Properties of Fluid

1. HYDRAULICS – I
(BTCVC 303)

2. MODULE -I
FUNDAMENTAL CONCEPTS
Avinash D.Jakate
Civil Engineering Department
Government College of Engineering Yavatmal

3. CONTENT
Module 1
Fundamental Concepts (Lectures 06)
Definition of fluids, fluid properties-density, specific weight,
specific volume, specific gravity, viscosity, compressibility,
surface tension, capillarity, vapor pressure, types of fluids -
Newtonian and non-Newtonian fluid, continuum, fluid pressure
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4. Hydraulics is the branch of engineering science which deals with the
study of liquid which is rest or in motion. The word , Hydraulics is
evolved from Greek word ‘Hudour’ ,which means Water.
Fluid
• A fluid is a substance which deforms continuously when subjected
to external shear stress however smaller the shear stress may be .
The continuous deformation of fluid under the action of shear stress
causes a flow .Figure shows a shear stress applied at certain
location in a fluid ,the element O11’ which is initially at rest ,will
move to O22’, then to O33’ and so on.
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• It is the substance which is capable to flow like air, water.
• A substance having particles which readily change their relative
positions.
• A substance which deforms continuously under the action of shear
stress.
• If a fluid is at rest , NO SHEAR STRESSES will act on it.
• Both liquid and gases comes under the category of fluid.

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Hydraulics is classified into three categories
1. Hydrostatic – which deal with the behavior of fluid at rest.
2. Hydrokinematics - which deal with the study of fluid in motion,
without considering pressure force .
3. Hydrodynamics - which deal with the study of fluid in motion,
where pressure force is considered.

7. Importance of Hydraulics with respect to Irrigation and Environmental
Engineering
1. To measure the velocity of flow at a point and discharge in an open channel.
2. To calculate total pressure, centre of pressure acting on any fluid retaining
structure.
3. With the help of different principles of hydraulics ,we can deign water supply
distribution scheme.
4. To measure the pressure at any point with the help of pressure measuring
instruments.
5. More economical channel sections can be design.
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8. Types of fluids
1. Ideal Fluid – A fluid ,which is incompressible, having no viscosity, no
surface tension. Do not offer shear resistance when fluid is in motion. It is
imaginary fluid. However, air and water are treated as ideal fluids.
2. Real fluid - A fluid ,which is compressible, having viscosity, surface
tension. It is real fluid. All fluids in actual practice are real fluids.
3. Newtonian fluid – A real fluid which obeys Newton's law of viscosity.
Newtonian fluid have constant viscosity. Viscosity is independent of rate of
deformation. There will be a linear relationship between shear stress and
resulting rate of deformation. Ex: Air ,water Light oil and Gasoline.(line OG)
4. Non-Newtonian fluid – A real fluid which does not obeys Newton's law of
viscosity. The study of Non-Newtonian fluid is called as Rheology.
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Relationship Between Shear stress And Velocity Gradient is
Where,
= Minimum Yield stress to start deformation.
A = a constant depending upon the type of fluid and conditions
imposed on flow.
n = Power index.
Based on “n “ and “A” Non-Newtonian fluid ‘s are:
1. Dilatant Fluid
2. Pseudo plastic fluid
3. Bingham Plastic Fluid
4. Thixotropic fluid
5. Rheopectic fluid
n
y 






dy
du
A
y

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1.Dilatant Fluid (represented by OC): Also called as Shear thickening fluid
= 0 and n >1y
dy
du
dy
du
A
1







n

e.g: Butter, Sugar Solution, Suspension of Rice starch and sand
2. Pseudo plastic fluid (represented by OE): Also called as Shear thinning fluid
= 0 and n<1
e.g: Blood, Milk, Paper pulp, Polymeric solutions
y

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3.Bingham Plastic Fluid (represented by OPD):
n= 1
e.g.: Sewage sludge, drilling mud, tooth paste
4. Thixotropic fluid (represented by OPQ):
n <1
e.g.: Printer ink, Lipstic
5. Rheopectic fluid (represented by OPR):
They are some fluids which require a gradually increasing shear
stress to maintain a constant strain rate
e.g. : Gypsum
n
yield 






dy
du

 n
yield
dy
du
  

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Newton's law of viscosity:
It states that ,shear stress in a fluid layer is
directly proportional to velocity gradient.
Where,
= Shear stress
= Dynamic Viscosity
= Velocity gradient


dy
dv dy
dv
. 

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Note : The velocity distribution is linear only if the thickness of the oil or
liquid film between two plate is very less
Distance travelled in time dt by the fluid layers
At a distance ‘y’ from origin = u.dt
At a distance ‘(y + dy)’ from origin = (u+du).dt
dy
du.dt
)tan(d 

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For small angles , tan θ = θ
= Rate of shear strain
=Rate of angular deformation
=Strain Rate
=Shear Strain Rate
=Velocity gradient
Newton from his experiment proved that , “The shear force per unit are on
a surface is proportional to strain rate”.
dy
du.dt
d  
dt
d
dy
du
dt
d
A
F 

dt
d
 

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dy
du

dy
du
  …..Newton’s law of viscosity
= The Proportionality constant
= Coefficient of Viscosity
= dynamic Viscosity

dy
du

 

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Newtonian Fluid
•A fluid which obeys Newton's law of viscosity.
•Have certain constant viscosity.
•Many common fluids such as air, water, light oils , and gasoline are
Newtonian Fluids.
Non-Newtonian Fluid
•A fluid which does not obey Newton's law of viscosity.
•Shear stress is not linearly dependent upon the velocity gradient.
•Common examples are Human blood, lubricating oils, clay suspension
in water, butter etc . are Non- Newtonian Fluids.

17. Physical properties of fluid
1. Specific mass or mass density or Density (ρ):
It is mass per unit volume of fluid .Mass density of water i.e.
ρw = 1000 kg/m3
ρ =
Dimensional formula of ρ : ML-3
• As temperature increases mass density decreases.
• As pressure increases mass density increases.
• Mass density is independent of “g”. Hence it is constant everywhere for a given
volume.
Standard values for different fluids
Volume
Mass
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Matter Mass density (Kg/m3)
Air 1.2
Water 1000
Mercury 13600

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2. Specific weight or Unit weight or weight density ( ):
It is weight per unit volume of fluid .Weight density of water
i.e.
= 9.81 KN/m3 =9810N/m3
It is not absolute quantity ,varies from place to place as ’g’ changes from
place to place, if volume is constant ,specific weight of a body is more at
poles compared to that of a Equator
“g” at poles =9.83 m/s2
“g” at equator =9.78 m/s2

Matter Weight density
Air 11.77N/m3
Water 9.81 KN/m3
g
V
Mg
V
W
 
Volume
Weight


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M
V

Mass
Volume
Vs
3. Specific Volume (Vs):
It is the volume occupied by unit mass of liquid. It is the reciprocal
of mass density .
Its S.I unit is m3/kg.

1
Vs 
4. Specific Gravity or Relative Density (S):
The ratio of mass density or weight density of fluid to the mass
density or weight density of pure water at standard temperature and pressure
is called as specific Gravity or relative Density .It has no unit as it tis the ratio
of similar properties.
•Specific gravity of pure water =1
•Specific gravity of Mercury =13.6
•Specific gravity of Air = 0.0012
•Specific gravity of wood = 0.6
w
l





w
l
S

20. 5. Viscosity :
It is defines as the property of fluid by virtue of which the motion of
lower layer is opposed by lower layer.
•All fluid offer resistance to motion because of internal friction. Viscosity is
measure of internal fluid friction.
•The viscosity of liquid drops with temperature ,because rise in temperature
decreases cohesive force between molecules resulting in decreasing viscosity.
• The rate of flow of oil would be slower than that of water as the adhesive
property of oil will have lore resistance to sliding.
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•Consider a fluid flowing along a large plane surface .Let us consider two
layers of fluid moving one over the other at a distance ‘dy’ apart .
•The lower layer having the velocity v and upper layer (v+dv).
•upper layer (v+dv).have more velocity than lower layer and it will try to
move lower layer with the same velocity .But the lower layer moving with
low velocity opposes the upper layer.
•These thing cause the shear stress in the opposite directions. From the
experimental observations ,this shear stress is directly proportional to the
rate of change of velocity w.r.to distance y

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According to Newton’s law, the shear stress between two adjacent fluid
layers is directly proportional to velocity gradient.
Shear stress
Where,
= Shear stress in N/mm2
= Dynamic Viscosity or coefficient of Viscosity or Absolute Viscosity
in N-s/m2 or Pa-s.
V = Velocity in m/s.
y = Distance in m.
= Velocity gradien.t
dy
dv



dy
dv
dy
dv

 
dy
dv
. 

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a)Dynamic Viscosity( ):
It is defined as the shear stress required to produce unit rate of
shear strain. Its S.I unit is N-s/m2 and C.G.S unit is Poise.
Note : 1 N-s/m2 = 10 Poise ; 1 Poise = 1 dyne-S/m2
Water at 200c= 1.005x10-3 Pa.s, Air at 200c= 1.81x10-5 Pa.s
b). Kinematic Viscosity( ) :
It is ratio of dynamic viscosity to the mass density of liquid.
Its S.I unit is m2/s
Note : 1 m2/s =104 stokes ; 1 Stoke = 1cm2/s.
dy
dv

 


 


 

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Factors affecting Viscosity:
1.Effect of Temperature:
In Liquids viscosity is due to intermolecular cohesion.
As Temperature Cohesion and hence viscosity .
In gases ,As Temperature gases becomes more dynamic due
to which viscosity
2.Effect of Pressure
The dynamic viscosity of either a liquid or a gas is practically
independent of the pressure for the range that is ordinarilly encountered in
practice.

25. 6. Surface Tension( ) :
It is the property of liquid which enables it to resist tensile stress and
expressed in N/.m
It is due to cohesion between particles at the surface of liquid. The
surface energy per unit area of interface is called as Surface tension.
Dimensional Formula : MT-2
A “Tensiometer” and “ stalagmometer” are the experimental instruments used
to measure the surface tension of liquid
As Temperature increases , surface Tension decreases
Standard Values of surface tension at 200 C and 1 atmosphere
Water – air interface : 0.073 N/m
Mercury-air interface : 0.44 N/m
Soap Solution –air interface :0.025 N/m

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A
W


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7. Compressibility (β) and Bulk modulus of Elasticity(K):
Compressibility (β) is the inverse of bulk modulus
β =1 /K
Bulk modulus of Elasticity(K) is the ratio of change in
pressure to the volumetric strain. It’s S.I unit is N/mm2
Bulk modulus of elasticity(k) increases with increase in pressure
Cohesion:
It is the property of fluid by virtue of which its molecules
remain attracted to each other .
Adhesion:
It is the property of fluid by virtue of which its molecules of
liquid are attracted to another body.
V
dV
dP
K



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8. Capillarity :
A phenomenon of rise or fall of a liquid surface in a small tube
relative to the adjacent general level of liquid when tube is held vertically
in the liquid.
• Capillarity is due to both cohesion and adhesion.
• Capillarity is inversely proportional to diameter of tube, Thinner the tube
is, the greater the rise or fall of the liquid in tube .
• Capillarity is inversely proportional to density of liquid .Hence Lighter
the liquid greater capillary rise.
Where,
h = Capillary Height
σ = Surface Tension (N/m)
d = diameter of tube (m)
= Specific weight of liquid
θ = Angle of contact between liquid and boundary

d
h

 cos4


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Sr.No Property Expression Unit
1 Mass Density Kg/m3
2 Weight Density N/m3
3 Specific Volume m3/Kg
4 Specific Gravity or
Relative Density
No Unit
5 Dynamic Viscosity Pa.s
6 Kinematic Viscosity m2/s
7 Surface Tension N/m
8 Bulk Modulus Pa
V
M

g
V
Mg
V
W
 
Volume
Weight

1
Vs 
w
l





w
l
S
dy
dv

 


 
A
W

V
dV
dP
K



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Fluid Continuum Concept:
“ The continuous sequence in which adjacent elements are not perceptibly different from each
other, but the extremes are quit distinct”
•A fluid is assumed to be continuum.
•A continuous and homogeneous medium is called as continuum.
•Any matter is composed of several molecules which may be widely
spaced apart, especially in the gas phase.
•The density of fluid is thus a point function . This method of considering
fluid as a continuous mass is stated as continuum principle
•To describe the degree of departure from continuum , a non – dimensional
number is known as Knudsen Number (Kn) is used.
flowoflengthsticCharacteri
PathFreeMean
nK 

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•Fluid can be treated as continuous when Kn<1%
•If Kn >1% the concept of continuum does not hold good.
Example :
Liquids, gases in compressed state will satisfy the continuum concept
Low dense gases and vacuum flow do not satisfy.

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References:
1. Dr. R.K.Bansal, A Text Book of Fluid Mechanics and Hydraulic
Machines .
2. Dr.P.N.Modi & S.M.Seth, Hydraulics & Fluid Mechanics .
3. K.Subramanya, Fluid Mechanics and Hydraulic Machines .