How to calculate potential energy of water in a tank?

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SUMMARY

The potential energy (PE) of water in a cylindrical tank can be calculated using the formula U = 1/2grAh², where g represents gravitational acceleration, A is the area of the water surface, r is the water density, and h is the height of the water. The total mass of the water, M, can be expressed as M = rAh. This formula indicates that the potential energy is relative to the base of the tank and can change as water flows out to another tank. Understanding these calculations is essential for applications involving fluid dynamics and energy conservation.

PREREQUISITES
  • Understanding of gravitational acceleration (g)
  • Familiarity with fluid density (r)
  • Knowledge of geometric properties of cylinders (A and h)
  • Basic principles of potential energy (U)
NEXT STEPS
  • Research the implications of gravitational potential energy in fluid dynamics
  • Explore advanced applications of potential energy in engineering contexts
  • Learn about energy conservation principles in hydraulic systems
  • Investigate the effects of varying water density on potential energy calculations
USEFUL FOR

Students in physics, engineers working with fluid systems, and anyone interested in the principles of energy conservation in hydraulics will benefit from this discussion.

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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