Pressure in the corners of a box

• oobgular
In summary, the question asks whether the force from pressure in a pressurized cube would be larger at the edges and corners of the box. There is a misconception that the pressure would be higher at the corners due to molecules bouncing off both sides, but this is not true as pressure is dimensionally different from force. In fact, the pressure in all parts of the box must be equal due to the concept of "uniform pressure". The idea that pressure would be higher in certain areas contradicts the equilibrium stipulation and the definition of "equal pressure". Any bursting or coming apart of the box at the edges and corners is due to those areas being weaker, not because of higher pressure.
oobgular
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!

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.

oobgular said:
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.

scottdave
Another thing about molecules bouncing off "both sides". The molecules also bounce off each other in random directions.

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.

1. What causes pressure in the corners of a box?

The pressure in the corners of a box is caused by the weight or force exerted on the walls of the box. This force is distributed unevenly, with more pressure being applied to the corners due to the change in direction of the walls.

2. How does the shape of a box affect the pressure in its corners?

The shape of a box can greatly affect the pressure in its corners. A box with sharp corners will have higher pressure in the corners compared to a box with rounded corners. This is because sharp corners concentrate the force, while rounded corners distribute it more evenly.

3. Can the pressure in the corners of a box be changed?

Yes, the pressure in the corners of a box can be changed by altering the weight or force being applied to the walls of the box. For example, adding more weight to the top of the box will increase the pressure in the corners.

4. How does pressure in the corners of a box affect the stability of the box?

The pressure in the corners of a box directly affects the stability of the box. Higher pressure in the corners can cause the walls of the box to buckle or collapse, making the box less stable. This is why it is important to evenly distribute weight or force in a box to maintain its stability.

5. Is there a maximum pressure that a box can withstand in its corners?

Yes, there is a maximum pressure that a box can withstand in its corners. This depends on the material and construction of the box. Exceeding this maximum pressure can result in the box collapsing or breaking at the corners.

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