# Potential Energy of Rising Water Container

• copria
In summary: However, you may want to clarify that the final height of the water column is zero, since it has all flowed out of the container. Additionally, you may want to mention that the container is being raised at a constant velocity, as that would affect the velocity of the container and the height of the water column over time. In summary, the total potential energy of the water and water container over a specific time period can be calculated by integrating the mass of the container and initial mass of water, subtracting the flow rate of water multiplied by the density and velocity of the water, and multiplying by the gravitational acceleration and height of the container over time. The final height of the water column is zero and the container is being raised at a constant velocity.
copria
A container with a hole in the bottom is filled with water. As the container is raised, water flows through the hole; thus the mass of the water in the container decreases. What is total potential energy of the water and water container over a specific time period as water escapes the container and the container is raised? As height increases, volume of water decreases.

Known:
Height of container
Initial volume of water
Final volume of water
Initial height of water column
Final height of water column
Mass of water container
Density of water
Gravitational acceleration
Time

Unknown:
Fluid Velocity
Total potential energy

Relevant Equations

Potential energy
PE=mgh

Flow rate
Q=Av$$_{}f$$
• A= cross sectional area (in this case, πr2)
• v$$_{}f$$= fluid velocity

Fluid velocity (as according to Bernoulli’s equation)
v$$_{}f$$= √(2gh$$_{}w$$)
• g= gravitational acceleration
• h$$_{}w$$= height of water column (measured from base of container)

Mass of water being lost
m$$_{}l$$= Qtρ
• t= time
• ρ= density of water
Velocity of container
v$$_{}c$$= h$$_{}c$$/t
• h$$_{}c$$= height of container (measured from ground)
Other Variables:
m$$_{}c$$= mass of container
m$$_{}i$$= initial mass of water
t= time
h$$_{}wi$$= initial height of water column
h$$_{}wf$$= final height of water column (zero)

Is this correct? Am I leaving any information out?

∫zero to t of {m$$_{}c$$+ m$$_{}i$$-[Atρ(∫h$$_{}wi$$ to h$$_{}wf$$ of √(2gh$$_{}w$$ )) ] }g h$$_{}c$$

Last edited:
dtThis looks correct. You have included all the relevant equations and variables needed to calculate the total potential energy of the water and water container over a specific time period.

## 1. What is potential energy of a rising water container?

Potential energy of a rising water container is the energy stored in the system due to its position in a gravitational field. It is the ability of the water to do work when released from a higher position to a lower position.

## 2. How is the potential energy of a rising water container calculated?

The potential energy of a rising water container is calculated using the formula PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the container.

## 3. What factors affect the potential energy of a rising water container?

The potential energy of a rising water container is affected by the mass of the water, the height of the container, and the strength of the gravitational field. It can also be affected by external forces such as air resistance or friction.

## 4. How does the potential energy of a rising water container change when the height of the container is increased?

The potential energy of a rising water container increases as the height of the container increases. This is because the water has to do more work against gravity to reach a higher position, resulting in an increase in potential energy.

## 5. Can the potential energy of a rising water container be converted into another form of energy?

Yes, the potential energy of a rising water container can be converted into other forms of energy such as kinetic energy when the water is released and flows downwards. It can also be converted into electrical energy if the water is used to turn a turbine.

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