Question

A thin capillary of inner radius r1 and outer radius r2(Inner tube is solid) is dipped in water

To how much height will water raise in the tube

Answer 1

Capillary action is a phenomenon where the adhesive force on the walls of the tube dominates or is much greater the cohesive force of the liquid molecules. The height to which water will rise due to capillary action depends on surface tension.

The upward force acting on the circumference of the water on outer tube is

$F=T(2\pi r_2)$

The upward force acting on the circumference of the water on inner tube is

$F=T(2\pi r_1)$

The height to which water rises depends upon the weight of the water which is being lifted due to the surface tension,

$T(2\pi r_2)+T(2\pi r_1)=\rho g(h\pi (r_2^2- r_1^2))$

So, height of water raised is,

$h=\frac{2T(r_1+r_2)}{\rho g(r_2^2-r_1^2)}$

$h=\frac{2T}{\rho g(r_2-r_1)}$