# How to calculate potential energy of water in a tank?

1. Sep 13, 2010

### fuzzylogic

Suppose you have a cylindrical tank of water that is filled to height h. Total mass of water is M. How do you calculate the potential energy of water relative to the base of the tank?

2. Sep 13, 2010

### Staff: Mentor

Welcome to the PF.

What is the context of the question? What do you intend to use the PE for?

3. Sep 13, 2010

### fuzzylogic

I just want to know what the stored p.e. is

4. Sep 13, 2010

### Staff: Mentor

How come? And how did the water get into the tank? And where is it going to go as it flows out of the tank?

PE is relative to something, it is not an absolute quantity. It is valid to say that the stored PE of water in a tank is zero. And then if the water flows out to some other tank, there may be a change in the stored PE...

5. Sep 13, 2010

### fuzzylogic

does this make sense:
g=gravitational acc
y=water level from base
A=area of water surface
r=water density
m=total mass of water
U=PE

then dU=grAydy
U=1/2grAh^2=1/2mgh (m=rAh)

6. Sep 13, 2010

### Staff: Mentor

Yes, that's fine.

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