# Confirming fact about potential energy of each particle in a fluid

• dE_logics
In summary, the potential energy of each particle in a cylinder filled with fluid on Earth is identical, regardless of their depth. This is because the weight experienced by each particle increases with depth, but this has no effect on potential energy. The potential energy does decrease as particles move closer to the Earth's center of mass, but this is due to gravity and not pressure. The relationship between potential energy and velocity only applies to a single particle moving under one potential field, but in a fluid, interactions with other fields, such as electrostatic repulsion, can change the kinetic energy and thus velocity of particles. In an ideal fluid, the total energy per particle is constant regardless of height. However, if the fluid is compressible, the relationship between volume
dE_logics
I just want to confirm this fact -

Referring to a point in a cylinder on earth, filled with a fluid; the potential energy of each particle in that cylinder is identical.Reason being the weight experienced by each particle increases as we goto more depths.

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The gravitational potential increases with height. Am I missing something?

What do you mean by the "weight experienced by each particle"? The weight of the particles above it? That has nothing to do with potential energy.

HallsofIvy said:
What do you mean by the "weight experienced by each particle"? The weight of the particles above it? That has nothing to do with potential energy.

There's lots of pressure on the lower part of the cylinder so each particle should contain lots of potential energy due to the pressure.

So potential energy of the particle decreases as we move towards the bottom part of the cylinder?

If I'm wrong in the main question I think this will be it, but this will again generate a series of doubts...

There is no potential energy due to pressure. Pressure is a thermodynamic variable, not a force, and you can only define potentials in terms of a conservative force field (for example, gravity gives you the gravitational potential).

The potential energy does decrease, but only because it is getting closer to the Earth.

If the potential energy does decrease, then the velocity of the particle which's x cm (perpendicular) from the orifice should be less than the particle at a height x + a (where a is a reasonable positive integer) since only the potential energy of the particle gets converted to kinetic (velocity).

But this does not happen...in ideal conditions the velocity of all particles are the same.

The relation between potential energy and velocity is applicable for a single particle moving under only the interaction of the field responsible for that potential energy, so PE + KE = constant in this case.

In the case of many particles in a fluid the kinetic energy of a particle (therefore velocity) will be changed many times a second by collisions, essentially interactions with a different field (electric), to which the gravitational potential is independent, so you can no longer say KE + PE = constant because you have a second potential field due to electrostatic repulsion.

The gravitational potential is still purely a function of distance from the centre of mass of the Earth, and does not couple to the electric potential which dominates particle velocity distributions in a fluid, especially in hydrostatic equilibrium where there is no net movement up or down of the particles due to gravity.

This is what I think, anyway, there may well be a better explanation out there.

Pressure energy = pressure x volume. Gravitational potential energy = gravitational potential x mass. If the volume and mass for each particle of fluid is known, you can multiply Bernoulli equation by mass where the total energy per particle in an ideal fluid (incompressable) is constant regardless of height. If the fluid is compressable, then the relationship between volume and mass changes and Bernoulli equation has to be modified to use an integral form for the pressure term.

Bernoulli equation for ideal fluid: pressure/density + g h + 1/2 v2 = constant

(pressure x volume) + m g h + 1/2 m v2 = total mechanical energy = constant

Assuming v = 0 you get:

(pressure x volume) + m g h = constant

http://en.wikipedia.org/wiki/Bernoulli_principle

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Consider only a situation where the fluid is under influence of a field which is not a function of distance (can be considered sorts of equal to the situation on Earth where the height of the apparatus is not reaching the sky...).

If orifice is opened, the particles at the lower part of the cylinder will initially accelerate more in comparative to the particles above them (cause the weight of the parciles above will act on the particles below), then the acceleration should reduce to a constant since G will pull each particle in an identical way...this is what I think will happen.

All this should result in all particles gaining a constant velocity regardless of their initial position in the cylinder...and we practically see this.

Jeff Reid said:
pressure energy = pressure x volume. Gravitational potential energy = gravitational potential x mass. If the volume and mass for each particle of fluid is known, you can multiply Bernoulli equation by mass where the total energy per particle in an ideal fluid (incompressable) is constant regardless of height. If the fluid is compressible, then the relationship between volume and mass changes and Bernoulli equation has to be modified to use an integral form for the pressure term.

Bernoulli equation for ideal fluid: pressure/density + g h + 1/2 v2 = constant

(pressure x volume) + m g h + 1/2 m v2 = total mechanical energy = constant

Assuming v = 0 you get:

(pressure x volume) + m g h = constant

http://en.wikipedia.org/wiki/Bernoulli_principle

Yes, exactly what I was saying.

## What is potential energy in a fluid?

Potential energy in a fluid is the energy that a particle possesses due to its position within the fluid, relative to other particles. It is a type of energy that can be converted into other forms, such as kinetic energy, when the particle moves.

## How is potential energy calculated in a fluid?

Potential energy in a fluid is calculated by multiplying the mass of the particle by the acceleration due to gravity and the height at which the particle is located. This is known as the equation for gravitational potential energy: PE = mgh.

## Does potential energy of a particle change in a fluid?

Yes, the potential energy of a particle in a fluid can change. It can change if the particle's position within the fluid changes, or if the fluid itself changes (such as temperature or pressure changes). In general, potential energy in fluids tends to decrease over time due to the movement of the particles.

## How does potential energy affect the behavior of particles in a fluid?

Potential energy plays a role in the behavior of particles in a fluid. Particles with higher potential energy tend to move towards areas with lower potential energy, which can result in changes in pressure and flow within the fluid. The potential energy of a particle can also determine its ability to escape the fluid, such as through evaporation or boiling.

## What factors can affect the potential energy of particles in a fluid?

The potential energy of particles in a fluid can be affected by a variety of factors, such as their mass, position within the fluid, and the surrounding temperature and pressure. Additionally, the type of fluid and any external forces acting on the particles can also impact their potential energy.

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