Answer: .25 gallon
Math:
Volume of a cylinder = pi * R2 * h
pi * 1.52 * 12 = 57.3 cubic inches
231 cubic inches in 1 gallon
57.5/231= .25 gallon (or one quart)
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if 3/4 in. is the diameter, you would need 410 2/3 feet of pipe
nominal 3/4 in. type K copper pipe - 132 1/2 feet holds 3 U.S. Gallons
nominal 3/4 in. type L copper pipe -119 1/3 feet holds 3 U.S. Gallons
A pipe is a cylinder and the volume of a cylinder is it's radius squared X pie X it's height. 12 inches of 10" pipe would hold more water than 12 inches of 1" pipe. In the same way 12" of 3 inch pipe would hold more water than 1 inch of pipe 3" in diameter. So what you're missing in this equation is; how long is the pipe?
Once you figure out the volume of the pipe, you'll have to convert that amount into gallons. If you're measuring the pipe in inches your end answer will be in cubic inches, you might be hard pressed to find a conversion table for that. Maybe not.
U.S.Gallons of water per foot = volume in cu. in. divided by 231 cu. in.(for U.S.gal)
= (Pi/4 x 32 x 12) / 231 = 0.3672 U.S. gal per foot of 3 inch pipe.