# Is Pascal's Law Wrong? Debunking the Myth of Equal Pressure in Fluids

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• physea
In summary, the conversation discusses Pascal's law and its consequences, specifically the fact that pressure is transmitted equally in all directions in a confined incompressible fluid. The participants also mention the influence of gravity on pressure and its role in creating a pressure gradient within a liquid. Overall, the conversation confirms that Pascal's law is correct, but there may be some confusion about its exact definition.
physea
In a fluid there is gravity exerted so we know that the lower layers have higher pressure. Does that prove that Pascal's law is wrong?

No.

Why.

You've cited a consequence of Pascal's law, not a counterexample.

The fact that gravity creates higher pressure at lower layers, is a consequence of Pascal's law? How can that be?
Pascal's law says that the pressure is everywhere the same, yet I say that gravity makes the pressure lower to be higher.

Can you state Pascal's principle? Just to make sure we're talking about the same thing.

Pascal's principle says that an incompressible liquid in a container exerts the same pressure at all its points.

physea said:
Pascal's principle says that an incompressible liquid in a container exerts the same pressure at all its points.
No, it says that at each point pressure is the same in all directions.

A.T. said:
No, it says that at each point pressure is the same in all directions.

And one of the consequences of this is the expression for hydrostatic pressure, ##p = \rho g h##, which is oftentimes referred to as Pascal's law.

Even if it says so, it is still wrong.

If I exert a pressure at the top of a tube, the pressure at the bottom of the tube will not be the same. It will be larger due to hydrostatic pressure (ie. the weight of the liquid itself)

Or another example, when we have a hydraulic piston. Pascal's law says that the pressure exerted in one piston will be transmitted in the other piston equally. However this is not true. If the second piston is below the first piston, the pressure will be larger, because of the hydrostatic pressure. Also, even if the second piston is in the same height with the first, and it is vertical, the pressure exerted at the top area of the piston will be lower that the bottom, again due to hydrostatic pressure.

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physea said:
Pascal's principle says that an incompressible liquid in a container exerts the same pressure at all its points.
Not really. A better expression of Pascal's principle would be: Any externally applied pressure will be transmitted equally to all parts of the fluid.

physea said:
If I exert a pressure at the top of a tube, the pressure at the bottom of the tube will not be the same. It will be larger due to hydrostatic pressure (ie. the weight of the liquid itself)
If you exert a pressure at the top of the tube, the pressure at the bottom of the tube will increase by the same amount. (This is in addition to the hydrostatic pressure that varies with height.)

Doc Al said:
Not really. A better expression of Pascal's principle would be: Any externally applied pressure will be transmitted equally to all parts of the fluid.

I can accept this only in zero gravity. Isn't that correct?

physea said:
I can accept this only in zero gravity. Isn't that correct?
No.

Ok, the pressure is exerted equally in any gravity, but it is tricky that you need to add the hydrostatic pressure to find the exerted pressure.

Note what A.T. said above:
A.T. said:
No, it says that at each point pressure is the same in all directions.
So at any point in the liquid the pressure is the same in all directions. Emphasize "at any point". It does not say that the pressure is the same at all points in the liquid.

Pascal Law: all points in a resting fluid medium and connected by the same fluid are at the same pressure IF they are at the same "depth".

I hope this doesn't confuse things: What Pascal's law specifically says is that a change in pressure exerted on a confined incompressible liquid is transmitted throughout the liquid evenly. If you have a container of liquid with no outlet there will be a pressure gradient from top to bottom due to the density of the liquid and gravity. If you exert a pressure (by adding liquid through a syringe, for example) that added pressure is transmitted throughout the liquid evenly. So if the pressure at the top was A and the pressure at the bottom was B and you exert an additional pressure C at the top then the resulting pressure at the top will be (A + C) and the pressure at the bottom will be (B + C). The change in pressure transmits equally throughout the liquid.

what do you mean "evenly" ? Is the pressure transmitted equally? Ie. the pressure applied in on side is equal to the pressure applied to the other side?

Any pressure applied anywhere will transmit throughout the fluid. If you put a bunch of pressure gauges at different points in the liquid and recorded the pressures they indicated, and then applied an additional 5 psi anywhere, then all the pressure gauges will go up 5 psi. Evenly, equally, uniformly, whatever.

From Wikipedia.[/PLAIN] (Yes, I know, it's not the ultimate authority, but this Wikipedia entry is well documented.)

"Pascal's law or the principle of transmission of fluid-pressure (also Pascal's Principle[1]<[2]) is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure variations (initial differences) remain the same.[3] The law was established by French mathematician Blaise Pascal.[4]"​

So it includes both ideas put forth here. If OP's issue was to try to understand Pascal Law, I think that has been well addresses in this thread.

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## 1. Is Pascal's Law completely wrong?

No, Pascal's Law is not completely wrong. It is a fundamental principle in fluid mechanics that states that pressure applied to an enclosed fluid is transmitted equally in all directions. However, there are some misconceptions and misunderstandings about this law that need to be addressed.

## 2. What are some common misconceptions about Pascal's Law?

One common misconception is that the pressure is always equal at all points in a fluid. This is not necessarily true, as pressure can vary depending on factors such as gravity and the shape of the container. Another misconception is that Pascal's Law only applies to liquids, when in fact it also applies to gases.

## 3. Can you explain the myth of equal pressure in fluids?

The myth of equal pressure in fluids comes from a misunderstanding of Pascal's Law. While the pressure may be equal at all points in a container, this does not mean that the pressure is always the same throughout the fluid. Pressure can vary depending on factors such as depth and density.

## 4. How does Pascal's Law actually work?

Pascal's Law states that pressure applied to an enclosed fluid is transmitted equally in all directions. This means that if a force is applied to a fluid in a closed container, the pressure will increase equally in all directions, regardless of the shape or size of the container. This is why hydraulic systems, which utilize Pascal's Law, are able to transmit force and motion through liquids.

## 5. Are there any exceptions to Pascal's Law?

While Pascal's Law is a fundamental principle in fluid mechanics, there are some cases where it may not apply. For example, when dealing with compressible fluids, such as gases, the volume of the fluid can change with changes in pressure. In these cases, the pressure may not be transmitted equally in all directions. Additionally, external factors such as friction and viscosity can also affect the transmission of pressure in fluids.

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