# Capillary rise

Hello everyone, we have studied the concept of surface tension, angle of contact in previous articles. In this article we are going to discuss the importance of surface tension in explanation of cracking of rock, sag supply to the plant leaves, function of nib in ink pen and many more.

Capillary and capillary action is one of the most important effect of surface tension. So let’s discuss the capillary and capillary rise in detail

### Let’s discuss the concept.……………!

Capillary

A tube having a very small bore is called a capillary tube r capillary.

Action of capillarity:-

The rise or fall of a liquid inside a capillary tube is called capillarity.

If the capillary tube is inserted into a liquid which wets the glass, the liquid rises in the capillary to a certain height.

Consider capillary of radius ‘r’ is dipped vertically in liquid of density ρ . Let ‘h’ is the height of liquid that rises in capillary when dipped in liquid. If ‘T’ is the surface tension of the liquid, the force acts along a tangent to the liquid meniscus, making an angle ‘θ’ with the well of the capillary. The meniscus is concave as shown in fig. below. At point of contact the surface tension T acts tangentially to the surface, which is resolved into,

a) T cosθ- acting vertically upward

b) T sin θ- in horizontal direction.

The horizontal component T sin θ  is directed outwards due to all molecules along circumference, hence cancels each other.  The only component of force acting due to surface is then Tcosθ which is nothing but the total vertical component of force is acting over complete circumference is,

∴ Total upward force on liq. = 2πr (T cosθ)………………………(1)

This force is balanced by the weight of liquid column inside capillary tube. So net downward force is given by,

Total downward force on liq. = mg           …….……(2)

But Mass of liquid column, m= ρV

∴ m =ρ πr2 h

On substituting in equation (2)

∴ Total downward force on liq = ρπr2hg

∴ Total downward force on liq = ρπr2hg      ……………………(3)

For equilibrium of liquid column inside capillary

Total upward force = Total downward force

∴ 2πr (T cosθ) =  ρπr2hg

∴ 2 (T cosθ) =  ρ r h g Equation (4) gives the formula for the rise in liquid in capillary when it is dipped in liquid, equation (5) gives the formula for surface tension of liquid.

### Some important terms…………….!

1) Rise in capillary is inversely proportional to the radius of capillary,

∴ h α1/r                       or                       hr = constant

2) Rise in capillary is increases when soluble impurities are added to liquid and decreases when insoluble impurities are added in liquid.

### Lets solve the numerical given below…..!

Ex:1) Capillary of radius 2 mm is dipped vertically in paraffin of 890 kg/m3 and havng angle of contact with glass of . Find rise in liquid in capillary if the surface tension of paraffin is 0.025 N/m.

Solution:

Here, r = 2 mm = 2 × 10-3  m , ρ = 890 kg/m3  , T = 0.025 N/m, θ = 1020

We have, Updated: January 13, 2022 — 2:19 pm