Vacuum force

[SC83]

Hi,

I have a bottom plate resting on a table (see figure in attachment).
On top of this bottom plate is are series of springs and on top of it rests a top plate.
Between the bottom and top plate (inside the springs) is a seal to create a vacuum chamber.
Question: what is the total vacuum force on the springs if the vacuum chamber (inside the seals) is 1 x 1 meter and the vacuum pressure is 1 mbar (atmospheric pressure outside)?

 

[GregLocock]

Sounds like homework to me.

Cheers

Greg Locock


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[SC83]

Hi Greg,

I hoped I was still a student ;-)

Ok, let’s put it differently. I doubt if it is one (only over the top plate) or two times (over the bottom and top plate) the pressure drop of 1 bar force that acts on the springs. Thus 100 kN or 200 kN.

 

[IRstuff]

Force is k * (compression distance of springs), and could anything from nearly zero, to nearly 101.3 kN, depending on how long the springs are and their spring constants, and the compressibility of the seal.

I could see maybe some funky approach where the seal is a latex-like material, and its stretching would impose tension that adds to the atmosphere pushing on the plate.

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[SC83]

Hi IRstuff,

I know how to calculate a spring force. That is not what I'm looking for.
I want to know what the total external force (atmospheric pressure) is that is acting on the springs, irregardless of the spring constant, seal properties etc. Is this 1 bar x the top surface or 1 bar x (top surface + bottom surface)?

 

[IRstuff]

No, as I stated, it could be close to zero. Just consider if the springs were 1 micron taller than the seal and the seal was incompressible. Your springs would then be compressed 1 micron and then be stopped by the seal itself. Alternately, if the seal were a impermeable latex, the vacuum would suck the latex inward, resulting in the latex pulling the plate downward against the springs. But without knowing the specifics, there cannot be a specific answer.

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[IRstuff]

In any case, the bottom plate does nothing, since you show it resting on the table. If the plates were vertical, then you could get both plates in action

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[IRstuff]

I assumed the plate was massless, otherwise, you're looking at around 1 kN for a steel plate.

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[SC83]

Ok, that's the answer I was looking for ;-)
Can you maybe explain why the bottom plate does nothing in this case and why it does when it was vertical?

 

[IRstuff]

Since it's on the table, the air pressure adds to the weight of the assembly, keeping the bottom plate on the table, so no air pressure on the bottom. If you supported the assembly by the seal, that would be different.

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[Compositepro]

IRstuff, think again. There is air under the bottom plate but that is not relevant to the problem. The force acting on the springs is 999 mbar times one square meter (with appropriate unit conversion factors). The force on the bottom plate does not add to the force of the top plate upon the springs, but only counter balances it. Otherwise the the assembly would just accelerate downward.

 

[hydtools]

The weight of all items from and including the bottom plate rest on the table. After evacuating the sealed space all the same weight, minus the weight of evacuated air, still rest on the table.

Ted