What is the meaning of pressure of a gas?

[smilingbuddha]

I understand the meaning of pressure on a surface to be force acting per unit area.

But when it comes to understanding pressure in the context of fluids in motion or at rest I think I am having some trouble grasping the concept.

When we say the pressure of a gas in a container (which may be of any arbitrary blobby shape) is say 2 Pascals, what does it really mean?

1) Does it mean the pressure of the gas on ANY small area considered on the surface of the container == 2 pascals?

2) Or Does it mean the pressure on a thin small wafer (possible imaginary?) placed anywhere inside the gas == 2 pascals?

I am really confused!

To add to my problem of understand pressure, is a sentence from Chorin and Marsden's a Mathemtical introduction to fluid dynamics when they define an ideal fluid.

*"Lets us define an ideal fluid with the following property: For any motion of the fluid there is a function p(x,t) called the pressure such that if S is a surface in the fluid with a chosen unit normal n, the force of stress exerted across the surface S per unit area at x in S at time t is p(x,t) n i.e.

force across S per unit area=p(x,T)n"*

Here is my problem: Suppose we have an ideal fluid and a time and position varying pressure function as above. For a thin small wafer placed at x at time t, there are two equal and oppsite forces acting across its surface i.e. p(x,t)n and -p(x,t)n since the surface has 2 forces in the direction of the two normals to it.

This reasoning means the force on the thin small wafer is zero. Which means that the force at any point the the fluid at any time is zero. Which is totally counterintuitive.

Further the pressure function (as defined above) does not depend on the orientation of the element. i.e. the normal n
I would expect the force magnitude to change if we change the orientation of the elment centered x

Why would they define an ideal fluid like that?

 

[MikkelM]

The force arises from particle collisions inside the pressurized vessel. If you immerse a wafer into the fluid/gas, the amount of particle collisions will average out symmetrically on all sides, resulting in a net force of zero. This is the net force acting on the wafer, hence there is no change in the wafer's momentum. However, anyone side of the wafer will still be experiencing a pressure of 2 Pa. If the wafer is compressible at this force, it will be compressed to the point where the external force of the pressurized gas is equal to the intermolecular bonding force of the solid.

 

[Rayquesto]

I just learned about this myself. But I have a fairly clear picture in my head. So, what pressure in terms of fluid means that the force perpendicular to the surface is pressure which affects any object surrounding the fluid. An object at rest in fluid will likely have pressure in all areas surrounding the object to cancel out each other. It's only when gravity and the normal force are acting on an object at rest when the pressure is not canceling itself out exactly. It's kind of cool when you think about this stuff, because there are amazing applications. For example, the other day, I thought of how this can apply to the squeezing of an egg; they say that no matter how hard you squeeze an egg, it can't break?... but I want a physics explanation you know! haha But I couldn't come up with one relating to pressure. you want to elaborate?

So, like I said, pressure affects a mass in a fluid in all areas and will cancel out if they are all the same affecting the mass in all directions.

 

[Rayquesto]

"which affects any object surrounding the fluid" not surrounding. It's what's in the fluid. Sorry...

 

[MikkelM]

It is very possible to break an egg with mechanical force, even if the force is perfectly distributed over the shell. There is only so much a poor egg shell can take.

The myth arises from the fact that it takes more force to break an egg when force is applied symmetrically (or at least somewhat symmetrical in case of hands and fingers), than if force is applied asymmetrically (say, on one specific point). That is a function of the shell geometry and how the force is propagated and absorbed through the medium of the shell itself.

Imagine the force trying to push apart the "shell particles" and how they in turn try to push each other. They will be pushing away from each other in a 180 degree sector opposite the direction of force. The result is that some of the force has been directed diagonally through the thickness of the shell, i.e. passing through more shell. This is sometimes called "effective thickness", which you might have seen used when describing the effectiveness of slanted tank armour. Obviously, the thicker the shell, the more of the force is propagated through the shell.

Now if this occurs symmetrically over the entire shell, the forces that propagate through the shell will cancel each other out. Though this only true for a sphere, we can for example's sake extend this to the egg as a "spheroid".

It is the same principle that makes domes and arches such good load bearers without the need for support pillars or trusses. It is also the same reason why the deepest going submarines (or bathyspheres) like the Trieste, were spherical.

However, this being a shell with limited thickness, there is still a considerable amount of force acting perpendicular to the shell curvature. This is obviously the axis with the least effective thickness. If this force exceeds the breaking strain of the shell material, the shell will implode at its weakest point.

I hope this was a worthwhile explanation. I never quite know whether something that makes perfect sense to me makes sense to others.

Just a pure side note: An egg is not actually sealed, but does exchange gases with the environment over the membrane (or amnion) through pores in the shell. Fetus got to breathe, poor thing. So theoretically, it could achieve internal pressure equalization and equal forces on both sides of the shell.