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Pascal's paradox?

by Clausius2
Tags: paradox, pascal
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Clausius2
#1
Sep25-03, 02:49 PM
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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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krab
#2
Sep25-03, 10:51 PM
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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.


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