Answer:
307,939 ft·lb
Step-by-step explanation:
The work done is the product of the weight of the water moved and the distance it is moved.
The height of the water column in the well is ...
170 ft -25 ft = 145 ft
The diameter of the column is (8 in)(1 ft)/(12 in) = 2/3 ft.
The volume is given by ...
V = π/4d²h = (π/4)(2/3 ft)²(145 ft) = 145/9π ft³
At 62.4 pounds per cubic foot, the weight of the water column is ...
(62.4 lb/ft³)(145π/9 ft³) ≈ 3158.35 lb
The average depth of the water is ...
(170 ft +25 ft)/2 = 97.5 ft
The problem can be treated as though the entire mass were concentrated at the center of mass: 3158.35 lb at 97.5 ft below the surface.
The work done moving this weight of water to the top of the well is ...
(97.5 ft)(3158.35 lb) = 307,939 ft·lb
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Additional comment
A 1 hp pump can move 1.98×10^6 ft·lb per hour, so it would take such a pump about 9 minutes 20 seconds to pump the well dry.
