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Capillary rise of liquid in a capillary

Water height in a capillary plotted against capillary diameter The height h of a liquid column is given by Jurin's law[31]

{\displaystyle h={{2\gamma \cos {\theta }} \over {\rho gr}},}h={{2 \gamma \cos{\theta}}\over{\rho g r}}, where {\displaystyle \scriptstyle \gamma }\scriptstyle \gamma 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 acceleration due to gravity (length/square of time[32]), 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, γ = 0.0728 N/m at 20 °C, ρ = 1000 kg/m3, and g = 9.81 m/s2. Because water spreads on clean glass, the effective equilibrium contact angle is approximately zero.[33] For these values, the height of the water column is

{\displaystyle h\approx {{1.48\times 10^{-5}\ {\mbox{m}}^{2}} \over r}.}{\displaystyle h\approx {{1.48\times 10^{-5}\ {\mbox{m}}^{2}} \over r}.} Thus for a 2 m (6.6 ft) radius glass tube in lab conditions given above, the water would rise an unnoticeable 0.007 mm (0.00028 in). However, for a 2 cm (0.79 in) radius tube, the water would rise 0.7 mm (0.028 in), and for a 0.2 mm (0.0079 in) radius tube, the water would rise 70 mm (2.8 in).