Pressure in the corners of a box

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I have a fairly simple physics question, which I probably should know, but somehow I have never encountered it before.

Suppose you have a pressurized cube, filled to a high uniform pressure P. Will the force from the pressure be larger at the edges and corners of the box?

At the corner, molecules can bounce off both sides, which seems like it would make pressure rise. Macroscopically, if each wall has uniform pressure on it, it seems that the intersection of the faces would experience a force greater by sqrt2, since it has two equal, orthogonal components. However, this seems to contradict the whole idea of "uniform pressure."

Can anyone enlighten me on this? Thanks!
 

Answers and Replies

  • #2
scottdave
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You have force on the edge. You have the total of the force on one face. And then you have pressure, which is dimensionally force / area, which is not the same as pressure.
 
  • #3
jbriggs444
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t the corner, molecules can bounce off both sides, which seems like it would make pressure rise.
It makes no essential difference to a parcel of air whether it is bounded by a box wall or by another parcel of air.

If there were an equilibrium and if the pressure within a parcel of air near the corner were greater than the pressure elsewhere in the box then the parcel near the corner would expand into the box. You would have a net flow of gas. But that contradicts the equilibrium stipulation. This is a proof by contradiction that the pressure in the corners must be equal to the pressure in the bulk of the box.
 
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scottdave
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Another thing about molecules bouncing off "both sides". The molecules also bounce off each other in random directions.
 
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Uniform/equal pressure in any volume of any size/shape bound within any object or surrounded by any other volume(s) is/are uniform/equal pressure at any/all points within said volume. To say that there would be any kind of difference in pressure of any kind at any point within that volume contradicts the very concept of "equal pressure", much less, it's definition.

A pressurized box may, at high pressures, burst or come apart at its edges and corners, but this isn't an effect of the pressure being higher in those areas, it's an effect of those areas being weaker than the other areas of its perimeter.
 

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