Question

Derive an expression for the height to which the liquid rises in capillarity tube of radius 'r'.

Answer 1

Answer:

h = 2 T cos Ф / r ρ g

Explanation:

Let the radius of the meniscus is R and radius of the capillary tube is r. The angle of constant is Ф , surface tension is T , density of the liquid is ρ and the liquid rises to the height .

Let us considered two points A and B are same level.

By pascal's law :

P_A = P_B

P_A  = P_C + ρ h g

The point C is  on the curved meniscus which has P_A a and P_B as two pressure on its both sides i.e. concave and convex side :

= > P_A - P_C = 2 T / R = 2 T / r / cos Ф

2 T / r / cos Ф = ρ h g

2 T cos Ф = r ρ h g

h = 2 T cos Ф / r ρ g

Therefore , height of liquid rise in capillary tube is 2 T cos Ф / r ρ g .