Help me settle a bet about water pressure

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Discussion Overview

The discussion revolves around a hypothetical scenario involving water pressure and the behavior of seals in three chambers under pressure. Participants are debating two main possibilities regarding the outcome of a slow leak in the first chamber and its effects on the subsequent chambers. The conversation touches on principles of fluid mechanics and the real-world implications of seal integrity.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant argues that once the first chamber fills, the pressure equalizes, nullifying the first seal's strength, leading to flooding in all chambers.
  • Another participant contends that the first seal retains its strength, allowing only a minimal amount of pressure to transfer to the second seal, which can hold back the water.
  • Some participants introduce the idea that the nature of the seal (e.g., O-ring) affects the leak's behavior and the pressure dynamics.
  • A later reply raises the importance of air or vacuum conditions in the chambers, suggesting that these factors could alter the pressure dynamics and outcomes.
  • Another participant notes that pressure increases with depth, which could influence the pressure experienced by the second and third chambers.

    • Areas of Agreement / Disagreement

    Participants do not reach a consensus, with multiple competing views on how the pressure dynamics will play out in the scenario. The discussion remains unresolved as different interpretations of the physical principles are presented.

    Contextual Notes

    Participants mention various assumptions, such as the presence of air or vacuum in the chambers, the nature of the seals, and the definition of pressure units, which may affect the conclusions drawn.

minsc_tdp
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Image: http://knepfler.com/images/pressure.gif

My brother and I completely disagree on what will happen to chambers 2 and 3 in this scenario. I won't skew the answers here by stating who holds which opinion.

To clarify, there is an underwater structure that is taking on 1000 LBs of water pressure. There are three chambers, each with a seal that can hold back 999 LBs of water. IMPORTANT: These numbers are chosen so that we both agree on the fact that the pressure is not enough to entirely destroy the seal and open a hole. It's just a slow leak.

Only one of two possibilities exist that we are arguing:

1. The slow leak will eventually fill the top chamber. At that moment the pressure equalizes and the strength of the first seal is nullified. The 1000 LBs of pressure is now instantly transferred to the second seal, and a similar leak occurs, therefore all chambers will eventually flood.

2. The slow leak will eventually fill the top chamber. However, the first seal still has 999 LBs of strength, so only 1 LB of pressure (plus whatever the weight of the water in the chamber is, but assume it is VERY small and thus irrelevant) is transferred to the second seal. So, the 2nd seal is more than capable of holding back the 1 LB of pressure, so it never leaks or floods chambers 2 and 3.

If I lose, I have to pay him $50. If I win, he has to do my laundry (easily worth more than $50. I'm a slob, it's like 6 loads and we both hate it.)

If you vote, please explain your logic, thanks!
 
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You can't have a leak that under nearly static conditions can hold back any amount of pressure.
 
The slow leak will gradually raise the pressure of the chamber, until the pressure is equal on both sides of the seal. In your scenario the limits of the second seal (and third) will be broken before this occurs. Whoever picked "1" wins.

There is one exception: if instead of a seal (that breaks when its rating is exceeded, leaving a small hole in its place that stays open for ever more) you used a pressure release valve (that opens a hole when the pressure difference goes above some figure, but closes the hole back up when the pressure decreases again) then only enough water will enter so as to lower the pressure difference to the valve rating, a la "2".

But since you so specifically chose that the pressure only "just barely" exceeds the rating of the seal ("not enough to entirely destroy the seal" unlike the way an ideal seal is supposed to work) you get the messy real world in which everything depends on (imprecise) materials: does the leak of water further erode the gap in the seal to produce a larger (permanent) hole, or does part of the seal merely bend open like a spring and later close itself more like a pressure valve? It seems the only fair compromise is for you to pay him the money and for him to do the laundry.
 
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russ_watters said:
You can't have a leak that under nearly static conditions can hold back any amount of pressure.

Can you explain? The example we were using for discussion was an O-ring, which seems reasonable, and is basically a seal that can slowly leak if it has a flaw which reduces it's strength at holding back pressure. Just like my bathroom faucet that is currently dripping...
 
While this is a physics question, it is also a real world question, and a huge part of his argument is that it doesn't matter the size of the hole and that the seal is still mostly intact. Cesium, the example we were using was an O-ring which I think is good, since it doesn't open/close like a valve and has a pretty consistent leak due to the material.
 
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Dear Minsc,

You have not mentioned the whole physics of the situation. Is there air in the chambers or vacuum? Also, you may not be correct in saying that only these two are the only possibilities. I am assuming that by 1 lb of pressure you mean 1 lb-weight/sq. inch or some proper unit of pressure.

If there is air in the chambers, and if it’s a slow leak, the air is compressed after a while such that the air pressure is equal to the applied pressure and the water cannot come in any more. I am assuming that there is no way for the air to escape, because the seals have extremely small openings and possibly are one-way.

If there is vacuum in the chambers, then all the chambers will eventually fill. You are wrong in saying that the pressure on the second seal is only 1 lb after the first chamber is full. It will be 1000 lb. Remember Pascal’s law? The pressure applied anywhere in a liquid is transmitted to all of parts of the liquid.

If the air can escape, then also all the chambers will be flooded by the same logic.
 
Just to throw in my 2 cents worth...Whoever picked #1 is correct. One thing that is missing is that the pressure (in units of psi, not Lbs) in chambers 2 and 3 will increase slightly due to the increased depth, i.e. pressure is a function of depth. Anyways, once the top chamber fills completely, the pressure will equalize and it will be like the first chamber doesn't exist. The second chamber will now have the same pressure on it and the process will continue.
 

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