Forces on a rod through a pressurized container

[mkartevoll]

Hi!

A colleague and I were discussing pressures and forces when we arrived at a special situation where we do not fully agree and would like some help to better our understanding.

Imagine a box/container with a hole in the middle of two of the opposite sides. A rod/cylinder goes fully through the box through the holes, which are fitted with frictionless seals around the rod (idealized situation). The pressure inside the container is Pbox and the length of the rod inside the box and diameter of the rod is Lrod and Drod respectively.

The question we were discussing is what will happen to the rod when pressure Pbox is applied inside the box. My colleague argued if a measurement device were to be fitted inside the middle of the rod it would measure a force equal to what would be expected if the pressure were acting on a cross sectional area of the rod. I argued the increase in pressure would compress the rod slightly and that the stress/strain regime would be a function of the length of the rod, the surface area and the pressure inside the box.

I have attached a crude drawing of the situation and would appreciate any feedback on this.

Rgrds
mkartevoll

 

[mkartevoll]

I see now I might have posted this question in the wrong forum! Is there a way to move it or should I delete it and post it again somewhere else?

 

[Bystander]

It counts as Gen. Phys.. See P. W. Bridgman, The Physics of High Pressure, for "pinch-off" effect.

 

[mkartevoll]

Thank you for the book suggestion, I will look into that when I can get myself to a library. If you are familiar with the parts of the book, do you know if the stress in the rod due to the pressure in the box would be equal to the force the same pressure would exert on the area of a cross section of the rod? Or is it a bit more complicated than that? Please excuse me if I am using the wrong terms in my questions, It's been a while since I studied and I think I might be mixing terms together.

 

[Bystander]

the stress in the rod due to the pressure in the box would be equal to the force the same pressure would exert on the area of a cross section of the rod

This is pretty much it, the "pinch off" effect. It also occurs in O-rings placed in high pressure vessels.