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I would like to get one thing straight in my mind:

If I fill a balloon let's say with 10 bar of air. Is there a formula that relates the force acting on a point $F(x)$ where $x$ is a point on the balloon to the pressure? Especially, it is actually not quite clear to me if the force that a certain point of the balloon experiences is the same everywhere or whether it is the same for all points?-Clearly the diameter is very different for our balloon, so I do not know. I expect the total force to be $$ F = pA$$ where $A$ is the area of the surface, but I don't know if the pressure at a single point of the surface is the same for every point?

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The force caused by the gas molecules at any point acting on the inside surface of the balloon is the same at every point on the inner surface of the balloon. Furthermore, this force is the same at all points inside the balloon whether this point is on the inner surface or at the exact centre point in the balloon.

Consequently, the equation you need $F(x)$ is simply what you had, and that is $F(x)=PA$ where $P$ is pressure and $A$ is an area on the inner surface of the balloon, or if you constructed an imaginary area $A$ anywhere at any point $x$ inside the balloon, the force imposed by the gas molecules there would still be the same.

Unless there are other forces/interactions, the force (pressure) in any enclosed volume is the same everywhere (on the inner surface or any other inner point elsewhere throughout the volume).

For example, if the balloon were placed in a strong gravitational field, the force (pressure) will be greater at the bottom of the balloon.

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  • $\begingroup$ I do not quite understand what the $A$ is you are taking now though. $\endgroup$
    – Martinique
    Apr 4 at 16:00
  • $\begingroup$ Any area A you take and then compute the pressure over that A. If you then multiply the the two you will get a value for F. If you did the same for any two pairs of P, A anywhere will give you the same value for F. $\endgroup$
    – joseph h
    Apr 4 at 20:26

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