Editing Capillary action (section)

== Height of a meniscus ==
=== Capillary rise of liquid in a capillary ===
[[File:2014.06.17 Water height capillary.jpg|thumb|Water height in a capillary plotted against capillary diameter]]

The height ''h'' of a liquid column is given by [[Jurin's law]]<ref name="Bachelor">[[George Batchelor|G.K. Batchelor]], 'An Introduction To Fluid Dynamics', Cambridge University Press (1967) {{ISBN|0-521-66396-2}},</ref>
:<math>h={{2 \gamma \cos{\theta}}\over{\rho g r}},</math>
where <math>\scriptstyle \gamma </math> is the liquid-air [[surface tension]] (force/unit length), ''θ'' is the [[contact angle]], ''ρ'' is the [[density]] of liquid (mass/volume), ''g'' is the local [[gravitational acceleration|acceleration due to gravity]] (length/square of time<ref>Hsai-Yang Fang, john L. Daniels, Introductory Geotechnical Engineering: An Environmental Perspective</ref>), and ''r'' is the [[radius]] of tube.

As ''r'' is in the denominator, the thinner the space in which the liquid can travel, the further up it goes. Likewise, lighter liquid and lower gravity increase the height of the column.

For a water-filled glass tube in air at standard laboratory conditions, {{nowrap|''γ'' {{=}} 0.0728 N/m}} at 20{{nbsp}}°C, <!--
It is not possible to have a contact angle of "zero". It would be nice if this equation were to reflect a real world example to help those trying to understand they physics of capillary action.
--> {{nowrap|''ρ'' {{=}} 1000 kg/m<sup>3</sup>}}, and {{nowrap|''g'' {{=}} 9.81&nbsp;m/s<sup>2</sup>}}. Because water [[Wetting|spreads]] on clean glass, the effective equilibrium contact angle is approximately zero.{{fact|date=November 2024}} For these values, the height of the water column is
:<math>h\approx {{1.48 \times 10^{-5} \ \mbox{m}^2}\over r}.</math>

Thus for a {{convert|2|m|ft|abbr=on}} radius glass tube in lab conditions given above, the water would rise an unnoticeable {{convert|0.007|mm|in|abbr=on}}. However, for a {{convert|2|cm|in|abbr=on}} radius tube, the water would rise {{convert|0.7|mm|in|abbr=on}}, and for a {{convert|0.2|mm|in|abbr=on}} radius tube, the water would rise {{convert|70|mm|in|abbr=on}}.

=== Capillary rise of liquid between two glass plates ===
The product of layer thickness (''d'') and elevation height (''h'') is constant (''d''·''h''&nbsp;=&nbsp;constant), the two quantities are [[Proportionality (mathematics)#Inverse proportionality|inversely proportional]]. The surface of the liquid between the planes is [[hyperbola]].
<gallery caption="Water between two glass plates" widths="130px" mode="packed">
file:Kapilláris emelkedés 1.jpg
file:Kapilláris emelkedés 2.jpg
file:Kapilláris emelkedés 3.jpg
file:Kapilláris emelkedés 4.jpg
file:Kapilláris emelkedés 5.jpg
file:Kapilláris emelkedés 6.jpg
</gallery>