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20.2.3: Capillary Rise

  • Page ID
    8529
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    When the lower end of a narrow capillary tube is immersed in a liquid, the liquid inside the tube rises a little above the level of the liquid outside. If is then very simple to calculate how far the liquid rises in terms of the surface tension, the angle of contact and the inside radius of the tube. See Figure XX.5.

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    The upward force due to surface tension is \( 2 \pi a \gamma \cos \theta \) where \(a\) is the inside radius of the tube, and, if we neglect the very small mass of the liquid in the meniscus (the curved surface at the top of the liquid column), the weight of the liquid column is \( \pi a^2 h \rho g \), and therefore

    \[ h = \frac{2 \gamma \cos \theta }{\rho g a }. \tag{20.2.6}\label{eq:20.2.6} \]

    Of course if \( \theta \) is obtuse (as with mercury in contact with glass), \(h\) will be negative, and the level of the mercury in the tube will be below the outside level.


    This page titled 20.2.3: Capillary Rise is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.