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Pascal's Law can be read anywhere online.

Now suppose I want to apply on earth taking into account the variation of pressure with depth. So I don't want to ignore the effect of gravity.

So I have colum like this, filled with a fluid, open at top, and due to gravity, pressure is continuously increasing with depth.

|        |
|        | --> P
|        |
|        |
|        |
|        |
|        | --> 2P
|        |
|        |
|        |
|        |
|        | --> 3P
|        |
|        |

The pressure let us say is incerasing as P, then 2P, then 3P with the depth.

Suppose I push a cylinder from the top and hence put an external additional pressure of 10P.

Wouldn't this external pessure of 10P be equally transmitted throughout the rod to increase the pressure at each point by 10P ?? Like this:

   |  |
  PISTON
|        |
|        | --> P + 10P = 11P
|        |
|        |
|        |
|        |
|        | --> 2P + 10P = 12P
|        |
|        |
|        |
|        |
|        | --> 3P + 10P = 13P
|        |
|        |

Or will the additional pressure of 10P also be variedly added to the pressure at each point like this??:

   |  |
  PISTON
|        |
|        | --> P + 5P (Let's say)
|        |
|        |
|        |
|        |
|        | --> 2P + 10P (Let's say)
|        |
|        |
|        |
|        |
|        | --> 3P + 15P (Let's say)
|        |
|        |

That is, will the extra pressure which is transmitted due to piston also vary?? Or will it remain constant ?? WHICH CASE IS TRUE ??

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The fact that $g$ appears explicitly in Pascal's law tells you the answer. Setting $g \rightarrow 0$ in a limiting procedure is identical to taking $\Delta h \rightarrow 0$ (or $\rho \rightarrow 0$).

So Pascal's law reduces in these (equivalent) limits as the rather trivial statement that $\Delta P =0 $.

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  • $\begingroup$ Oops my bad.... Sorry The question title should be: Isn't Pascal law valid even if we DONT ignore gravity ??? plz tell which case will be true...the first one or the second one ?? I think the first should be true, and if it is so.... Then pascals law holds even in presence of gravity... $\endgroup$ – AneesAhmed777 Feb 9 '15 at 10:31
  • $\begingroup$ Oh, well Pascal's law certainly does not ignore gravity--it's a crucial ingredient. Without gravity, Pascal's law reduces to a very trivial statement, as I said in my answer. $\endgroup$ – Surgical Commander Feb 9 '15 at 20:44
  • $\begingroup$ like i thought....obviously it does not ignore gravity.....sorry my stupid school textbooks and stupid colleagues and stupid teachers...they all think I'm misunderstanding the law because it is written in textbook that pascal law holds only in absence of gravity!! How do I convince them ??? ........... Plz link to some article where it is written in bold that pascal law holds true in gravity......only then i can convince them.... $\endgroup$ – AneesAhmed777 Feb 10 '15 at 15:00

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