How long would it take to fill a pipe 1500 feet long and 15 inches in diameter with a garden hose that fills a gallon in 8 seconds?

Answer 1

There are 231 in3 in a gallon of water. That means the hose puts out 1848 in3 of water per minute. The pipe is a big, skinny cylinder. It's volume is the area of its base times its height. That's pi times the square of the radius of the base times the height. That's pi times (7.5)2 times the height or pi times 56.25 times the height. The height (actually, the length - because the cylinder is lying down) is 1500 feet. That's 1500 times 12 to get us to inches, or 18,000 inches. The area of the base, which is 56.25 square inches, times the length of the cylinder, which is 18,000 inches, is 1,012,500 cubic inches. That's how much we have to fill. Filling the cylinder is done at the rate of 1848 in3 per minute. Our volume of 1,012,500 in3 divided by 1848 in3 is 547.889 minutes, or 9.13 hours, or about 9 hours 7 minutes and 53 seconds.