The inlet to the pump is located 10 ft below the water surface, and the water level in the tank is constant at 160 ft above the reservoir surface. The pump delivers 150 gpm. If the total loss of energy due to friction in the piping system is 35 ft·lbf/lb, calculate the horsepower required to do the pumping. The pump and its motor have an overall efficiency of 55 percent. write out the equations you use. specificy what each variable stands for.

Answer 1

The flow diagram is shown below

Point a is at the datum

Point b is at 160 ft high from the datum (point a)

Apply the Bernoulli's equation at point a and point b

Total energy remains constant

Pressure energy at point a + kinetic energy at point a + potential energy at point a + work done by pump * efficiency of pump = Pressure energy at point b + kinetic energy at point b + potential energy at point b + head loss due to friction

Pa/ + Va²/2gc + gZa/gc + Wp= Pb/ + Vb²?/2gc + gZb/gc + hf

Pa = Pb = 1 atm = pressure at point a and b respectively

Va = Vb = 0 = velocity at point a and b respectively

Za = 0 (as datum point)

Zb = 160 ft

hf = 35 ft·lbf/lb = head loss due to friction

= efficiency of pump

= kinetic energy correction factor

1/ + *0²/2gc + g*0/gc + 0.55*Wp= 1/ + *0²?/2gc + g*160/gc + 35

0.55Wp = 160 + 35

Wp = 354.54 ft·lbf/lb

Mass flow rate m = density of water at 60°F x volumetric flow

= 62.37 lb/ft3 x 150 gal/min x 1ft3/7.481gal x 1min/60s

= 20.85 lb/s

Power required = Wp x m

= 354.54 ft·lbf/lb x 20.85 lb/s x [1hp/(550 ft·lbf/lb)]

= 13.44 hp