Need formula for idea of diving using two chambers

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Discussion Overview

The discussion revolves around calculating the dynamics of two chambers connected by an escape tube, particularly focusing on the effects of a leak in the lower chamber. Participants explore how water entering the chamber affects air pressure in both chambers and the escape tube, considering various depths, sizes, and configurations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks help with physics formulas to calculate water fill rates and air pressure changes in two chambers connected by a tube.
  • Another participant states that water pressure approximately doubles for every 10 meters of depth, equating 10 meters to 2 ATM pressure outside the chamber.
  • A different participant challenges this by stating that water pressure starts at 0.1 ATM for the first meter and takes 10 meters to reach 1 ATM, suggesting a more complex equation is needed.
  • One participant mentions the Ideal Gas Law as potentially relevant to the problem, questioning whether the complexity lies in the pressure gradient of the leaking water or the fill rate based on hole size and pressure differences.
  • Another participant agrees that the complexity involves the fill rate with water and the difference in pressures, while also correcting the previous claim about water pressure at 10 meters, asserting it is not 2 ATM.
  • A participant expresses uncertainty about their previous understanding of water pressure at depth and acknowledges the need to correct their earlier statements.

Areas of Agreement / Disagreement

Participants express differing views on the correct understanding of water pressure at various depths, with no consensus reached on the complexity of the calculations required for the problem. Multiple competing views remain regarding the pressure dynamics involved.

Contextual Notes

Participants have not fully resolved the assumptions regarding pressure calculations, the effects of depth on pressure, and the specific equations needed for the scenario described.

DiveBuddy
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Wanting to put numbers into a spreadsheet for two chambers joined by an escape tube. If the bottom chamber sprang a leak (circular - for calculations) how quickly it would full with water & resultant air pressure in upper chamber. What air pressure at any given time, in both lower & upper chambers plus through tube. Need to calculate when rooms are placed at varying depths & size with varying escape tube circumference & length.

I'm good with spreadsheets but have no idea about physics formulas.

Help!, please

thanks in advance :)
 
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DiveBuddy said:
Wanting to put numbers into a spreadsheet for two chambers joined by an escape tube. If the bottom chamber sprang a leak (circular - for calculations) how quickly it would full with water & resultant air pressure in upper chamber. What air pressure at any given time, in both lower & upper chambers plus through tube. Need to calculate when rooms are placed at varying depths & size with varying escape tube circumference & length.

I'm good with spreadsheets but have no idea about physics formulas.

Help!, please

thanks in advance :)

Welcome to the PF.

Sounds like you are a diver. What is the equation for water pressure as a function of depth?
 
Water pressure doubles for every 10 metres of depth (approx), with 10m = 1 ATM.
 
DiveBuddy said:
Water pressure doubles for every 10 metres of depth (approx), with 10m = 1 ATM.

So at the surface, the pressure inside and outside is 1ATM, at 10m, the pressure outside in the water is 2ATM and you have 1ATM inside. So if you open a hole in the bottom of the lower chamber and the pressures equalize, how far has the water risen?
 
No. Water starts with a pressure of 0.1 ATM for first metre & takes 10 metres to reach 1ATM.

What I am asking is a very complex equation. I suspect from your two posts you won't know how to structure the solution.

thanks anyway
 
DiveBuddy said:
No. Water starts with a pressure of 0.1 ATM for first metre & takes 10 metres to reach 1ATM.

What I am asking is a very complex equation. I suspect from your two posts you won't know how to structure the solution.

thanks anyway

It's possible that I'm not seeing a complexity in your setup, but so far I don't think so. I'm a diver, and I understand the Ideal Gas Law. That seems like most of what is needed for this problem.

http://en.wikipedia.org/wiki/Ideal_gas_law

And no, 1ATM is defined as the air pressure at sea level (for the most part). So the water pressure at the water's surface is 1ATM. As you go down, the pressure climbs from there at the rate you mentioned. So your vessel with 1ATM air pressure in it will be feeling 2ATM of water pressure at a depth of 10m.

Is the complexity that you are alluding to that there will be a pressure gradient in the water that leaks into the vessel? That would certainly seem to be part of the pressure & delta-volume of air calculation.

Or is the complex part more about the fill rate with water, given some hole size in the bottom of the vessel and the difference in pressures?
 
Last edited:
Yes. "the complex part more about the fill rate with water, given some hole size in the bottom of the vessel and the difference in pressures"

Also @ 10M depth water is 1ATM not 2. Look it up.

Appreciate people who looked but did not reply. I'm assuming because of the number of messages in this thread it may be overlooked by someone able to help so may ask on a different physics board.
 
DiveBuddy said:
Yes. "the complex part more about the fill rate with water, given some hole size in the bottom of the vessel and the difference in pressures"

Also @ 10M depth water is 1ATM not 2. Look it up.

Appreciate people who looked but did not reply. I'm assuming because of the number of messages in this thread it may be overlooked by someone able to help so may ask on a different physics board.

I'll move this to the ME forum to try to get some help on the fill rate question versus pressure differential and hole size.

And no, the pressure at 10m under water is not 1ATM. Have you ever tried to breathe through a hose underwater? No workie...
 
I was so sure I had it right I didn't check.

Thanks for putting me right about water pressure at 10 metres!

Now I have to clean up my mess when discussing my ideas using the wrong pressure. I must have looked like an idiot. Darn!
 

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