How to calculate potential energy of water in a tank?

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Discussion Overview

The discussion revolves around calculating the potential energy of water in a cylindrical tank, specifically focusing on the relationship between the height of the water, its mass, and gravitational acceleration. Participants explore the concept of potential energy in relation to the tank's base and the implications of relative measurements.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks how to calculate the potential energy of water in a cylindrical tank filled to height h with total mass M.
  • Another participant inquires about the context of the question and the intended use of the potential energy calculation.
  • A participant expresses a desire to know the stored potential energy without providing further context.
  • It is noted that potential energy is relative and can be considered zero in certain contexts, depending on the reference point chosen.
  • A mathematical expression for potential energy is proposed, including variables for gravitational acceleration, water level, area of the water surface, density, and total mass, leading to a derived formula for potential energy.
  • A later reply confirms the mathematical expression as acceptable.

Areas of Agreement / Disagreement

Participants express differing views on the context and implications of potential energy, particularly regarding its relative nature. While some mathematical expressions are accepted, the overall discussion remains unresolved regarding the broader implications of potential energy in this scenario.

Contextual Notes

There are limitations regarding the assumptions made about the reference point for potential energy and the conditions under which the calculations are valid. The discussion does not resolve these assumptions.

fuzzylogic
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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?
 
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fuzzylogic said:
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?

Welcome to the PF.

What is the context of the question? What do you intend to use the PE for?
 
I just want to know what the stored p.e. is
 
fuzzylogic said:
I just want to know what the stored p.e. is

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...
 
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)
 
fuzzylogic said:
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)
Yes, that's fine.
 

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