Jurin’s Law:

The liquid in a capillary tube rises to a maximum height h from the outer level of the liquid, given by

\( \displaystyle{T=\frac{r(h+\frac{r}{3})\rho{g}}{2\cos\theta}} \) [Read In Detail]

where, \( r \) is the radius of the capillary tube, \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, \( \theta \) is angle of contact.

If the capillary tube is very fine, \( r \) is very very small and \( \frac{r}{3} \) can be neglected with respect to \( h \). In such a case,

\( \displaystyle{T=\frac{\rho{r}gh}{2\cos\theta}}\\or,\ \displaystyle{h=\frac{2T\cos\theta}{\rho{r}g}} \)

or, \( \displaystyle{rh=\frac{2T\cos\theta}{\rho{g}}} \)

For a given liquid \( rh=constant \), this means that the elevation of a liquid in a capillary tube is inversely proportional to the radius of the capillary tube. This is known as the Jurin’s law.