# Is Pascal's law wrong?

• I
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?

Gold Member
No.

Why.

Gold Member
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.

Doc Al
Mentor
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.

A.T.
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.

Gold Member
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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Doc Al
Mentor
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.

Doc Al
Mentor
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.)

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?

Doc Al
Mentor
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:
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.

SammyS
Staff Emeritus