Properties of Fluid
Fluid Properties
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Definition of fluid:
We can define a
fluid as a substance capable of flowing, so it can be gases or liquids.
So
when we apply some force, some shear force especially it will deform or it will
start to flow
Concept of continuum:
The
concept of continuum is a kind of idealization of the continuous description of
matter where the properties of the matter are considered as continuous
functions of space variables. Although any matter is composed of several
molecules, the concept of continuum assumes a continuous distribution of mass
within the matter or system with no empty space, instead of the actual
conglomeration of separate molecules.
Viscosity (μ):
It
is resistance to flow. This property of fluid is observed when fluid is in
motion.
Consider
a flow (Fig. 1) in which all fluid particles having layer 1 to 6 are moving in
the same direction in such a way that the fluid layers move parallel with
different velocities.
The
upper layer, which is moving faster, tries to draw the lower slowly moving
layer along with it by means of a force F along the direction of flow on
this layer. Similarly, the lower layer tries to retard the upper one, according
to Newton's third law, with an equal and opposite force F on it.
Hence,
the dragging effect of one layer on the other is result in a tangential force F
on the respective layers. If F acts over an area of contact A, then
the shear stress τ is defined as
τ = F/A
Newton stated that,
τ α Δu/
Δy
where,
Δy - distance of separation
of the two layers and Δu - difference in their velocities.
τ = μ
(Δu/ Δy)
Where, the constant of proportionality μ is
known as the coefficient of viscosity
or simply viscosity or Newton’s law of viscosity.
Types of fluid:
Basically there
are two types of fluids,
1. Newtonian
Fluid
2.
Non-Newtonian Fluid.
The fluid which obey
Newton’s law of viscosity that fluid known as Newtonian Fluid.
e.g. water, air,
mercury, etc.
The fluid which not obey Newton’s law of
viscosity that fluid known as Non-Newtonian
Fluid.
e.g.
polymer solution, blood, milk, etc.
=> Consider a fluid having a zero viscosity (μ = 0).
Such a fluid is called an ideal fluid and the
resulting motion is called as ideal or inviscoused flow.
In an ideal flow, there is no
existence of shear force because of vanishing viscosity.
τ = μ
(Δu/ Δy) = 0 since μ = 0
In practice every
fluid have some viscosity (μ
> 0) hence they are termed
as real fluid and their motion is
known as viscous flow. 
The non-Newtonian fluids are
further classified as pseudo-plastic,
dilatant and Bingham plastic.
If you plot graph between shear
stress τ
on Y axis and velocity gradient (du/dy) on X- axis, we can get two curves one
is for n less than one known as pseudo plastic fluid and with n greater than one
this is known as dilatant fluid.
Where n - flow
behavior index.
=>The causes of viscosity in a fluid are possibly attributed to
two factors:
(i) Intermolecular force of
cohesion.
(ii) Molecular momentum exchange.
(ii) Molecular momentum exchange.
Compressibility:
Compressibility of any substance is the measure of its change in
volume under the action of external forces.
Normal
compressive stress act on any fluid when it at rest is known as hydrostatic pressure p.
The degree of
compressibility of a substance is characterized by the bulk modulus of elasticity E defined as ratio of pressure difference
acting on fluid to the volumetric strain.
E = -Δp/
(ΔV/ V)
Where
ΔV and Δp are the changes in the volume and pressure respectively, and is the
original volume V. The negative sign (-sign) is included to make E positive,
since increase in pressure would decrease the volume i.e. for Δp>0 , ΔV<0
in volume.
For a given mass
of a substance, the change in its volume and density satisfies the relation
(ΔV/
V) = - (Δρ/ ρ)
E =
-Δp/ - (Δρ/ ρ)
E =
ρ *(Δp/Δρ)
E =
ρ *(dp/dρ)
Value of E is high for liquid
than the gases because density of liquid is more than gases. Hence liquid is
termed as incompressible fluid.
For gases
another characteristic parameter, known as compressibility
K, is usually defined, it is the reciprocal of E.
K = 1/E
K = (1/ρ)
*(dρ/dp)
K = - (1/V)
*(dV/dp)
A functional relationship between the
pressure, volume and temperature at any equilibrium state is known as thermodynamic equation for the gas
state.
For an ideal
gas, the thermodynamic equation of state is given by
p = ρRT
Where, T – Temperature
R - Characteristic gas constant
For air, the
value of R is 287 J/kg.
=>Distinction between an Incompressible and a
Compressible Flow.
We know that
E =
ρ *(dp/dρ)
dρ /
ρ = dp/E
Using Bernoulli's equation,
p +
(1/2) ρV2= constant
Where, (1/2) ρV2 = dp
= change in pressure =
Therefore,
dρ /
ρ = (1/2) * (ρV2/E)
If
Δρ/ρ is very small, the flow of gases can be treated as incompressible.
According to Laplace's equation,
the velocity of sound is given by,
Therefore,
dρ /
ρ = (1/2) * (V2/a2)
dρ /
ρ = (1/2) * Ma2
Where, Ma2
– Match number, defined as ratio of velocity
of flow to the acoustic velocity of flowing medium.
So, we can
conclude that the compressibility of gas in a flow can be neglected if Δρ/ρ is
considerably smaller than unity, i.e. (1/2) Ma2 < 1.
Surface
Tension:
The phenomenon
of surface tension observed due to the two kinds of intermolecular forces:
1)
Cohesion: The force of
attraction between the molecules of a liquid by virtue of which they are bound
to each other is known as the force of cohesion.
This
property of liquid is responsible for resisting tensile stress.
2)
Adhesion: The force of
attraction between unlike or different molecules is known as the force of
adhesion.
This property is
responsible for adhere two different liquids or adhere liquid and solid surface
to each other.
=>From (fig.
2) A and B subjected equal force of cohesion in all directions.
=>C
experiences a net force interior of the liquid.
=>D
experiences maximum net force inside of the liquid.
The magnitude of surface tension is
defined as the ratio of tensile force to the length.
The dimensional formula is F/L or MT-2.
It is usually expressed in N/m in SI units.
Surface tension decreases slightly with
increasing temperature. The surface tension of water in contact with air at
20°C is about 0.073 N/m.
Capillarity:
The tendency of a
liquid in a capillary tube or absorbent material to rise or fall as a result of
surface tension. 
Where,
h = rise or fall in capillary tube,
σ = liquid-air surface tension,
θ = angle of tangent at capillary,
ρ = density of liquid,
g = gravitational force,
D = Diameter of capillary tube.
=>For pure
water in contact with air in a clean glass tube, the capillary rise takes place
with θ = 0.
=>Mercury causes capillary
depression with an angle of contact of about 1300 in a clean glass
in contact with air.
Vapour
pressure:
All liquids have
a tendency to evaporate when exposed to a gaseous atmosphere. The vapour
molecules exert a partial pressure in the space above the liquid, known as
vapour pressure.
The rate of evaporation depends upon type
of liquid and its temperature.
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