Help me settle a bet about water pressure

[minsc_tdp]

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!

 

[russ_watters]

You can't have a leak that under nearly static conditions can hold back any amount of pressure.

 

[cesiumfrog]

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.

 

[minsc_tdp]

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...

 

[minsc_tdp]

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.

 

[Shooting Star]

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.

 

[FredGarvin]

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.