A question for the asylum physicists (or engineers)

[MapisM]

Context:
A tank of 1 sqm volume is press tested with air, at a pressure of 200 millibar.
There's some fuel left in the tank bottom, say 50 litres or so.

Question:
If the tank would leak one litre of liquid from its bottom, what sort of pressure reduction should show an instrument placed on the top of the tank (hence obviously reading the air pressure)?

Serious question, no hidden tricks, I promise!

 

[RIN]

Context:
A tank of 1 sqm volume is press tested with air, at a pressure of 200 millibar.
There's some fuel left in the tank bottom, say 50 litres or so.

Question:
If the tank would leak one litre of liquid from its bottom, what sort of pressure reduction should show an instrument placed on the top of the tank (hence obviously reading the air pressure)?

Serious question, no hidden tricks, I promise!

at 200 millibar you would be vacuum testing the tank so its unlikely to lose fuel

 

[TheOrs]

Unless I've misunderstood; I would say 199 mBar (ish)

 

[Bouba]

If you cannot maintain anything over atmospheric pressure then you have a leak, or a breather pipe

 

[Portofino]

Context:
A tank of 1 sqm volume is press tested with air, at a pressure of 200 millibar.
There's some fuel left in the tank bottom, say 50 litres or so.

Question:
If the tank would leak one litre of liquid from its bottom, what sort of pressure reduction should show an instrument placed on the top of the tank (hence obviously reading the air pressure)?

Serious question, no hidden tricks, I promise!

Would have thought depends on the surface area the air /liquid interface ,and the temp change too .
You have only said the vol .

 

[Freebee]

Have you locked that pressure in the tank or are you topping it up? If you locked it in I would say after the fuel leakage there would be no pressure left.

 

[jfm]

I'm with the Ors. If you want the maths, it is this, and I assume you mean 1 cubic metre volume tank, aka 1000 litres.

Loss of 1 litre fuel allows air to expand from 950 litres to 951. If the previous pressure was 200 millibars above atmospheric, it was 1200 millibars absolute. The new pressure will be 950/951 x 1200 = about 1199. So the gauge that read 200 before will now read about 199, as theOrs said. ( All assuming no trick question)

 

[Cymrogwyllt]

Context:
1 sqm volume

There is no such thing.

 

[Momac]

199.8
assuming you mean the tank is 1000litres (1 cubic metre)

 

[MapisM]

Sorry folks for the typo, yeah, 'course I meant one cubic rather than square meter, i.e. 1k litres.
And yes, obviously I did mean 200 mbar above atmospheric pressure - i.e. a 2 meters column of liquid, unless my scuba diving memories are completely wrong...

I'm just not sure to understand Freebee's point.
Just to better explain the context which I introduced, we are talking of a 1000 litres tank, almost empty, pressurized with air at 200 mbar above atmospheric, and kept closed like that for one day.
What I was suspecting - and essentially this has been confirmed from other replies - is that a small leak (say one litre) of fuel from the tank bottom would have a negligible impact on the reading of the manometer.
Freebee, how can you envisage no (AIR) pressure left after just one liter of liquid escapes?

Anyway, the next question is, am I right in assuming that by filling the tank with fuel almost completely, and then repeat the test with air pressure (whereas the air volume, with a full tank, is restricted to just a few litres left in the hose connecting the manometer), the pressure reduction in the event of the same fuel leakage would be MUCH more relevant?

Btw, since boatbuilders usually stick a plate on their tanks with a pressure test value, if anyone know what the recognized/correct procedure is, I'm all ears.

 

[TheOrs]

If you fill your 1000 litre tank with 999 litres of fuel, pressurise it to 200mBar and over a period of time 1 litre of fuel leaks out, your gauge will then read 100mBar.

 

[prv]

at 200 millibar you would be vacuum testing the tank so its unlikely to lose fuel

200mb gauge pressure, I think we can assume.

Pete

 

[MapisM]

If you fill your 1000 litre tank with 999 litres of fuel, pressurise it to 200mBar and over a period of time 1 litre of fuel leaks out, your gauge will then read 100mBar.

Thanks, understood & agreed.

But on second thought, this makes me wonder even more what the correct tank testing procedure is.
I mean, when the 1 cubic meter tank is filled with 999 litres of fuel, the tank is already withstanding 100 millibar of pressure at its bottom because of fuel alone, unless I'm missing something.
So, by pressurizing the 1 liter of air left at 200 millibar, isn't it true that we are actually testing the top of the tank at 200 and the bottom at 300? All the tank test plates I've seen only mention one number (mostly in kPa btw, not that I think it makes any difference - see example below).
Now, how can such test be done, I wonder...

 

[Momac]

Liquids are said to be incompressible. While gas such as air is compressible.

But a better explanation is liquids are quasi incompressible. When you apply pressure to a liquid its volume does not change. A gas , such as air ,reduces in volume as it is compressed.

Therefore apply pressure to a near full tank and a small loss of liquid will make a big loss in pressure .
Apply pressure to a near empty tank and you are compressing the air . A small loss of liquid (or air) makes a smaller reduction in the pressure in the large volume of air.

 

[MapisM]

If you fill your 1000 litre tank with 999 litres of fuel, pressurise it to 200mBar and over a period of time 1 litre of fuel leaks out, your gauge will then read 100mBar.

Hang on a minute. After sleeping on it, this doesn't sound so convincing anymore.

I mean, coming to think of it, I believe that the correct train of thought/math is as follows:
1) in order to pressurize a 950 liters with air at 1200 mbar absolute, you must fill it with 1140 liters of atmospheric air (950*1.2)
2) when the air space (so to speak) in the tank increases to 951 liters due to the leak of one liter of fuel, what we have is the same 1140 liters of atmospheric air which can now expand to 951 liters.
New pressure is now 1198.7 mbar absolute (1140/951)
So far so good - the conclusion is still that the pressure loss is negligible.

But if the tank has 999 liters of fuel and one liter of volume left, and you pressurize it again at 1200 mbar abs, you are actually pumping in it 1.2 liters of atmospheric air.
Therefore, after the fuel leak of one liter, this air has 2 liters of volume to expand, which is more than the volume of atmospheric air.
Which means that as soon as the leak has reached 0.2 liters volume, the air inside the tank is back to atmospheric pressure, and from that point onward it actually acts as a "brake" to the leak, because in order to leak the other 0.8 liters, the fuel should create a vacuum in the air space, eventually ending with 600 mbar absolute pressure inside it (2 liters of empty space divided by 1.2 liters of atmospheric air).
Or am I missing something?

All the above leaves open the question about what is the correct/normal tank testing procedure, anyway...

 

[Nick_H]

Thanks, understood & agreed.

But on second thought, this makes me wonder even more what the correct tank testing procedure is.
I mean, when the 1 cubic meter tank is filled with 999 litres of fuel, the tank is already withstanding 100 millibar of pressure at its bottom because of fuel alone, unless I'm missing something.
So, by pressurizing the 1 liter of air left at 200 millibar, isn't it true that we are actually testing the top of the tank at 200 and the bottom at 300? All the tank test plates I've seen only mention one number (mostly in kPa btw, not that I think it makes any difference - see example below).
Now, how can such test be done, I wonder...

I'd always assumed the tank test pressure was a record of the test performed during the manufacturing process, which would of course be done with the tank empty? Do some tanks need periodic testing in service? If they needed a re-test due to being modified, then I guess they would also be empty for the mods to be done.

 

[jfm]

Anyway, the next question is, am I right in assuming that by filling the tank with fuel almost completely, and then repeat the test with air pressure (whereas the air volume, with a full tank, is restricted to just a few litres left in the hose connecting the manometer), the pressure reduction in the event of the same fuel leakage would be MUCH more relevant?

Btw, since boatbuilders usually stick a plate on their tanks with a pressure test value, if anyone know what the recognized/correct procedure is, I'm all ears.

Ref first para above you are 100% correct

Ref 2nd para, a pressure test isn't a leak test (even if the procedures overlap). It is a test to ensure tank can withstand a certain pressure. The tests are normally done with liquid not air so that if the test is failed the "explosion" is very small. Pressurised liquid contains far far less potential kinetic energy than pressurised gas.

 

[jfm]

If you fill your 1000 litre tank with 999 litres of fuel, pressurise it to 200mBar and over a period of time 1 litre of fuel leaks out, your gauge will then read 100mBar.

The one litre of air is at 1200 absolute pressure. If you put the same air in a 2 litre space it' pressure is 600 mbar absolute. It's all in the maths that I set out above.

 

[jfm]

I'd always assumed the tank test pressure was a record of the test performed during the manufacturing process, which would of course be done with the tank empty? Do some tanks need periodic testing in service? If they needed a re-test due to being modified, then I guess they would also be empty for the mods to be done.

Nick you pressure test tanks by filling with liquid. So the explosion is tiny if they fail. Good luck to anyone pressure testing a thousand litre tank using gas!

 

[BruceK]

All the above leaves open the question about what is the correct/normal tank testing procedure, anyway...

I'm not sure about tanks of your size, but a standard test for testing tanks is the bubble test. i.e. dunk it under water and watch for bubbles not so easy when they're big. I'd have thought using air was a bit iffy in your scenario as it's more temperature volatile with moisture content etc and that an inert gas such as helium would be used.
Another trick from the DIY book is the soap bubble test .... fasten a kids balloon to the vent. When you fill with air and seal it should inflate and provide pressure, but not enough to deform the tank or put too much pressure on a pinhole (too much pressure and it wont bubble but just blow the soap water clear)

None of this definitively answers your question though