MECHANICAL ENGINEERING: Pump work - work done by a pump in lifting a fluid

Wp = F * h


where:

Wp = pump work, the work done by the pump

F = weight of fluid

h = lifting height, measured from the centroid


1. Find the work needed to pump all the water in an 8-ft radius hemispherical tank to a height of 10 ft above the top of the tank.


find:

Wp = pump work


given:

Hemispherical tank (Centroid: y = 3/8 r)

D = Water Density = 62.4 lb/cu.ft

r = 8 ft

h1 = 10 ft


solution:

V = 2/3 pi * r^3

V = 2/3 * 3.14 * 8^3

V = 1072 cu.ft


F = D * V

F = 62.4 * 1072

F = 66,893 lb


h = h1 + yCentroid

h = 10 + 3/8 r

h = 10 + 3/8 (8)

h = 10 + 3

h = 13 ft


Wp = F * h

Wp = 66,893 * 13

Wp = 869,609 lb.ft