I looked at this question, however, it pumps water of a full tank out from the top of the tank. My question is a bit different, but mostly similar.
There is a cylindrical tank with a radius of 3ft, height of 15ft. It is partially filled with water (4ft deep). We want to pump the water out of a spigot that is 20ft off the floor. The water weighs 62.4 pounds per cubic foot.
How can I set up the integral to represent the work done in pumping out that water? I'll evaluate it on my own.
If the tank was full, and we weren't pumping the water from a spigot 20 ft off the floor, I know the integral representation of the work required would be
Which, cleaned up, is:
But I'm unsure of how to set up the integral when the tank isn't full of water, and when the water is being pumped from a height higher than the top of the tank. Can anyone steer me in the right direction?