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Consider the figure given below. enter image description here

Here I'm gonna talk about capillarity. The liquid inside the beaker as well as the column is water. As water has a tendency to rise in the capillary as shown, doesn't it violate Pascal's law.

At equilibrium when water has risen in the tube, pressure at point A as well as the pressure at water surface which is open to atmosphere will be $1$ $atm$. In turn pressure at point B will be $1$ $atm$ as it is at the same level above the ground as water in beaker ( Pascal's law ). Which means that $P_a-P_b$ is zero but according to Pascal's law it should have been $h\rho g$.

What's wrong then.

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    $\begingroup$ Pressure at Point A(just inside liquid) is less than a point just above it. The discontinuity is due to the phenomenon of surface tension due to which the pressure across the meniscus is different.(Pressure suffers discontinuity at the meniscus) $\endgroup$ – Prasanna Aug 26 '18 at 16:27
  • $\begingroup$ Again, asking "Is this well-established law incorrect?" appeals to me as a drastically bad question. It's much more reasonable to ask how a certain law can be applied to the given situation. Can you edit the title? $\endgroup$ – user191954 Sep 2 '18 at 6:10
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As stated in the comments, the pressure at B is (approximately) equal to atmospheric pressure, so Pascal's law holds. The pressure in the tube above B is lower than atmospheric ($p_a=p_b-\rho gh$). The difference in pressure between the liquid and the atmosphere at A is compensated by the force of surface tension at the meniscus.

When you insert a thin tube into a beaker of water, the water will rise up the tube until the weight of water above the point B equals the force exerted by the meniscus. This is why the water rises higher in a thinner tube, because a greater height is required to achieve the same balancing volume/weight. You can find more details on the Wikipedia page for capillary action.

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    $\begingroup$ Going a bit beyond this, it is perfectly possible for the pressure to be negative, giving a liquid under tension - and this goes on regularly in trees if they are tall enough. $\endgroup$ – Emilio Pisanty Aug 26 '18 at 18:31
  • $\begingroup$ @EmilioPisanty I assume you mean negative gauge pressure, not absolute? Surely below the vapor pressure, the water would vaporize/flash? $\endgroup$ – Time4Tea Aug 26 '18 at 21:24
  • $\begingroup$ See the video. I mean absolute pressure. $\endgroup$ – Emilio Pisanty Aug 26 '18 at 21:36
  • $\begingroup$ @EmilioPisanty wow. Mind --> blown. Great video, that's really fascinating! Thanks :-) $\endgroup$ – Time4Tea Aug 26 '18 at 21:46

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