Fluid Properties | Fluid Mechanics for Mechanical Engineering PDF Download

 Page 1


Properties of Fluids
Definition of Fluid
A fluid is a substance which deforms continuously when subjected to external 
shearing forces.
Characteristics of Fluid
1. It has no definite shape of its own, but conforms to the shape of the containing 
vessel.
2. Even a small amount of shear force exerted on a fluid will cause it to undergo 
a deformation which continues as long as the force continues to be applied.
3. It is interesting to note that a solid suffers strain when subjected to shear 
forces whereas a fluid suffers Rate of Strain i.e. it flows under similar 
circumstances.
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. 
Describing a fluid flow quantitatively makes it necessary to assume that flow 
variables (pressure, velocity etc.) and fluid properties vary continuously from one 
point to another. Mathematical descriptions of flow on this basis have proved to be reliable 
and treatment of fluid medium as a continuum has firmly become established. 
For example density at a point is normally defined as 
Here ? is the volume of the fluid element and m is the mass 
If ? is very large ? is affected by the inhomogeneities in the fluid medium. 
Considering another extreme if ? is very small, random movement of atoms (or 
molecules) would change their number at different times. In the continuum 
approximation point density is defined at the smallest magnitude of ? , before 
statistical fluctuations become significant. This is called continuum limit and is 
denoted by ? c. 
One of the factors considered important in determining the validity of continuum 
model is molecular density. It is the distance between the molecules which is 
Page 4 of 307
Page 2


Properties of Fluids
Definition of Fluid
A fluid is a substance which deforms continuously when subjected to external 
shearing forces.
Characteristics of Fluid
1. It has no definite shape of its own, but conforms to the shape of the containing 
vessel.
2. Even a small amount of shear force exerted on a fluid will cause it to undergo 
a deformation which continues as long as the force continues to be applied.
3. It is interesting to note that a solid suffers strain when subjected to shear 
forces whereas a fluid suffers Rate of Strain i.e. it flows under similar 
circumstances.
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. 
Describing a fluid flow quantitatively makes it necessary to assume that flow 
variables (pressure, velocity etc.) and fluid properties vary continuously from one 
point to another. Mathematical descriptions of flow on this basis have proved to be reliable 
and treatment of fluid medium as a continuum has firmly become established. 
For example density at a point is normally defined as 
Here ? is the volume of the fluid element and m is the mass 
If ? is very large ? is affected by the inhomogeneities in the fluid medium. 
Considering another extreme if ? is very small, random movement of atoms (or 
molecules) would change their number at different times. In the continuum 
approximation point density is defined at the smallest magnitude of ? , before 
statistical fluctuations become significant. This is called continuum limit and is 
denoted by ? c. 
One of the factors considered important in determining the validity of continuum 
model is molecular density. It is the distance between the molecules which is 
Page 4 of 307
characterised by mean free path ( ? ). It is calculated by finding statistical average 
distance the molecules travel between two successive collisions. If the mean free 
path is very small as compared with some characteristic length in the flow domain 
(i.e., the molecular density is very high) then the gas can be treated as a 
continuous medium. If the mean free path is large in comparison to some 
characteristic length, the gas cannot be considered continuous and it should be 
analysed by the molecular theory. 
A dimensionless parameter known as Knudsen number, K
n
 = ? / L, where ? is the 
mean free path and L is the characteristic length. It describes the degree of 
departure from continuum. 
Usually when K
n
> 0.01, the concept of continuum does not hold good. 
Beyond this critical range of Knudsen number, the flows are known as 
slip flow (0.01 < K
n
 < 0.1), 
transition flow (0.1 < K
n
 < 10) and 
free-molecule flow (K
n
 > 10).
However, for the flow regimes considered in this course, K n is always less than 0.01 
and it is usual to say that the fluid is a continuum. 
Other factor which checks the validity of continuum is the elapsed time between 
collisions. The time should be small enough so that the random statistical 
description of molecular activity holds good. 
In continuum approach, fluid properties such as density, viscosity, thermal 
conductivity, temperature, etc. can be expressed as continuous functions of space 
and time. 
Ideal and Real Fluids
1. Ideal Fluid
An ideal fluid is one which has 
no viscosity
no surface tension
and incompressible
2. Real Fluid
An Real fluid is one which has 
viscosity
surface tension
and compressible
Naturally available all fluids are real fluid.
Viscosity
Definition: Viscosity is the property of a fluid which determines its resistance to 
shearing stresses.
Cause of Viscosity: It is due to cohesion and molecular momentum exchange 
between fluid layers. 
Newton’s Law of Viscosity: It states that the shear stress (t) on a fluid element 
layer is directly proportional to the rate of shear strain.
The constant of proportionality is called the co-efficient of viscosity.
Page 3


Properties of Fluids
Definition of Fluid
A fluid is a substance which deforms continuously when subjected to external 
shearing forces.
Characteristics of Fluid
1. It has no definite shape of its own, but conforms to the shape of the containing 
vessel.
2. Even a small amount of shear force exerted on a fluid will cause it to undergo 
a deformation which continues as long as the force continues to be applied.
3. It is interesting to note that a solid suffers strain when subjected to shear 
forces whereas a fluid suffers Rate of Strain i.e. it flows under similar 
circumstances.
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. 
Describing a fluid flow quantitatively makes it necessary to assume that flow 
variables (pressure, velocity etc.) and fluid properties vary continuously from one 
point to another. Mathematical descriptions of flow on this basis have proved to be reliable 
and treatment of fluid medium as a continuum has firmly become established. 
For example density at a point is normally defined as 
Here ? is the volume of the fluid element and m is the mass 
If ? is very large ? is affected by the inhomogeneities in the fluid medium. 
Considering another extreme if ? is very small, random movement of atoms (or 
molecules) would change their number at different times. In the continuum 
approximation point density is defined at the smallest magnitude of ? , before 
statistical fluctuations become significant. This is called continuum limit and is 
denoted by ? c. 
One of the factors considered important in determining the validity of continuum 
model is molecular density. It is the distance between the molecules which is 
Page 4 of 307
characterised by mean free path ( ? ). It is calculated by finding statistical average 
distance the molecules travel between two successive collisions. If the mean free 
path is very small as compared with some characteristic length in the flow domain 
(i.e., the molecular density is very high) then the gas can be treated as a 
continuous medium. If the mean free path is large in comparison to some 
characteristic length, the gas cannot be considered continuous and it should be 
analysed by the molecular theory. 
A dimensionless parameter known as Knudsen number, K
n
 = ? / L, where ? is the 
mean free path and L is the characteristic length. It describes the degree of 
departure from continuum. 
Usually when K
n
> 0.01, the concept of continuum does not hold good. 
Beyond this critical range of Knudsen number, the flows are known as 
slip flow (0.01 < K
n
 < 0.1), 
transition flow (0.1 < K
n
 < 10) and 
free-molecule flow (K
n
 > 10).
However, for the flow regimes considered in this course, K n is always less than 0.01 
and it is usual to say that the fluid is a continuum. 
Other factor which checks the validity of continuum is the elapsed time between 
collisions. The time should be small enough so that the random statistical 
description of molecular activity holds good. 
In continuum approach, fluid properties such as density, viscosity, thermal 
conductivity, temperature, etc. can be expressed as continuous functions of space 
and time. 
Ideal and Real Fluids
1. Ideal Fluid
An ideal fluid is one which has 
no viscosity
no surface tension
and incompressible
2. Real Fluid
An Real fluid is one which has 
viscosity
surface tension
and compressible
Naturally available all fluids are real fluid.
Viscosity
Definition: Viscosity is the property of a fluid which determines its resistance to 
shearing stresses.
Cause of Viscosity: It is due to cohesion and molecular momentum exchange 
between fluid layers. 
Newton’s Law of Viscosity: It states that the shear stress (t) on a fluid element 
layer is directly proportional to the rate of shear strain.
The constant of proportionality is called the co-efficient of viscosity.
When two layers of fluid, at a distance ‘dy’ 
apart, move one over the other at different 
velocities, say u and u+du.
Velocity gradient = 
du
dy
According to Newton’s law   
du
dy
t 8
   
or        
=
du
dy
t µ
Velocity Variation near a solid 
boundary
Where 
µ
 = constant of proportionality and is known as co-efficient of Dynamic 
viscosity or only Viscosity
As 
du
dy
t
µ =
? ?
? ?
? ?
Thus viscosity may also be defined as the shear stress required 
producing unit rate of shear strain. 
Units of Viscosity
S.I. Units: Pa.s or N.s/m
2
C.G.S Unit of viscosity is Poise= dyne-sec/cm
2
One Poise= 0.1 Pa.s
1/100 Poise is called centipoises.
Dynamic viscosity of water at 20
o
C is approx= 1 cP
Kinematic Viscosity
It is the ratio between the dynamic viscosity and density of fluid and denoted by 
Mathematically 
dynamic viscosity
density
µ
?
?
= =
Units of Kinematic Viscosity
S.I units: m
2
/s
C.G.S units: stoke = cm
2
/sec
One stoke = 10
-4
 m
2
/s
Page 4


Properties of Fluids
Definition of Fluid
A fluid is a substance which deforms continuously when subjected to external 
shearing forces.
Characteristics of Fluid
1. It has no definite shape of its own, but conforms to the shape of the containing 
vessel.
2. Even a small amount of shear force exerted on a fluid will cause it to undergo 
a deformation which continues as long as the force continues to be applied.
3. It is interesting to note that a solid suffers strain when subjected to shear 
forces whereas a fluid suffers Rate of Strain i.e. it flows under similar 
circumstances.
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. 
Describing a fluid flow quantitatively makes it necessary to assume that flow 
variables (pressure, velocity etc.) and fluid properties vary continuously from one 
point to another. Mathematical descriptions of flow on this basis have proved to be reliable 
and treatment of fluid medium as a continuum has firmly become established. 
For example density at a point is normally defined as 
Here ? is the volume of the fluid element and m is the mass 
If ? is very large ? is affected by the inhomogeneities in the fluid medium. 
Considering another extreme if ? is very small, random movement of atoms (or 
molecules) would change their number at different times. In the continuum 
approximation point density is defined at the smallest magnitude of ? , before 
statistical fluctuations become significant. This is called continuum limit and is 
denoted by ? c. 
One of the factors considered important in determining the validity of continuum 
model is molecular density. It is the distance between the molecules which is 
Page 4 of 307
characterised by mean free path ( ? ). It is calculated by finding statistical average 
distance the molecules travel between two successive collisions. If the mean free 
path is very small as compared with some characteristic length in the flow domain 
(i.e., the molecular density is very high) then the gas can be treated as a 
continuous medium. If the mean free path is large in comparison to some 
characteristic length, the gas cannot be considered continuous and it should be 
analysed by the molecular theory. 
A dimensionless parameter known as Knudsen number, K
n
 = ? / L, where ? is the 
mean free path and L is the characteristic length. It describes the degree of 
departure from continuum. 
Usually when K
n
> 0.01, the concept of continuum does not hold good. 
Beyond this critical range of Knudsen number, the flows are known as 
slip flow (0.01 < K
n
 < 0.1), 
transition flow (0.1 < K
n
 < 10) and 
free-molecule flow (K
n
 > 10).
However, for the flow regimes considered in this course, K n is always less than 0.01 
and it is usual to say that the fluid is a continuum. 
Other factor which checks the validity of continuum is the elapsed time between 
collisions. The time should be small enough so that the random statistical 
description of molecular activity holds good. 
In continuum approach, fluid properties such as density, viscosity, thermal 
conductivity, temperature, etc. can be expressed as continuous functions of space 
and time. 
Ideal and Real Fluids
1. Ideal Fluid
An ideal fluid is one which has 
no viscosity
no surface tension
and incompressible
2. Real Fluid
An Real fluid is one which has 
viscosity
surface tension
and compressible
Naturally available all fluids are real fluid.
Viscosity
Definition: Viscosity is the property of a fluid which determines its resistance to 
shearing stresses.
Cause of Viscosity: It is due to cohesion and molecular momentum exchange 
between fluid layers. 
Newton’s Law of Viscosity: It states that the shear stress (t) on a fluid element 
layer is directly proportional to the rate of shear strain.
The constant of proportionality is called the co-efficient of viscosity.
When two layers of fluid, at a distance ‘dy’ 
apart, move one over the other at different 
velocities, say u and u+du.
Velocity gradient = 
du
dy
According to Newton’s law   
du
dy
t 8
   
or        
=
du
dy
t µ
Velocity Variation near a solid 
boundary
Where 
µ
 = constant of proportionality and is known as co-efficient of Dynamic 
viscosity or only Viscosity
As 
du
dy
t
µ =
? ?
? ?
? ?
Thus viscosity may also be defined as the shear stress required 
producing unit rate of shear strain. 
Units of Viscosity
S.I. Units: Pa.s or N.s/m
2
C.G.S Unit of viscosity is Poise= dyne-sec/cm
2
One Poise= 0.1 Pa.s
1/100 Poise is called centipoises.
Dynamic viscosity of water at 20
o
C is approx= 1 cP
Kinematic Viscosity
It is the ratio between the dynamic viscosity and density of fluid and denoted by 
Mathematically 
dynamic viscosity
density
µ
?
?
= =
Units of Kinematic Viscosity
S.I units: m
2
/s
C.G.S units: stoke = cm
2
/sec
One stoke = 10
-4
 m
2
/s
Thermal diffusivity and molecular diffusivity have same dimension, therefore, by 
analogy, the kinematic viscosity is also referred to as the momentum diffusivity of 
the fluid, i.e. the ability of the fluid to transport momentum.
Classification of Fluids
1. Newtonian Fluids 
These fluids follow Newton’s viscosity equation. 
For such fluids viscosity does not change with rate of deformation.
2. Non- Newtonian Fluids
These fluids does not follow Newton’s viscosity equation. 
Such fluids are relatively uncommon e.g. Printer ink, blood, mud, slurries, polymer 
solutions.
Non-Newtonian Fluid       (
dy
du
µ t ?
)
Purely Viscous Fluids Visco-elastic 
Fluids
Time - Independent Time - Dependent Visco-elastic 
Fluids
E
dy
du
a µ t + =
Example: Liquid-
solid 
combinations in 
pipe flow.
1. Pseudo plastic Fluids
1 ; <
?
?
?
?
?
?
?
?
= n
dy
du
n
µ t
Example: Blood, milk
2. Dilatant Fluids
1 ; >
?
?
?
?
?
?
?
?
= n
dy
du
n
µ t
Example: Butter
3. Bingham or Ideal 
Plastic Fluid
n
o
dy
du
?
?
?
?
?
?
?
?
+ = µ t t
Example: Water 
suspensions of clay and 
flash
1.Thixotropic Fluids
) (t f
dy
du
n
+
?
?
?
?
?
?
?
?
= µ t
                         f(t)is 
decreasing
Example: Printer ink; 
crude oil
2. Rheopectic Fluids
) (t f
dy
du
n
+
?
?
?
?
?
?
?
?
= µ t
                         f(t)is 
increasing 
Example: Rare liquid solid 
suspension
Page 5


Properties of Fluids
Definition of Fluid
A fluid is a substance which deforms continuously when subjected to external 
shearing forces.
Characteristics of Fluid
1. It has no definite shape of its own, but conforms to the shape of the containing 
vessel.
2. Even a small amount of shear force exerted on a fluid will cause it to undergo 
a deformation which continues as long as the force continues to be applied.
3. It is interesting to note that a solid suffers strain when subjected to shear 
forces whereas a fluid suffers Rate of Strain i.e. it flows under similar 
circumstances.
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. 
Describing a fluid flow quantitatively makes it necessary to assume that flow 
variables (pressure, velocity etc.) and fluid properties vary continuously from one 
point to another. Mathematical descriptions of flow on this basis have proved to be reliable 
and treatment of fluid medium as a continuum has firmly become established. 
For example density at a point is normally defined as 
Here ? is the volume of the fluid element and m is the mass 
If ? is very large ? is affected by the inhomogeneities in the fluid medium. 
Considering another extreme if ? is very small, random movement of atoms (or 
molecules) would change their number at different times. In the continuum 
approximation point density is defined at the smallest magnitude of ? , before 
statistical fluctuations become significant. This is called continuum limit and is 
denoted by ? c. 
One of the factors considered important in determining the validity of continuum 
model is molecular density. It is the distance between the molecules which is 
Page 4 of 307
characterised by mean free path ( ? ). It is calculated by finding statistical average 
distance the molecules travel between two successive collisions. If the mean free 
path is very small as compared with some characteristic length in the flow domain 
(i.e., the molecular density is very high) then the gas can be treated as a 
continuous medium. If the mean free path is large in comparison to some 
characteristic length, the gas cannot be considered continuous and it should be 
analysed by the molecular theory. 
A dimensionless parameter known as Knudsen number, K
n
 = ? / L, where ? is the 
mean free path and L is the characteristic length. It describes the degree of 
departure from continuum. 
Usually when K
n
> 0.01, the concept of continuum does not hold good. 
Beyond this critical range of Knudsen number, the flows are known as 
slip flow (0.01 < K
n
 < 0.1), 
transition flow (0.1 < K
n
 < 10) and 
free-molecule flow (K
n
 > 10).
However, for the flow regimes considered in this course, K n is always less than 0.01 
and it is usual to say that the fluid is a continuum. 
Other factor which checks the validity of continuum is the elapsed time between 
collisions. The time should be small enough so that the random statistical 
description of molecular activity holds good. 
In continuum approach, fluid properties such as density, viscosity, thermal 
conductivity, temperature, etc. can be expressed as continuous functions of space 
and time. 
Ideal and Real Fluids
1. Ideal Fluid
An ideal fluid is one which has 
no viscosity
no surface tension
and incompressible
2. Real Fluid
An Real fluid is one which has 
viscosity
surface tension
and compressible
Naturally available all fluids are real fluid.
Viscosity
Definition: Viscosity is the property of a fluid which determines its resistance to 
shearing stresses.
Cause of Viscosity: It is due to cohesion and molecular momentum exchange 
between fluid layers. 
Newton’s Law of Viscosity: It states that the shear stress (t) on a fluid element 
layer is directly proportional to the rate of shear strain.
The constant of proportionality is called the co-efficient of viscosity.
When two layers of fluid, at a distance ‘dy’ 
apart, move one over the other at different 
velocities, say u and u+du.
Velocity gradient = 
du
dy
According to Newton’s law   
du
dy
t 8
   
or        
=
du
dy
t µ
Velocity Variation near a solid 
boundary
Where 
µ
 = constant of proportionality and is known as co-efficient of Dynamic 
viscosity or only Viscosity
As 
du
dy
t
µ =
? ?
? ?
? ?
Thus viscosity may also be defined as the shear stress required 
producing unit rate of shear strain. 
Units of Viscosity
S.I. Units: Pa.s or N.s/m
2
C.G.S Unit of viscosity is Poise= dyne-sec/cm
2
One Poise= 0.1 Pa.s
1/100 Poise is called centipoises.
Dynamic viscosity of water at 20
o
C is approx= 1 cP
Kinematic Viscosity
It is the ratio between the dynamic viscosity and density of fluid and denoted by 
Mathematically 
dynamic viscosity
density
µ
?
?
= =
Units of Kinematic Viscosity
S.I units: m
2
/s
C.G.S units: stoke = cm
2
/sec
One stoke = 10
-4
 m
2
/s
Thermal diffusivity and molecular diffusivity have same dimension, therefore, by 
analogy, the kinematic viscosity is also referred to as the momentum diffusivity of 
the fluid, i.e. the ability of the fluid to transport momentum.
Classification of Fluids
1. Newtonian Fluids 
These fluids follow Newton’s viscosity equation. 
For such fluids viscosity does not change with rate of deformation.
2. Non- Newtonian Fluids
These fluids does not follow Newton’s viscosity equation. 
Such fluids are relatively uncommon e.g. Printer ink, blood, mud, slurries, polymer 
solutions.
Non-Newtonian Fluid       (
dy
du
µ t ?
)
Purely Viscous Fluids Visco-elastic 
Fluids
Time - Independent Time - Dependent Visco-elastic 
Fluids
E
dy
du
a µ t + =
Example: Liquid-
solid 
combinations in 
pipe flow.
1. Pseudo plastic Fluids
1 ; <
?
?
?
?
?
?
?
?
= n
dy
du
n
µ t
Example: Blood, milk
2. Dilatant Fluids
1 ; >
?
?
?
?
?
?
?
?
= n
dy
du
n
µ t
Example: Butter
3. Bingham or Ideal 
Plastic Fluid
n
o
dy
du
?
?
?
?
?
?
?
?
+ = µ t t
Example: Water 
suspensions of clay and 
flash
1.Thixotropic Fluids
) (t f
dy
du
n
+
?
?
?
?
?
?
?
?
= µ t
                         f(t)is 
decreasing
Example: Printer ink; 
crude oil
2. Rheopectic Fluids
) (t f
dy
du
n
+
?
?
?
?
?
?
?
?
= µ t
                         f(t)is 
increasing 
Example: Rare liquid solid 
suspension
Fig. Shear stress and deformation rate relationship of different fluids
Effect of Temperature on Viscosity
With increase in temperature 
Viscosity of liquids decrease
Viscosity of gasses increase
Note: 1. Temperature responses are neglected in case of Mercury.
2. The lowest viscosity is reached at the critical temperature.
Effect of Pressure on Viscosity
Pressure has very little effect on viscosity.
But if pressure increases intermolecular gap decreases then cohesion increases so 
viscosity would be increase.
Surface tension
Surface tension is due to cohesion between particles at the surface.
Capillarity action is due to both cohesion and adhesion.
Surface tension
The tensile force acting on the surface of a 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.