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Suppose there is a slanted capillary tube and a fluid rises in it. Why does the fluid rise to the same vertical height as when the tube is perfectly vertical?

If I'm right surface tension force balances the weight of the lifted fluid. But in the case of a slanted tube, more fluid will be lifted and thus weight also increases. So why will fluid rise to same height?

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  • $\begingroup$ If you put in the number , i.e. the mass of the fluid and the attraction of gravity versus the adhesion electromagnetic forces creating the capillary effect you will find that gravity is insignificant. you will need micron accuracy to see the difference $\endgroup$ – anna v Dec 3 '13 at 12:09
  • $\begingroup$ @annav wouldn't hurt to quote the numbers, since surf. tension depends heavily on the choice of fluid and tube materials :-) $\endgroup$ – Carl Witthoft Dec 3 '13 at 12:36
  • $\begingroup$ @CarlWitthoft Sorry, I would have answered if I had the numbers ready.(It is just a coincidence that I asked a similar question in a lecture today on nanotechnology created channels !) In any case no such choices are given in the question. $\endgroup$ – anna v Dec 3 '13 at 13:10
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The stretching of the air-liquid meniscus matches the pressure exerted by the liquid, not the mass of liquid in the tube.

Tubes

In a closed tube of water the pressure at the top of the tube is $P = P_0 - \rho g h$ where $h$ is the vertical distance (P_0 is atmospheric pressure), so in the diagram above $P_1 = P_2$. So if we replace the closed end of the tubes by the air-water meniscus the curvature of the meniscus will be the same. It doesn't matter that there is a greater weight of water in the slanted tube. That's why the vertical height of the capillary rise is the same.

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