Pascal's Law - pressure inside the liquid vs. force needed to lift the liquid

  1. I'm going to steal a picture that was used in a different thread in this forum.

    [​IMG]

    (both containers are open at the top, and both contain water)

    I watched an MIT video of professor Walter Lewin, who used these very same illustrations and stated that the pressure at point A and point B are the same.
    (see minutes 18 through 21 of the video: http://www.youtube.com/watch?v=265icrI3HkM&feature=related)

    Although it is not intuitive, I accept that the pressure is the same at the bottom of both containers.

    My question is this....

    Imagine that the bottom of both containers is actually a piston (of equal area in both containers).

    Obviously there is a smaller amount of weight sitting on the piston in the left container, as opposed to the right container.

    So intuitively, to begin ejecting water out the top of each container, I have assumed that less upward force would need to be applied to the piston of the left container... than the piston of the right container (more total water weight over the same piston area).

    My confusion is how the pressure on the piston inside both containers can be the same.... yet the force needed to eject water out the top of both containers is different.
     
  2. jcsd
  3. ideasrule

    ideasrule 2,323
    Homework Helper

    Actually, the force needed to lift the water is exactly the same in both containers, assuming the bottom of the containers have the same cross-sectional area. To lift the water, you just need to overcome the water pressure over the entire area of the piston. Both pressure and the area are the same for both containers, so force should also be the same.

    This is counterintuitive, but it doesn't violate any laws of physics. The natural question would be to ask where all the energy went in lifting the water by a small distance L, since both containers should have received F*L of energy from the piston. For the right container, the water's center of mass rises by L, so the water gains mgL of potential energy. For the left container, the water is forced into a thin tube, so its center of mass rises by much more than L. Although the water also has less mass, this difference in mass is more than offset by the larger increase in center of mass, so this is where all the work went.
     
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