Question

An 80% efficient pump draws 68.5 gallons per minute of water from an aquifer through a 4-inch ID pipe and discharges it through a 2-inch ID pipe to a tank, which is 100 ft above the water level in the aquifer. The friction loss in the pipe is 15 ft.lbf/lbm. What is the required pump horsepower?

Answer 1

From the Bernoulli's theorem

P1/ + V1²/2 + g*z1 + Wp = P2/+ V2²/2 + g*z2 + hf

At constant pressure

V1²/2 + gz1 + Wp = V2²/2 + gz2 + hf

At suction, flow rate Q = area x velocity

68.5 gal/min x 1min/60s x 1ft3/7.48gal = (3.14/4)*(4in x 1ft/12in)² x V1

V1 = 1.75 ft/s

From the continuity equation

A1V1 = A2V2

V2 = A1V1 / A2

= (4/12)² x 1.75 / (2/12)²

= 7 ft/s

1.75²/2 + 0.80Wp = 7²/2 + 32.174*100 + 15

0.80Wp = 3255.36

Wp = 4069 ft-lbf/lbm

Mass flow of water = flow rate x density

=( 68.5 gal/min x 1min/60s x 1ft3/7.48gal) x 62.43 lbm/ft3

= 9.528 lbm/s

Wp = 4069 ft-lbf/lbm x 9.528 lbm/s

= 38772 ft-lbf/s x 1 hp / 550 ft-lbf/s

= 70.5 hp