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Pascal's Principle

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Homework Statement


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?

Homework Equations


[tex]
p_\text{gauge} = \rho g h
[/tex]
Pascal's principle.

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....

 

Answers and Replies

  • #2
Bystander
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and that will be rho g a.
only height that seems to matter
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....
... and, your question is --- what?
 
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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?
 
  • #4
pbuk
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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?
 
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pbuk
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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?
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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