# Hydrostatic Pressure - Theoretical Scenario

• EnquiringMind
In summary, the scenario described involves a piston at the bottom of a chamber of water that is attached to the ground. The key to determining if the container will collapse onto the piston is to examine the potential energy of the system before and after a small movement. If the area of the water around the piston is larger than the area in the neck, the container will collapse. Additionally, the pressure exerted by the walls and the water may not be equal, leading to net forces and possible acceleration of the container. This requires further examination and calculation.
EnquiringMind
I have come to understand the basics of Pascal's Principle/Hydrostatic pressure, but there is one scenario I am looking for help with.

If I have a piston at the bottom of a chamber of water, and I want to push the piston up to lift the water, I understand that I need to exert a greater PSI on the Piston than the PSI the water is exerting on the surface of the Piston.

However, let's say that (as indicated by the attached picture) I have a Piston that is attached to the ground, and the container of water is "free standing"... meaning the container of water can collapse onto the Piston (thereby displacing the water upwards).

How do I know if the container would indeed fall on the Piston and thereby displace the water?

Aren't the walls (and thereby the Piston) exerting the same PSI on the water as the water is exerting on the walls (and Piston)? If so, who wins?

Intuitively, I want to say that no matter what... in any scenario such as I pictured... the container of water will fall on top of the Piston every time... but my intuition has proved wrong many times before.

Is it really possible that the PSI of the water at the bottom of the container could hold the container up and prevent it from collapsing onto the Piston?

Are there scenarios where the container of water will hold itself up? Or will it collapse every time?

Thanks for any help. This is one where I don't really know how to even begin doing the calculation.

#### Attachments

• Free Floating Pascal Example.png
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Here is a response I received to the same question/example on another forum. It helps a little, but am still hoping someone can be more detailed.

"Are there scenarios where the container of water will hold itself up? Or will it collapse every time?"

Yes, there are. Let's take the limit where there is no overlap around the piston, so all the water is above the piston. Also imagine the container to be massless. If the container were to lower itself...*none* of the water would go down with it. In fact some water would be raised up into the thin neck. Since overall the water would be higher, this position has more potential energy. It won't move into that position spontaneously.

In general you can examine what the potential energy of the system before and after a small movement to see if it would be spontaneous.

In your image, if the area of the water that is "around" or "outside" the piston is larger than the area in the neck, it will collapse.

In cases where you're working with small quantities of water, the mass of glass, metal, or even plastic container will tend to overwhelm the mass of the water, and will overcome the water pressure. For a massless container, it may well move in ways that intuition does not expect.

"Aren't the walls (and thereby the Piston) exerting the same PSI on the water as the water is exerting on the walls (and Piston)? If so, who wins?"

No, the walls and the water may not be pushing the same. They are *if* it is in equilibrium. Otherwise there are net forces and the container will be accelerated. For instance, if there is no overlap, the a massless container will not be pushing down on the water, but the water will be pushing up (if there is water in the neck), and the container will accelerate upward.

## 1. What is hydrostatic pressure?

Hydrostatic pressure refers to the pressure exerted by a fluid at rest, due to the weight of the fluid above it.

## 2. How is hydrostatic pressure calculated?

Hydrostatic pressure can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.

## 3. What is the theoretical scenario for hydrostatic pressure?

The theoretical scenario for hydrostatic pressure involves a fluid being contained in a vessel and exerting pressure on the walls and bottom of the vessel due to its weight.

## 4. How does hydrostatic pressure affect the human body?

Hydrostatic pressure can affect the human body when diving or being submerged in water, as the pressure increases with depth and can cause discomfort or even injury if not properly managed.

## 5. What are some practical applications of hydrostatic pressure?

Hydrostatic pressure has practical applications in various fields such as engineering, meteorology, and medicine. It is used in hydraulic systems, weather prediction, and in medical devices such as blood pressure monitors.

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