Question

What is the phenomenon of capillary derive an expression for rise of liquid in a capillary tube given example of capillary of our life

Answer 1

The derivation can be thought of as this:

Let,

Radius of Capillary be r

Density of the liquid ρ

Height of the liquid be h

Surface Tension of Liquid be S=T

Contact angle θ

Weight of liquid inside capillary = Volume * Density * g

$= \pi{r}^{2} hpg$


Which is the downward force, and the force that is balancing this is the force due to Surface tension.

Now, Surface tension is defined as the Force acting on a line which is on the surface. In this case the surface tension is acting on the circumference.

Hence, total force upwards: component of Surface Tension upwards * length of the line it acts on

Tcosθ(2πr)

The sinθθ components gets cancelled as it is radially outward throughout the circumference.

Equating the forces we get:

$= \pi{r}^{2} hpg$
=Tcosθ(2πr)

⟹h=2Tcosθ/rρg

Note: In cases of some liquids the θ is very close to 0 degrees and hence the cosθ term can be taken as 1.