# Jurin’s Law Derivation

## Jurin’s Law:

The ascent or descent of a liquid inside a capillary tube is inversely propositional to the radius of the tube.

From this law, it is conducted that the smaller the radius (r) of the tube, the higher the rise (h) of the liquid level inside the tube. But if the radius of the tube is large, i.e, if the capillarity of the tube isn’t maintained, then this law becomes erroneous.

If the angle of contact is less than 90°, then cosθ is positive and hence the value of h as indicated by equation(1) is also positive.

In this case, the liquid rises upwards in the capillary tube. On the other hand, if the angle of contact is more than 90°, then cosθ becomes negative and hence h will also be negative.

In this case, the liquid level falls downwards in the capillary tube. In the case of clean glass and pure water, the angle of contact θ=0°, so cosθ=1 and hence from equ(1)

h = 2T/rρg
or, T = (1/2)*rhρg

Note: Measuring the rise of water in a capillary tube, its surface tension can be determined from this equation.