The pumping work has the equation written below:
W = mΔh,
where m is the mass
Δh is the difference in height
We determine the mass from the density of water which is 62.5 lb/ft³.
Density = Mass/Volume
Mass = m = Density*Volume
m = (62.5 lb/ft³)(π/4)(24 ft)² = 9,000π
The lb is in lbm or pound-mass. To convert it to pound-force, lbf, we use the g/gc conversion factor which is equal to 1 lbf/lbm. Thus,
W = (9,000π lbm)(5 ft - 4 ft)(1 lbf/lbm) = 28,274 lbf·ft
