We were discussing the basic definition and significance of Kinematic viscosity, Dynamic viscosity, various properties of fluid, type of fluids, Newton’s law of viscosity, Compressibility and bulk modulus in our previous posts.

We will discuss here the basic concept of capillarity, capillary rise and capillary depression with the help of this post. Simultaneously, we will also find out the expression for capillary rise and capillary depression.

### Capillarity

Capillarity is basically defined as the phenomenon of rise or fall of liquid surface in small tube with respect to the adjacent general level of liquid when tube will be held vertically in the liquid.

Phenomenon of rise of liquid surface in small tube with respect to the adjacent general level of liquid, when tube will be held vertically in the liquid, will be termed as capillary rise.

Phenomenon of fall of liquid surface in small tube with respect to the adjacent general level of liquid, when tube will be held vertically in the liquid, will be termed as capillary fall or capillary depression.

Unit of capillary rise or capillary depression will be mm or cm.

### Let us find out the expression for capillary rise

Let us consider one tank of liquid i.e. water and tank is filled with water. Let us consider that one glass tube, opened at its both ends, of diameter d is held vertically in the liquid as displayed in following figure.
Once the glass tube will be held vertically in the water, shape of the water in glass tube will be concave upward as displayed in above figure. In order to secure the condition of equilibrium, water will rise in the glass tube above the outside surface of water or above the level of water in tank.

Let us consider the following terms required for securing the expression for capillary rise.
h = Height of water in glass tube above the level of water in tank
σ = Surface tension of liquid i.e. surface tension of water
θ = Angle of contact between glass tube and liquid (Water)
ρ = Mass density of the liquid i.e. density of the water, we have considered here water
ρ g = Specific weight of the liquid (water)

#### Let us consider the condition of equilibrium

Weight of the liquid of height h in glass tube = Force due to surface tension at the liquid surface in the tube
Angle of contact between clean glass tube and Water will be approximately equivalent to zero i.e. θ = 0. Therefore Cos θ, in above expression, will be taken as unity.

### Let us find out the expression for capillary fall or depression

Let us consider one tank of liquid and tank is filled with Mercury. Let us consider that one glass tube, opened at its both ends, of diameter d is held vertically in the liquid (Mercury) as displayed in following figure.
When glass tube will be held vertically in the mercury, in order to secure the condition of equilibrium, Mercury will go down in the glass tube below the outside surface of mercury or below the level of mercury in tank.

Let us consider the following terms required for securing the expression for capillary depression.
h = Height of mercury in glass tube below the level of mercury in tank
σ = Surface tension of liquid i.e. surface tension of mercury
θ = Angle of contact between glass tube and liquid (mercury)
ρ = Mass density of the liquid i.e. density of the mercury, we have considered here mercury
ρ g = Specific weight of the liquid (mercury)

#### Let us consider the condition of equilibrium

There will be two forces acting on mercury in the glass tube i.e. Force due to surface tension acting in downward direction and Hydrostatic force acting in upward direction.

Force due to surface tension acting in downward direction = Hydrostatic force acting in upward direction
Angle of contact between clean glass tube and mercury will be approximately equivalent to 128 degree i.e. θ = 1280.

### Note:

As we can see from the expression of capillary rise and capillary depression, we can say that capillary rise and capillary depression will be directly proportional with the surface tension of liquid and it will be indirectly proportional with the specific weight of the liquid and glass tube diameter.

So we have seen here the basic concept of capillarity and we have also derived here the expression for capillary rise and capillary depression.

Now, we will go ahead and will start a new topic i.e. Vapour pressure and cavitation in our next post.

Do you have any suggestions? Please write in comment box.

### Reference:

Fluid mechanics by R. K. Bansal
1. 