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°) |