NPTEL – Mechanical – Principle of Fluid Dynamics
Module1 : Lecture 1
BASIC CONCEPTS AND PROPERTIES OF FLUIDS
BASIC CONCEPTS
• Mechanics is the oldest physical science that deals with both stationery and
moving boundaries under the influence of forces. The branch of the mechanics
that deals with bodies at rest is called statics while the branch that deals with
bodies in motion is called dynamics.
• Fluid Mechanics is the science that deals with behavior of fluids at rest (fluid
statics) or in motion (fluid dynamics) and the interaction of fluids with solids or
other fluids at the boundaries.
• A substance in liquid / gas phase is referred as ‘fluid’. Distinction between a solid
& a fluid is made on the basis of substance’s ability to resist an applied shear
(tangential) stress that tends to change its shape. A solid can resist an applied
shear by deforming its shape whereas a fluid deforms continuously under the
influence of shear stress, no matter how small is its shape. In solids, stress is
proportional to strain, but in fluids, stress is proportional to ‘strain rate.’
Fig. 1.1.1: Illustration of solid and fluid deformation.
Referring to Fig. 1.1.1, the shear modulus of solid (S ) and coefficient of
viscosity ( µ ) for fluid can defined in the following manner;
=S
Shear stress
=
(=F A)
; µ
Shear stress
=
( F A) (1.1.1)
Shear strain ( ∆x h ) Shear strain rate ( ∆u h )
Here, the shear force ( F ) is acting on the certain cross-sectional area ( A ) , h is
the height of the solid block / height between two adjacent layer of the fluid
element, ∆x is the elongation of the solid block and ∆u is the velocity gradient
between two adjacent layers of the fluid.
Joint initiative of IITs and IISc – Funded by MHRD Page 1 of 18
,NPTEL – Mechanical – Principle of Fluid Dynamics
• Although liquids and gases share some common characteristics, they have many
distinctive characteristics on their own. It is easy to compress a gas whereas
liquids are incompressible. A given mass of the liquid occupies a fixed volume,
irrespective of the size and shape of the container. A gas has no fixed volume and
will expand continuously unless restrained by the containing vessel. For liquids a
free surface is formed in the volume of the container is greater than that of the
liquid. A gas will completely fill any vessel in which it is placed and therefore,
does not have a free surface.
Dimension and Unit
A dimension is the measure by which a physical variable is expressed quantitatively
and the unit is a particular way of attaching a number to the quantities of dimension.
All the properties of fluid are assigned with certain unit and dimension. Some basic
dimensions such as mass (M), length (L), time (T) and temperature (θ) are selected as
Primary/Fundamental dimensions/unit. While others such as velocity, volume is
expressed in terms of primary dimensions and is called as secondary/derived
dimensions/unit. In this particular course, SI (Standard International) system of units
and dimension will be followed to express the properties of fluid.
Fluid as Continuum
Fluids are aggregations of molecules; widely spaced for a gas and closely spaced for
liquids. Distance between the molecules is very large compared to the molecular
diameter. The number of molecules involved is immense and the separation between
them is normally negligible. Under these conditions, fluid can be treated as continuum
and the properties at any point can be treated as bulk behavior of the fluids.
For the continuum model to be valid, the smallest sample of matter of practical
interest must contain a large number of molecules so that meaningful averages can be
calculated. In the case of air at sea-level conditions, a volume of 10-9mm3 contains
3×107 molecules. In engineering sense, this volume is quite small, so the continuum
hypothesis is valid.
In certain cases, such as, very-high-altitude flight, the molecular spacing becomes
so large that a small volume contains only few molecules and the continuum model
fails. For all situations in these lectures, the continuum model will be valid.
Joint initiative of IITs and IISc – Funded by MHRD Page 2 of 18
,NPTEL – Mechanical – Principle of Fluid Dynamics
Properties of Fluid
Any characteristic of a system is called property. It may either be intensive (mass
independent) or extensive (that depends on size of system). The state of a system is
described by its properties. The number of properties required to fix the state of the
system is given by state postulates. Most common properties of the fluid are:
1. Pressure ( p ) : It is the normal force exerted by a fluid per unit area. More details
will be available in the subsequent section (Lecture 02). In SI system the unit and
dimension of pressure can be written as, N/m2 and M L-1 T -2 , respectively.
2. Density: The density of a substance is the quantity of matter contained in unit
volume of the substance. It is expressed in three different ways; mass density
mass
ρ = , specific weight ( ρ g ) and relative density/specific gravity
volume
ρ
SG = . The units and dimensions are given as,
ρ water
For mass density; Dimension: M L−3 Unit: kg/m3
For specific weight; Dimension: M L-2 T -2 Unit: N/m3
The standard values for density of water and air are given as 1000kg/m3 and 1.2
kg/m3, respectively. Many a times the reciprocal of mass density is called as specific
volume ( v ) .
3. Temperature (T ) : It is the measure of hotness and coldness of a system. In
thermodynamic sense, it is the measure of internal energy of a system. Many a times,
the temperature is expressed in centigrade scale (°C) where the freezing and boiling
point of water is taken as 0°C and 100°C, respectively. In SI system, the temperature
is expressed in terms of absolute value in Kelvin scale (K = °C+ 273).
Joint initiative of IITs and IISc – Funded by MHRD Page 3 of 18
, NPTEL – Mechanical – Principle of Fluid Dynamics
4. Viscosity ( µ ) : When two solid bodies in contact, move relative to each other, a
friction force develops at the contact surface in the direction opposite to motion. The
situation is similar when a fluid moves relative to a solid or when two fluids move
relative to each other. The property that represents the internal resistance of a fluid to
motion (i.e. fluidity) is called as viscosity. The fluids for which the rate of deformation
is proportional to the shear stress are called Newtonian fluids and the linear
relationship for a one-dimensional system is shown in Fig. 1.1.2. The shear stress (τ )
is then expressed as,
du
τ =µ (1.1.2)
dy
du
where, is the shear strain rate and µ is the dynamic (or absolute) viscosity of the
dy
fluid.
The dynamic viscosity has the dimension M L-1T -1 and the unit of kg/m.s (or,
N.s/m2 or Pa.s) . A common unit of dynamic viscosity is poise which is equivalent to
0.1 Pa.s. Many a times, the ratio of dynamic viscosity to density appears frequently
µ
and this ratio is given by the name kinematic viscosity ν = . It has got the
ρ
dimension of L2 T -1 and unit of stoke (1 stoke = 0.0001 m2/s). Typical values of
kinematic viscosity of air and water at atmospheric temperature are 1.46 x 10-5 m2/s
and 1.14 x 10-6 m2/s, respectively.
Fig. 1.1.2: Variation of shear stress with rate of deformation.
Joint initiative of IITs and IISc – Funded by MHRD Page 4 of 18
Module1 : Lecture 1
BASIC CONCEPTS AND PROPERTIES OF FLUIDS
BASIC CONCEPTS
• Mechanics is the oldest physical science that deals with both stationery and
moving boundaries under the influence of forces. The branch of the mechanics
that deals with bodies at rest is called statics while the branch that deals with
bodies in motion is called dynamics.
• Fluid Mechanics is the science that deals with behavior of fluids at rest (fluid
statics) or in motion (fluid dynamics) and the interaction of fluids with solids or
other fluids at the boundaries.
• A substance in liquid / gas phase is referred as ‘fluid’. Distinction between a solid
& a fluid is made on the basis of substance’s ability to resist an applied shear
(tangential) stress that tends to change its shape. A solid can resist an applied
shear by deforming its shape whereas a fluid deforms continuously under the
influence of shear stress, no matter how small is its shape. In solids, stress is
proportional to strain, but in fluids, stress is proportional to ‘strain rate.’
Fig. 1.1.1: Illustration of solid and fluid deformation.
Referring to Fig. 1.1.1, the shear modulus of solid (S ) and coefficient of
viscosity ( µ ) for fluid can defined in the following manner;
=S
Shear stress
=
(=F A)
; µ
Shear stress
=
( F A) (1.1.1)
Shear strain ( ∆x h ) Shear strain rate ( ∆u h )
Here, the shear force ( F ) is acting on the certain cross-sectional area ( A ) , h is
the height of the solid block / height between two adjacent layer of the fluid
element, ∆x is the elongation of the solid block and ∆u is the velocity gradient
between two adjacent layers of the fluid.
Joint initiative of IITs and IISc – Funded by MHRD Page 1 of 18
,NPTEL – Mechanical – Principle of Fluid Dynamics
• Although liquids and gases share some common characteristics, they have many
distinctive characteristics on their own. It is easy to compress a gas whereas
liquids are incompressible. A given mass of the liquid occupies a fixed volume,
irrespective of the size and shape of the container. A gas has no fixed volume and
will expand continuously unless restrained by the containing vessel. For liquids a
free surface is formed in the volume of the container is greater than that of the
liquid. A gas will completely fill any vessel in which it is placed and therefore,
does not have a free surface.
Dimension and Unit
A dimension is the measure by which a physical variable is expressed quantitatively
and the unit is a particular way of attaching a number to the quantities of dimension.
All the properties of fluid are assigned with certain unit and dimension. Some basic
dimensions such as mass (M), length (L), time (T) and temperature (θ) are selected as
Primary/Fundamental dimensions/unit. While others such as velocity, volume is
expressed in terms of primary dimensions and is called as secondary/derived
dimensions/unit. In this particular course, SI (Standard International) system of units
and dimension will be followed to express the properties of fluid.
Fluid as Continuum
Fluids are aggregations of molecules; widely spaced for a gas and closely spaced for
liquids. Distance between the molecules is very large compared to the molecular
diameter. The number of molecules involved is immense and the separation between
them is normally negligible. Under these conditions, fluid can be treated as continuum
and the properties at any point can be treated as bulk behavior of the fluids.
For the continuum model to be valid, the smallest sample of matter of practical
interest must contain a large number of molecules so that meaningful averages can be
calculated. In the case of air at sea-level conditions, a volume of 10-9mm3 contains
3×107 molecules. In engineering sense, this volume is quite small, so the continuum
hypothesis is valid.
In certain cases, such as, very-high-altitude flight, the molecular spacing becomes
so large that a small volume contains only few molecules and the continuum model
fails. For all situations in these lectures, the continuum model will be valid.
Joint initiative of IITs and IISc – Funded by MHRD Page 2 of 18
,NPTEL – Mechanical – Principle of Fluid Dynamics
Properties of Fluid
Any characteristic of a system is called property. It may either be intensive (mass
independent) or extensive (that depends on size of system). The state of a system is
described by its properties. The number of properties required to fix the state of the
system is given by state postulates. Most common properties of the fluid are:
1. Pressure ( p ) : It is the normal force exerted by a fluid per unit area. More details
will be available in the subsequent section (Lecture 02). In SI system the unit and
dimension of pressure can be written as, N/m2 and M L-1 T -2 , respectively.
2. Density: The density of a substance is the quantity of matter contained in unit
volume of the substance. It is expressed in three different ways; mass density
mass
ρ = , specific weight ( ρ g ) and relative density/specific gravity
volume
ρ
SG = . The units and dimensions are given as,
ρ water
For mass density; Dimension: M L−3 Unit: kg/m3
For specific weight; Dimension: M L-2 T -2 Unit: N/m3
The standard values for density of water and air are given as 1000kg/m3 and 1.2
kg/m3, respectively. Many a times the reciprocal of mass density is called as specific
volume ( v ) .
3. Temperature (T ) : It is the measure of hotness and coldness of a system. In
thermodynamic sense, it is the measure of internal energy of a system. Many a times,
the temperature is expressed in centigrade scale (°C) where the freezing and boiling
point of water is taken as 0°C and 100°C, respectively. In SI system, the temperature
is expressed in terms of absolute value in Kelvin scale (K = °C+ 273).
Joint initiative of IITs and IISc – Funded by MHRD Page 3 of 18
, NPTEL – Mechanical – Principle of Fluid Dynamics
4. Viscosity ( µ ) : When two solid bodies in contact, move relative to each other, a
friction force develops at the contact surface in the direction opposite to motion. The
situation is similar when a fluid moves relative to a solid or when two fluids move
relative to each other. The property that represents the internal resistance of a fluid to
motion (i.e. fluidity) is called as viscosity. The fluids for which the rate of deformation
is proportional to the shear stress are called Newtonian fluids and the linear
relationship for a one-dimensional system is shown in Fig. 1.1.2. The shear stress (τ )
is then expressed as,
du
τ =µ (1.1.2)
dy
du
where, is the shear strain rate and µ is the dynamic (or absolute) viscosity of the
dy
fluid.
The dynamic viscosity has the dimension M L-1T -1 and the unit of kg/m.s (or,
N.s/m2 or Pa.s) . A common unit of dynamic viscosity is poise which is equivalent to
0.1 Pa.s. Many a times, the ratio of dynamic viscosity to density appears frequently
µ
and this ratio is given by the name kinematic viscosity ν = . It has got the
ρ
dimension of L2 T -1 and unit of stoke (1 stoke = 0.0001 m2/s). Typical values of
kinematic viscosity of air and water at atmospheric temperature are 1.46 x 10-5 m2/s
and 1.14 x 10-6 m2/s, respectively.
Fig. 1.1.2: Variation of shear stress with rate of deformation.
Joint initiative of IITs and IISc – Funded by MHRD Page 4 of 18
