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A water well has an 8-inch diameter and is 170 feet deep. The water is 25 feet from the top of the well. Determine the amount of work (in ft-lb) done in pumping the well dry. (Use 62.4 pounds per cubic foot for the weight of water)

User Shumi Gupta
by
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1 Answer

9 votes
9 votes

Answer:

307,939 ft·lb

Explanation:

The work done is the product of the weight of the water moved and the distance it is moved.

Volume of water

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

Weight of water

At 62.4 pounds per cubic foot, the weight of the water column is ...

(62.4 lb/ft³)(145π/9 ft³) ≈ 3158.35 lb

Distance moved

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.

Work done

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.

User Malganis
by
3.1k points
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