Solve Pascal's Paradox | Vessels D1 & D2 Filled with Water

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In summary, there are two vessels, D1 and D2, both filled with a height H of water and with a piston at the bottom of each vessel to prevent water from escaping. D1 has a top area S1 and a piston above it, while D2 has a top area S2, which is smaller than S1. It is uncertain which vessel requires a greater external force on the piston's surface to prevent water from escaping. However, based on the volume, V1 is greater than V2. The force on the piston is determined by pressure and the energy involved in moving the piston must equal the potential energy change.
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Clausius2
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We have two vessels D1 and D2 filled with a height H of water (the same for each one).
At the bottom of each vessel there is a piston of area S avoiding that water could escape out.
The characteristics of the vessels are:
D1: It has at the top an area S1 and there is the piston, above described, at the bottom. Let's know S1>S. If we could see it far away it would seem the letter V.
D2: it has top area S2 (S2<S) and the piston at the bottom. If we could see it far away it would seem like the letter V upside down (capital Lambda).
In which of the two vessels the external force required on piston's surface in order to avoid water escape is greater?
I'm not sure. Obviously the volume V1>V2. So we could apply Newton's law taking into account the total weight of water, or merely the water that is just upon the piston.
Well, i'll better wait your answers.
 
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Think of the energy involved in moving the piston. The force on the piston is P*S where P is the pressure. Move the piston down a tiny distance dz, and it has done work on you to the amount P*S*dz. But you know the difference in energy between before and after the piston moved: effectively, you've moved a volume of liquid S*dz from the top of the container to the bottom. So calculate the potential energy change. It must equal the work done.
 

FAQ: Solve Pascal's Paradox | Vessels D1 & D2 Filled with Water

What is Pascal's Paradox?

Pascal's Paradox is a scientific principle that states that when two vessels are filled with water and connected by a tube, the water levels will eventually equalize regardless of the difference in their initial water levels.

How is Pascal's Paradox related to Vessels D1 & D2 Filled with Water?

Vessels D1 & D2 Filled with Water is a specific example of Pascal's Paradox, where two vessels (D1 and D2) are connected by a tube and filled with water. The water levels in these vessels will eventually equalize, proving Pascal's Paradox.

What factors contribute to the equalization of water levels in Pascal's Paradox?

The equalization of water levels in Pascal's Paradox is due to the principle of communicating vessels, which states that when two vessels are connected, the fluids within them will seek to reach the same level.

Are there any real-life applications of Pascal's Paradox?

Yes, Pascal's Paradox has several real-life applications, such as in hydraulic systems, where the principle of communicating vessels is used to transfer pressure and force throughout the system.

Can Pascal's Paradox be disproven?

No, Pascal's Paradox has been observed and proven in various experiments and real-life situations. However, there may be certain exceptions or limitations in specific scenarios that require further investigation and research.

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