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.
<h3>Volume of water</h3>
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
<h3>Weight of water</h3>
At 62.4 pounds per cubic foot, the weight of the water column is ...
(62.4 lb/ft³)(145π/9 ft³) ≈ 3158.35 lb
<h3>Distance moved</h3>
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.
<h3>Work done</h3>
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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<em>Additional comment</em>
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.
