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Pascal Paradox

08/25/2023 8:51 PM

Here is an interesting demonstration. 2.2 pounds of water can burst a 50 liter flask. The physics is straight forward, but the results are counterintuitive.

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#1

Re: Pascal paradox

08/25/2023 9:18 PM

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Guru

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#2

Re: Pascal paradox

08/26/2023 10:46 AM

As Johnny Jett would say, "The power of Hydaulics!"

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#3

Re: Pascal paradox

08/26/2023 3:53 PM

Actually, she added 2.2 pounds of water to about 110 pounds of water to shatter a 50-liter flask.

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Guru

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#4

Re: Pascal paradox

08/27/2023 12:06 AM

Very nice demo! My question now is: What did Pascal use for a hose/tube? I'm pretty sure it wasn't Tygon...

...nice presenter, too!

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#5

Re: Pascal paradox

08/28/2023 5:35 PM

The quantity of water added is unimportant. What mattered was the pressure imposed by the depth of water in the very high filling tube. With a different diameter tube, the quantity of water would have been different. The telling indication was the pressure gauge, which read just over 30 when the bottle burst. Since water is essentially non-compressable (at least under the conditions shown), all we are witnessing is a valid demonstration of the omni-directional characteristic of pressure.

Pressure matters, not volume of water. Pressure was obtained by height of the water column.

--JMM

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#8
In reply to #5

Re: Pascal paradox

08/29/2023 12:39 AM

I would assume that pressure in the pipe would be in all directions as well (not only in the glass bottle) and burst the wall of the hosepipe....

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#9
In reply to #8

Re: Pascal paradox

08/29/2023 1:35 AM

True. That is precisely why I asked what Pascal used for his hose. Leather perhaps?

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#10
In reply to #9

Re: Pascal paradox

08/29/2023 8:03 AM

Maybe it was really a thought experiment. It does seem that he would have had trouble with that much pressure.

"

Pascal's barrel[edit]

An illustration of Pascal's barrel experiment from The forces of nature by Amédée Guillemin (1872).

Pascal's barrel is the name of a hydrostatics experiment allegedly performed by Blaise Pascal in 1646.[9] In the experiment, Pascal supposedly inserted a long vertical tube into a barrel filled with water. When water was poured into the vertical tube, the increase in hydrostatic pressure caused the barrel to burst.[9]

The experiment is mentioned nowhere in Pascal's preserved works and it may be apocryphal, attributed to him by 19th-century French authors, among whom the experiment is known as crève-tonneau (approx.: "barrel-buster");[10] nevertheless the experiment remains associated with Pascal in many elementary physics textbooks.[11]

"

https://en.wikipedia.org/wiki/Pascal%27s_law#:~:text=Pascal's%20barrel%20is%20the%20name,caused%20the%20barrel%20to%20burst.

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#13
In reply to #5

Re: Pascal paradox

08/29/2023 8:11 PM

Pressure matters, not volume of water. Pressure was obtained by height of the water column.

You're completely correct. I think few people would be surprised at the amount of pressure if the water column had the same cross section top to bottom and the water column had a lot of weight.

Just like a lever where force1 x distance1 = force2 x distance2, the water in the filling tube with a very small crosssectional area, A1, moves a much larger distance than the water pressing up against the larger area of the flask, A2. The multiplication of the force, F2/F1, is the same as the ratio of the two areas, A2/A1 = F2/F1. This is the principle of the hydraulic jack.

So 2.2 pounds of water moving a larger distance can exert enough force over a smaller distance to break the flask.

Lever

Hydraulic Jack

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#6

Re: Pascal paradox

08/28/2023 10:48 PM

Initially she didn't explain that the flask was connected to a tube that went 150 feet up in the air.

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#7

Re: Pascal paradox

08/28/2023 11:37 PM

Same reason dams are very thick at the bottom--the greater the distance to the surface of the water the greater the pressure on the dam.

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#11
In reply to #7

Re: Pascal paradox

08/29/2023 1:21 PM

This (burst resistance - also could be equated to tension) is but one reason dams at thick on the bottom. Overturning forces, sliding forces, bouyant forces, and bending forces also come into play.

Overturning - The pressure of the water wants to tip the dam over.

Sliding - The pressure of the water wants to push the dam forward.

Bouyance - The amount of water displaced by the dam wants to float the volume of water that is discplaced. This is more applicable if water gets under the dam.

Bending - the pressure of the water causes a narrow segment of the dam to bend as if it were a fixed end or cantilevered beam. Cantilevered in the vertical direction and fixed end in the horizontal direction

And don't forget that water acts a lubricant. Thus weakening internal and external resistance to these forces.

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#12
In reply to #11

Re: Pascal paradox

08/29/2023 5:37 PM

Thanks for the additional info about dam design.

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