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Assuming that the interior diameter of the pipe is 1/4 inch.

Volume = Pi x radius2 x height

radius = 1/8 inch = 0.125 inches

radius2 = 0.015625

height = 1000 feet = 12000 inches

substituting

Volume = 3.1415926 x 0.015625 x 12000

Volume = 589.0486125 inches3

Using Google calculator (589.0486125 cubic inches to gallons)

589.0486125 (cubic inches) = 2.54999399 US gallons

about 2.55 US gallons
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Q: How much water does a quarter inch pipe hold in 1000 feet?
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