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Pascal's Principle

  1. Sep 10, 2015 #1
    1. The problem statement, all variables and given/known data
    A small tube is connected to the top of a larger one and the whole thing is filled with water. The small tube has height a and the larger tube has height b.

    What happens to the pressure at the bottom of the larger tube as (1) a is varied, and (2) a is held constant but the diameter of the upper tube is increased?

    2. Relevant equations
    p_\text{gauge} = \rho g h
    Pascal's principle.
    3. The attempt at a solution

    (1) According to Pascal's principle, the larger tube will see a pressure increase of rho g a. This will increase the downward force at the bottom of the larger barrel, and that will be rho g a.

    (2) I don't think the diameter matters, but intuitively I can't see why! If b is the diameter of a straw (a few millimeters), the smaller tube will increase the pressure on the larger one just as much as a big tube on top. It is only height that seems to matter, then, and if I took a really tall straw and put it over a large vat of water, I would see a huge increase in force at the bottom of the vat. Confused....

  2. jcsd
  3. Sep 10, 2015 #2


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    ... and, your question is --- what?
  4. Sep 10, 2015 #3
    Is height really the only thing that matters here? Intuitively, this just doesn't make sense to me. How can a small straw of liquid (say 10 cm high) exert the same pressure at the surface of the barrel as, say, a huge vat that is just as high?
  5. Sep 10, 2015 #4
    Dive 2 m down to the bottom of a swimming pool. Dive the same distance below the surface of the ocean: do you feel more pressure?
  6. Sep 10, 2015 #5
    Well you do of course because ocean water is denser due to dissolved salts, but do you feel thousands of times more pressure?
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