2. FLUID
What is Fluid ?
A) Solid material consider as fluid
B) All Liquids are fluid
C) All gases are fluid
D) All liquid and gases are fluid
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3. A fluid is a substance which having the ability to flow or deform
continuously under the action of shear force.
shear force
θ1 θ2
Boundary
Free Surface
Fluid
Fluid Molecule
No Slip Condition
dθ
dt
=
Rate of
deformation
with respect to
Note : For static fluid
Shear
force is zero. 3
4. Difference between Solid & Fluid :
In case of solid deformation is constant with respect to time where as in case
of fluid the deformation is continuous with respect to time hence rate of
deformation is more important in case of fluid then deformation.
On removal of load solid will try to regain their original position but in case
of fluid they never try to regain their original position on removal of load.
Solid will show resistance to all types of load where as fluid will shows
resistance to only compressive load.
Hence all liquid and all gases are taken as fluid.
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5. FLUID PROPERTIES
Properties are certain measurable characteristics that can be
quantified, with the help of property we can identify fluid.
1. Density or Mass
density
3. Specific gravity
5. Viscosity
7. Capillarity
2. Specific weight or Weight density
4. Compressibility
6. Surface Tension
8. Vapour Pressure
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6. 1. Density or Mass density
Density basically represent the number of molecules of a fluid in a given
volume, so more number of molecules more is the mass and heavier is the fluid.
ρ
Volume (m3)
=
Mass (kg) ρ (Solid) > ρ (Liquid) > ρ (Gas)
ρ Water = 1000 kg/m3 (at 40C)
ρ Air = 1.2 kg/m3 (at 00C and 1 bar)
Note : Density will
increases with increase in
Pressure .
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Density is defined as the ratio of the mass of mass per unit volume and its SI
unit is (kg/m3).
Hence density can also be define as the representative of heaviness of the fluid.
7. 2. Specific weight or Weight density
It basically represent the force exerted by fluid due to gravity in a given volume.
Note : Density is an absolute quantity with respect to location
where as specific weight is a variable quantity with respect to
location.
w
Volume (m3)
=
Weight [ mass (kg) x gravity (m/s2) ]
= ρ*g (N/m3)
Weight of a fluid of a given volume is
W = Sp. Weight * Volume = ρ*g * v (N)
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Specific weight is defined as the weight of the fluid per unit volume and its SI
unit is (N/m3).
8. 3. Specific Gravity
Specific gravity is define as the ratio of the density of the fluid to the density of
standard fluid.
Standard fluid in case of liquid is taken as water where as in case of gases is
taken as air .
fs
ρ (Standard Fluid)
=
ρ (Fluid)
= Dimensionless
Specific gravity basically shows which fluid are heavier then water or air and
which fluid are lighter then water or air.
Example : s = 1 …………..For Water
s = 0.760……... Fluid is lighter then water
s = 13.6………..Fluid is heavier then water
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9. 4. Compressibility
If there is a change in volume or density of fluid with respect to pressure applied
such fluid called as compressible fluid.
With increase in pressure variation of volume of gas is large hence gases are
compressible.
Cylinder
Gas
molecules
Piston
pressur
e
9
Example:
10. 4. Compressibility
If there is a very small change in volume or density of fluid with respect to
pressure applied such fluid called as incompressible fluid.
Hence Small change in density or volume with respect to large pressure
applied can be neglected.
Cylinder
Liquid
molecules
Piston
pressur
e
At 1 Atm. Pressure = density of liquid is 998 kg/m3
& at 100 Atm. Pressure = density of liquid is 1003 kg/m3
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Example:
11. 4. Compressibility
All those fluid are said to be incompressible fluid whose density is constant with
respect to pressure applied.
Liquid are generally incompressible fluid where as gasses are generally
compressible.
Compressibility is define as the reciprocal of bulk modulus of elasticity.
Compressing a gas adiabatically is more difficult then compressing a gas
isothermally because while adiabatic compression, due to increase in
temperature randomness of molecules increases and hence it provide resistance
to compression.
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12. 5. Viscosity
Consider two layer of a fluid , a distance ‘dy’ apart, move one over the another
at a different velocity, say ‘u’ and ‘u+du’ as show in fig.1 :
y
u
du
dy
u
u+du Veloci
ty
profile
Fig.1: Velocity variation near a solid
boundary
The viscosity together with relative velocity
causes a shear stress acting between the fluid.
This shear stress is proportional to the rate of
change of velocity with respect ‘y’ which is
distance from boundary.
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Viscosity is define as the property of a fluid which offers resistance to the
movement of one layer of fluid over another adjacent layer of the fluid.
13. 5. Viscosity
Mathematically ,
τ
d
u
dy
α τ
d
u
dy
= μ
‘μ’ (called mu) is the constant of proportionality and is known as the co-
efficient of dynamic viscosity or only viscosity, and (du/dy) represents the rate
of shear deformation or velocity gradient.
The unit of dynamic viscosity in SI unit is Pascal-sec. and in CGS unit is poise
which is equal to (dyne*sec)/cm2
μ =
τ
du
dy
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14. 5. Viscosity
Kinematic Viscosity :
It is define as the ratio between the dynamic viscosity and density of fluid
which denoted by the Greek symbol (υ) ‘nu’.
Mathematically, υ
μ
ρ
=
14
Dynamic viscosity shows resistance to motion where as kinematic viscosity
shows resistance to molecular momentum transfer. (molecular collision in
case of gases)
The unit of kinematic viscosity in MKS and SI system is m2/s , While in
CGS unit is it is written as cm2/s , Kinematic viscosity also called as stoke
Thus, one stoke = cm2/s = 10-4 m2/s
15. 5. Viscosity
Variation of Viscosity with Temperature :
In case of liquid with increase in temperature of liquid viscosity decreases
because the main reason of viscosity is molecular bonding and with
increases in temperature molecular bonding brake down and viscosity
decreases.
Where as in case of gases the main reason of viscosity is the molecular
collision and with increase in temperature molecular collision increases
which act as resistance to flow hence viscosity increases.
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16. 5. Viscosity
Newton Law of Viscosity :
For a Newtonian fluid viscosity is constant with respect to deformation
and relation between shear stress and rate of deformation is linear.
τ
d
u
dy
α τ
d
u
dy
= μ
Mathematically ,
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It is state that the shear stress (τ) on a fluid element layer is directly
proportional to the rate of shear strain. The constant of proportionality is
called the coefficient of viscosity.
17. 5. Viscosity
The fluid which obey the newton law of viscosity are knows as Newtonian
fluid.
Example : Water, Air, petrol, Hg, etc.
Non-Newtonian fluids :
The fluids are the one whose viscosity is going to vary with rate of
deformation called non-Newtonian fluid and the study of Non-Newtonian
fluid is known as Rheology.
1. Dilatant Fluids
dilatant fluids also called as shear thickening fluid, are
liquids or solutions whose viscosity increases as stress is applies.
Example : Sugar in water solution, Rice solution.
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18. 5. Viscosity
Non-Newtonian fluid :
2. Pseudo-Plastic Fluids
Pseudo-Plastic fluids are also referred to as shear-thinning
fluids, The viscosity of these fluids will decrease with increasing shear rate.
Example : paints, Blood, etc.
3. Bingham-Plastic Fluids
A Bingham plastic is a visco-plastic material that behaves
a as a rigid body at low stresses but flows as a viscous fluid at high stress.
Example :Tooth pest gel, Sewage sludge etc.
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19. 5. Viscosity
Non-Newtonian fluid :
4. Rheopecty
Rheopecty or rheopexy is the rare property of some non-
Newtonian fluids to shows a increase in viscosity with respect to time.
5. Thixotropy
Thixotropy is the time dependent property of non-Newtonian
fluid in this viscosity is decrease with respect to time.
Note: A fluid which is incompressible and is having no viscosity is known
as an ideal fluid.
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20. 5. Viscosity
Classification of fluids With shear stress as a function of shear rate :
Shear Stress
Shear rate ( Velocity gradient)
Ideal Fluid
Ideal Solid Bingham-Plastic Fluid
Dilatant Fluid
Pseudo-Plastic Fluids
Newtonian fluids
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21. 6. Surface Tension
Cohesion
It is a intermolecular force of attraction between molecule of same nature
Example: water & water, Hg & Hg , etc.
Adhesion
It is a intermolecular force of attraction between molecule of Different nature.
Example: water & glass , Hg and glass , etc.
Note: Cohesion and Adhesion depends upon the nature of surface in contact.
Example:
1. Water in glass Shows adhesion more
2. Mercury in glass shows cohesion more
3. Water on plastic sheet will shows cohesion more
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22. 6. Surface Tension
Free SurfaceAir
Liquid
Liquid Molecule A
Liquid Molecule B
Balanced cohesive force
Unbalanced cohesive force
Boundary
Let us consider a molecule of liquid ‘A’ which is under the surface of a liquid,
due to the cohesive forces molecule ‘A’ is attracted in all direction equally by
surrounding molecules of liquid, thus resultant forces acting on the molecule
‘A’ is zero.
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23. 6. Surface Tension
Free SurfaceAir
Liquid
Liquid Molecule A
Liquid Molecule B
Balanced cohesive force
Unbalanced cohesive force
Boundary
Let us consider a molecule of liquid ‘B’ which is situated on the free surface of
liquid, due to cohesive force this liquid molecule is under the action of
downward force.
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24. 6. Surface Tension
There are large number of molecules on free surface and all the molecules are
under downward pull due to this there appears to be a membrane on surface of
liquid which can bear small load, this property known as Surface Tension.
Free SurfaceAir
Liquid
Liquid Molecule A
Liquid Molecule B
Balanced cohesive force
Unbalanced cohesive force
Boundary
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25. 6. Surface Tension
Surface tension is define as the tensile force acting on the surface of liquid in
contact with a gas or on the surface between two immiscible liquids such that
the contact surface behaves like a membrane under tension.
Surface tension is also given as
the force acting per length over
which surface tension acting.
Mathematically,
Surface
Tension
Surface tension force
=
Length over which
surface tension acting
(Perimeter of contact
surface)
Fig.2: Water striders can walk on
water because of the surface
tension of water
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26. 6. Surface Tension
Mathematically,
Note :
Liquid droplet take the shape of sphere due to surface tension because drop
tries to minimize its surface area and mathematically sphere has the
minimum surface area.
Detergent are used while washing cloth to reduce surface tension so that
dirt particles can come out.
σ
Fs
=
L
N
m
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27. 7. Capillarity
Capillarity is the define a phenomenon of rise or fall of liquid surface when
small diameter glass tube is inserted vertically in liquid relative to the adjacent
general level of liquid.
Capillary rise occurs due to adhesion.
Example: Water in glass tube.
Fig.3: Capillary Rise
h
Capillary tube
Water
θ
d
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The rise of liquid surface is known as
capillary rise as shown in figure no 3.
28. 7. Capillarity
If the capillary tube is dipped in mercury, the level of mercury in the tube will
be lower then the general level of the outside liquid as shown in figure No. 4.
.
Fig.4: Capillary fall
Capillary rise or fall (h) can be calculated by
following formula:
h
4σ cosθ
ρ*g*d
=
Where,
θ :Angle of contact between liquid & capillary
tube
d :Diameter of capillary tube
h
Capillary tube
Mercury
θ
d
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Capillary fall occurs due to cohesion.
29. 8. Vapour Pressure
A change from the liquid state to the gaseous state is knows as vaporization.
The vaporization ( which depends upon the pressure and temperature) occurs
because of continuous escaping of the molecules through the free surface.
Let us consider a closed vessel which is
partially filled with liquid ( Say water)
as shown in fig.
The molecules on the free surface of the
liquid are in highly excited state and by
taking energy from molecules beneath it,
this molecules evaporate.
Fig.5: closed vessel
Liquid
Air
250C
Evaporated
molecules
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30. 8. Vapour Pressure
The air above the free surface of liquid can absorb the vapour molecules up to
the certain limit known as saturation.
Once saturation is reached, the number of vapour molecules evaporated from
the free surface of liquid become equal to number of vapor molecules
condensed back to the liquid.
The pressure exerted by the liquid
molecules over the free surface of liquid
under saturation condition at given
temperature is known as saturation
vapour pressure or Vapour pressure.
Fig.6: closed vessel
Note : With increase in temperature vapour
pressure increases
Liquid
Saturated
Air
250C
Evaporated
molecules
Condensed
molecules
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31. 8. Vapour Pressure
Cavitation
If the pressure above the liquid surface is reduced by some means , the
boiling temperature will also reduce.
If the pressure is reduced to such an extent that it become equal to or less
than the vapour pressure, the boiling will start, thus a liquid may boil even
at ordinary temperature.
Note : 1.Highly volatile fluid for example petrol have higher vapour pressure.
2.Mercury (Hg) having least vapour pressure because it have strong.
“Cavitation is the phenomenon of formation of vapour bubbles of a
flowing liquid in a region where the liquid falls below the vapor pressure and
sudden collapsing of these vapour bubbles in a region of high pressure.”
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