Module 2. Static pressure of liquids

Lesson 4

COMPRESSIBLE AND NON COMPRESSIBLE FLUIDS, SURFACE TENSION AND CAPILLARITY

4.1   Compressible and Non Compressible Fluids

1.      Compressible fluids:  The fluids which undergoes a change in volume or density when subjected to external forces.

2.      Incompressible fluids: The fluid which does not show a change in volume or density when subjected to external forces.

Compressibility

 It is the property of the liquid or fluid due to which there will be a change in volume/density when the fluid is subjected to an external force and is represented by Bulk Modulus of Elasticity (k). Compressibility is the reciprocal of Bulk Modulus of Elasticity.

           

           

Ideal Fluids are incompressible.

Real Fluids are compressible.

4.1.1 Numericals

Q.1. Change in pressure for a liquid is 2 MN/m2. The volumetric strain induced in the liquid was 0.05. Determine the bulk modulus of elasticity for the liquid.

         

Q.2. A cylinder having 10 litre volume is completely filled with oil. When a pressure of 9.2 MN/m2 is applied the volume decreases by 500 ml. Find the bulk modulus of oil.

Pressure (P) = 9.2 MN/m2 = 9.2 × 106 N/m2

Change in volume = ∆v = 500 ml = 0.5 L

Q.3. Bulk modulus of water is k = 2.07 × 106 kN/m2. Determine the pressure required to compress 10 litre of water by 0.1 litre.

Bulk modules =

Change in volume v= 0.1 L

4.2 Surface Tension

The cohesive force of attraction between molecules is responsible for the phenomenon of surface tension. The molecules beneath the free liquid surface are surrounded by other molecules creating an equilibrium. The force of attraction (cohesion) acting on the molecules will be balanced but at the free liquid surface there are no molecules above the liquid surface, therefore a net force pulls the molecules in inward direction. This force causes the molecules at the surface to cohere (stick) more strongly with the molecules beneath them. Thus a surface film is formed which acts as an elastic or stretched membrane. (Fig. 4.1)

Surface tension depends on the following factors:

i)        Nature of the liquid.

ii)      Nature of Surroundings (gas, liquid or solid)

iii)    Kinetic Energy of molecules

iv)    Temperature.

Unit of Surface Tension: N/m

Surface tension is denoted by σ = Force per unit length having units N/m

With increase in temperature, the surface tension decreases.

Phenomena and examples of surface tension in daily life:

1.      Walking of insect on the surface of water

2.      Fully filled glass of water does not over flow immediately

3.      Rise of liquid in capillary

4.      Detergents are also called surfactant. It reduces the surface tension of water and water enters into cloth layer which enables proper cleaning

5.      Emulsion: It is a liquid-liquid dispersed phase. Oil separated from water due to surface tension

Collection of dust on the water surface

6.      Liquid drops take a spherical shape

4.2.1        Different cases for surface tension

(Fig. 4.2 :Water droplet and its sectional view)

Case 1: Water droplet

           

Surface tension force acting around the circumference =

Where, σ = Surface tension

Under equilibrium

Case 2: Soap bubble

           

Surface tension force acting around the circumference =

Where, σ = Surface tension

Under equilibrium

Case 3: Liquid Jet (Fig. 4.3: Sectional view of water jet)

Pressure force f = p. L. d 

Surface tension force acting around the circumference =

Under equilibrium

4.2.2 Capillarity

It is a phenomenon in which liquid in a glass tube capillary rises or falls from its original level due to the combined effect of cohesion and adhesion.(Fig. 4.4)

Let glass tube of diameter = d

   Density of liquid = ρ

Rise in liquid level = h

Angle of contact between water surface and glass = θ

Force in upward direction = σ.π.d.Cosθ                                                                                                                                                                                                               ………(i)

                                                                                                                                                                                                               ………(ii)

Equation (i) = (ii)

           

           

Note

a)      For laboratory purpose the diameter of the glass tube should be greater than 8 mm.

b)      For glass tube with length more than 12 cm; the effect of capillarity becomes negligible.

c)      Capillary rise occurs in the case of water. But in other case like in mercury there is capillary depression.

4.2.3 Non-wetting and wetting liquid

According to the surface wetting ability liquids can be classified as

Non-wetting liquid: Angle of contact θ > π/2

 e.g. Mercury with density 13600 kg/m3

Wetting liquid: Angle of contact θ < π /2

e.g. Water with density 1000 kg/m3  (Fig. 4.5)

Table 4.1 Condition for capillary rise and depression

Sl. No.

Condition

Capillary action

Type of meniscus formed

Angle of contact between liquid surface and glass

1

When adhesion is greater than cohesion

Rise in capillarity

Concave

 θ < π/2

2

When cohesion is greater than adhesion

Fall in capillarity

Convex

θ > π/2 (for mercury 130° - 150°)