# Pressure: Measurement vs Definition?

I'm a bit confused about the relation between how we measure pressure and how it is defined. Consider a gas inside a container, if we connect a manometer and read the height difference, we say that the "pressure" for example is x mmHg (if mercury is used). Now, we do we say that this "Reading" is equal to the weight of the column of mercury that was raised divided by the cross sectional area?
I get that we can define a quantity called pressure that is equal to the "intensity" of the force over the area, so that P=F/A. And we can say that the weight of the column of mercury would exert a pressure of x Pa over some area. But, my question is, why do we say that this reading means that the gas is exerting a pressure (equal to the pressure that the column of mercury would exert) on the container walls? Such that on each small area A of the walls of the container, there is a force equal to PA? How do we know that? Is there a way of measuring the force on an area A on the walls?

There are many ways to measure pressure - but it always comes down to "force per unit area".

The example of the manometer could easily be modified very slightly. If, instead of the usual liquid in contact with the gas, you had a low-friction piston like this: you would perhaps see more clearly that the force on the piston (which is pressure times area) is what supports the weight of the liquid (I conveniently made the walls of the container 'massless' to simplify things).

Now remove the piston (or rather - make the piston out of the liquid) and you have the usual situation. Obviously you can add a bend in the pipe containing the liquid so you can change the height of the column more easily.

I hope this helps clear up some of your confusion.

• Thanks it really helped. One other thing though, when we say that the pressure of the gas acts equally in all directions, can this somehow be proved or is it because if it didn't act equally in all directions then that would mean that some parts of the container walls would deform more than others which doesn't happen so this must mean that the pressure is on all parts the same? – Khalid T. Salem Apr 6 '17 at 20:46
• "Pressure acts equally in all directions" is something that follows directly from statistical mechanics / entropy. Let's imagine for a moment that all gas molecules move exactly in a horizontal plane - so there will be pressure only on the vertical walls. As soon as the molecules hit another molecule, they will be redirected in a random direction: this will give them some vertical velocity. It turns out that "on average" there cannot be a preferred direction: and if they are equally likely to move in any direction then pressure will be isotropic. – Floris Apr 6 '17 at 20:49