help me win a bet regarding subs/water pressure physics
 

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!

Not really knowing much about physics my logic seems to tell me that all the chanbers would eventualy flood since when the pressure in chamber 1 is equal to that of the pressure outside it exeeds the pressure the valve for chamber 2 can hold so slowly forcing water into that chamber and so on to the third.

Turn your chambers horizontally to give equal pressure on all seals, otherwise the lower seals will actually have a higher pressure upon them. The pressure upon the seal is generally depth related, and as the depth increases, so does the pressure.

Either way, as the 1st chamber fills, pressure will reach 1000 lbs, and breach the next seal... etc...untill all are flooded.

The biggest problem most people have is grasping the difference between PRESSURE and FLOW.

People constantly try to reduce water pressure in their houses by turning down the meter. This just gives you reduced flow. Pressure will seem to be lower with an open discharge from a tap, but when the tap is closed, pressure will rise to its normal level.:up:

Keep in mind that the structure taking on this pressure is at the bottom (see the sea floor?) So it's a consistent 1000 LBs of pressure, it doesn't change. Also consider that the structure is very tiny, so the bottom chambers are, like, 1001 LBs of pressure at most due to the additional depth. This is a hypothetical scenario, keep in mind.

Regardless of the extra 1 LB of pressure, if Answer #2 is correct, it is due to the fact that there is only 1 or 2 LBs of pressure once the first chamber is full, due to the fact that the first seal still has 999 LBs of strength, so the 2nd seal only has to hold back 1 or 2 LBs of water with 999 LBs of strength which is no problem. Remember, the first seal is never fully destroyed, just a slow leak.

No, the pressure upon the top seal will be 1000lbs, while the pressure upon the bottom seal will be greater. How much so depends upon the size of the canister.

For example if the bottom seal is physically 1m lower than the top seal, the pressure upon it is roughly 1001lb.

If the canister is the size of a matchbox, then the difference would be minimal.
If the canister was a sub, sticking out of the bottom of the seabed, the differences could be 10-20 lbs per seal.

Fine, then say we turn it on it's side. The orientation is not part of the argument, since we were talking about horizontal plumbing as well as a submerged vessel.

No problems.

....either way, you're still gonna get very wet, no matter which chamber you're in.:D

In reality, I imagine the chambers would all simply flood.

However, on paper It seems that Chamber 1 would flood, Then as it hit 999 pounds of pressure (When Chamber one is almost entirely flooded) the second chamber would begin leaking and the air in chamber 2 would begin leaving to chamber 1, whereby most of it would leave through the hole but a small amount would remain trapped. When chamber 2 fills to 999 pounds (which would take much longer than it took chamber 1 to fill) , Chamber 3's air would have to start leaving, but since it would have to pass through Chambers 1 and 2, both of which in theory are 99.99% flooded, It would take some deal of time for this to happen.

Basically, each chamber would fill progressively slower, but would always retain some small amount of air in the upper corners. In theory the air pressure in Chamber 3 (or some subsequent chamber) might very well equal enough to prevent the water from chamber 2 from entering.

If I might suggest, someone with a larger bathtub than myself should try building a model of this. It would be very interesting to see the results.

Agree,:yep: This is the case.:up:

Ok, at this point I might be revealing my position but I must.

When the first chamber fills, the seal still has 999 LBs of strength holding back the water. It's not enough to keep it out completely, thus the slow leak. Once the first chamber fills, how does that change the strength properties of the seal? It doesn't. It still holds back the water above it with 999 LBs of strength, so the only pressure pushing down on seal 2 is the miniscule weight of the water in chamber 1, which is not enough to put any flow of water past seal 2. So, based on that logic, chambers 2 and 3 will never flood.

If that's wrong, please explain how the pressure on the first seal is only enough to push through a very small flow, yet once it is filled with water, that small amount of flow leaking through somehow magically becomes a full 1000 LBs of pressure on the second seal. I can't see how that is the case.

In essence, the second answer is theorizing that the water pressure will never equalize since the first seal is holding, although weaker than the pressure on it by 1 LB, but it is still holding. Granted, if the seal blew and there was an open flow between the ocean and the first seal, the pressure on the 2nd would be 1000 LBs. But it hasn't blown, and won't.

Not to complicate things further, but in fact, I believe once the first chamber fills, the presence of water in the first chamber will create additional outward strength assisting the first seal, easily keeping any more water from entering, so the outer water pressure in fact would have zero effect on the 2nd seal. The only pressure on it would be the weight of the water in the first chamber, which (as defined) is miniscule and nowhere near 999 LBs required to cause the 2nd seal to leak.

I realize that the size of the leak might actually be an important factor here. In our arguments, he stated it didn't matter if it was pinhole sized or not. I think the amount of pressure that enters the chamber from the outside would probably depend on the size of the leak. For this case though, assume it is pinhole sized resulting in a slow drip.

Water (like most people :lol: ) will take the path of least resistance. In this case, that is the pinhole. The leak may be slow, but flooding is inevitable.

Sorry.:down:


Anyway, it's not too late for a second opinion. Im sure somebody around here can come up with an opposing theory.

It's not so much that the water in the second chamber becomes an independent body of water . . . thus asserting its own pressure . . . its that due to depth, and the weight of the water above it at that depth . . . that causes the pressure . . . therefore the weight of the water, if the structure was horizontal . . . since the water is one large body . . . will continue to exert the same amount of pressure at that constant depth . . . furthermore what is exerting the 999 lbs of pressure for the seal . . . the seal itself . . . or the air pressure behind it? If it's the airpressure behind it . . . then with no air in the first pressure the seal looses its strength and will eventually open to the out water with time and the flow of the water.

I think.

Been a (really) long time since I studied fluid mechanics, but I'm afraid I believe you lose this one. I don't believe that the size of the hole in the seal makes any difference at all to the end result, though it may well affect the amount of the flow and time to flood.

I believe that the idea that the broken seal will somehow "retain 999 psi of strength" is where you're getting led astray here. The compromised seal in effect will not retain any of its strength at all (or, perhaps more accurately, whatever "strength" that seal may retain will not matter, any more than it matters that the walls of the chamber still retain their greater-than-999-psi strength even if the whole seal is opened) - once the water starts penetrating to the first compartment, the pressure in that compartment is going to equalize with that outside (1,000 psi) no matter what, and when that happens the water (and any air that might still be trapped inside, which will be highly compressed by then) in the first chamber will indeed be exerting an equal, 1,000 psi pressure on all of the interior surfaces of the first chamber - including, unfortunately, the seal into the 2nd chamber, which will then fail in just the same manner as did the first seal. Once the 2nd chamber fills and equalizes, the third seal will fail just as the others did.

Sorry - I hope for your sake I've got this wrong, but I don't think so

Unfortunately I have to agree with panthercules. The water pressure in the first chamber will eventually equalize with the water on the outside, therefore breaching the second seal in the same way it did the first. As for the third chamber - lather, rinse, repeat...

All three chambers will flood.