Question

What is capillarity ? Derive expression for the height to which a liquid rises in a capillary tube of radius r ?

Answer 1

capillarity
if a capillary tube is dipped in a liquid whose angle of contact is acute , thn the liquid raises though the tube which is knw as capillary rise or capillarity



Actually capillary tube is soo small
I have drawn in a big size so tht it is visible for u ..
hope u can understand my answer

Answer 2

Given:

A capillary tube of radius r

To derive:

An expression for the height to which a liquid rises

Solution:

The ability of a liquid to rise or depress inside a capillary tube due to the surface tension of the liquid. This is called capillarity.

Consider a capillary tube of radius r that is open at both ends dipped in a liquid of density d and surface tension T.

The lower end of the tube is in contact with water and its upper end with air. Let the liquid rise to a height h.

The weight of the liquid that rises in the tube = W = mg

Here, m is the mass of the liquid and g is the acceleration due to gravity.

The volume of this risen liquid = V = πr²h

We know that density = mass / volume

⇒ m = d X V

= dπr²h

Substituting the value of m in W,

W = dπr²hg

The surface tension acts tangentially to the surface of the meniscus. Lrt the vertical component of this force be Ty.

Ty = T cos∅ X 2πr

Here ∅ is the meniscus angle

This vertical component of the surface tension balances the downward weight.

⇒ Ty = W

or T cos∅ X 2πr = dπr²hg

or drhg = 2 T cos∅

or h = 2 T cos∅ / rdg