In math/calculus classes, a problem frequently posed asks how much work (J) is required to pump water out of the top of differently shaped water tanks.
If you are unsure of what I am referring to, here are some example problems:
- Emptying water out of a Conical Tank? (Calculus)?
- Work required to pump water out of tank in the shape of a paraboloid of revolution
- Example 9.5.4 in https://www.whitman.edu/mathematics/calculus_online/section09.05.html
Is it ever actually feasible to pump water out of the top of a tank, as is modeled by the solutions to these problems? Does some sort of pump actually exist that is able to pull water from its surface in a tank, ever?
This might be a question better suited for engineering forums, but I'm unsure. I'm writing a mathematics paper and am currently struggling to find the real-world application of pumping water out of the top of a tank. And really hoping that there is one.
Most soap dispensers are examples of tanks where you pump a liquid from the surface. The tube extending to the bottom is irrelevant - the work required is the same as if the tube magically expanded and contracted to just reach the surface, because the pressure will cause the liquid inside and outside the tube to be at the same height.
A more practical problem would be finding the work to pump some quantity of oil from beneath the ground to the surface.