How to calculate potential energy of water in a tank?

Click For Summary
To calculate the potential energy (PE) of water in a cylindrical tank, the formula U = 1/2 mgh can be used, where m is the total mass of water, g is the gravitational acceleration, and h is the height of the water. The potential energy is relative to the base of the tank, meaning it can be considered zero at that point. The discussion emphasizes that potential energy is not an absolute quantity and can change when water flows to another location. The derivation involves integrating the differential potential energy dU = grAydy, where A is the area of the water surface and r is the water density. Understanding these calculations is essential for assessing the stored potential energy in the tank.
fuzzylogic
Messages
8
Reaction score
0
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?
 
Physics news on Phys.org
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.
 

Thread 'Is energy really conserved?'

I built a device designed to brake angular velocity which seems to work based on below, i used a flexible shaft that could bow up and down so i could visually see what was happening for the prototypes. If you spin two wheels in opposite directions each with a magnitude of angular momentum L on a rigid shaft (equal magnitude opposite directions), then rotate the shaft at 90 degrees to the momentum vectors at constant angular velocity omega, then the resulting torques oppose each other...
View full post »

Similar threads

Water in a tank being driven up and down
  • · Replies 34 ·
2
Replies
34
Views
3K
Confusion about potential energy in a tank filled with water
  • · Replies 22 ·
Replies
22
Views
6K
Needing to know the pressure in a water tank
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Collision when a falling tank impacts the surface of a lake
  • · Replies 7 ·
Replies
7
Views
3K
Energy of a water tank with compressed air
  • · Replies 5 ·
Replies
5
Views
1K
Calculating Filling Time for a Diving Tank with Changing Hydrostatic Pressure
  • · Replies 2 ·
Replies
2
Views
2K
Can someone help me find a method to measure water level in a tank
  • · Replies 18 ·
Replies
18
Views
3K
How Much Work to Fill a Cylindrical Tank with Water?
  • · Replies 22 ·
Replies
22
Views
3K
Question about potential energy: gravity and a vertical spring
  • · Replies 12 ·
Replies
12
Views
4K
Pressure drop across a valve in tank
  • · Replies 4 ·
Replies
4
Views
2K