Hello, there everybody. In this video course
on fluid mechanics the main objectives are
introduce fluid mechanics and establish its
relevant in civil engineering develop the
fundamental principles demonstrates how these
are used in engineering, especially in civil
engineering field. This video course consist
about forty lectures presenting the concepts
theory and applications.
The important topics covered in this course
include the fundamental concepts of fluid
flow, fluid statics, kinematics of fluid flow,
dynamics of fluid flow, laminar and turbulent
flows
Pipe flow systems, Dimensional analysis, navier
stoke equations and applications and boundary
layer theory and applications.
So in these forty lectures, all this topics
will be covered with various examples with
theories and fundamental principles. The important
references used in this course include the
fundamentals of fluid mechanics by Bruce R
Munson and others, the fluid mechanics with
engineering applications. Daugherthy and others,
fluid mechanics the Douglas and others, fluid
mechanics by Granger, fluid mechanics by streeter
and V.L.Wylie and mechanics of fluid by shames.
In this introductory lecture today, we will
discuss mainly the fundamental concepts and
fundamental properties and fundamental definitions
of fluid mechanics.
So the main objectives in this lecture are
to discuss the nature of fluids to introduce
fluid properties; discuss the flow characteristics;
discuss the flow visualization techniques
and illustrate the foundations of fluid flow
analysis.
So, all of you know the importance of fluid
mechanics it is the most important subject
in all science including physics, chemistry,
biology and mathematics.
And all branches of engineering involving
civil engineering, mechanical engineering,
chemical, metallurgy and aerospace and all
this science branches and engineering branches
will be studying fluid mechanics in one way
or another way and its related theories and
applications.
So, first we will discuss what fluid is and
then what are the difference between fluids
and solids and how the fluid is behaving and
what are the fundamental properties of fluids.
So what is a fluid, we can define a fluid
as a substance capable of flowing, so it can
be gases or liquids, so here you can see a
glass of water.
So when we apply some force, some shear force
especially it will deform or it will start
to flow like you can see in this glass of
water or here you can see bottle of water
when we apply some shear stress or some shear
force it will start to deform are it will
start to flow.
So, this fluid is the most vital for all forms
of life as you know we will be using fluids
as water or liquids we will be drink using
for drinking purpose it will be used for say
all types of life activities including bathing,
taking bath whether drinking water or irrigation
purpose or navigation purpose or recreation
purpose for all purposes fluid say in liquid
form of water is used or in the form of gases
the air which we are breathing or all other
aspects of life is required this fluids either
in liquid form or gases form.
So, as I mentioned fluid always deforms continuously
when subjected to a shear stress whether it
is gas or liquid. So, fluid mechanics is mainly
the study of what is happening when some forces
applied on a fluid where it is at rest or
it is emotion.
So fluid mechanics can be mainly divided in
to statics and dynamics. So, statics will
be discussing what is happening, the fluids
or liquids especially in the condition of
the static that means which is not moving
say for example if we consider the water store
in a reservoir or in tank, so it is static
it is not moving.
So, that branch of fluid mechanics study is
called statics and if we consider flowing
water say for example in a river flow is concerned
over the pipe flow is concerned it is dynamics
of fluids are the fluid is moving and hence
a study is called dynamics. So, in all this
we will be analyzing the fluid behavior based
on various fundamental principles.
So, the fundamental principles using mechanics
such as consideration of masks, consideration
of momentum, consideration of energy and a
loss of thermodynamics. All this fundamental
principles are very much used in fluid mechanics
also. So, let us see what is the major difference
between fluids and solids? Here, in this figure.
In this slide you can see a fluid element,
so when we are applying shear stress it is
deforming, say an angle theta like this it
deforms and it undergoes strain theta due
to the shear stress and if you consider solids
and solid discontents say here you can see
a small ball.
So here even if you applied some shear stress
it will not deform to certain level that means
and it reaches its elastic limit it can sustain
the shear stress and it will not deform. So
as you can see here in this slide, so then
a shear stress is applied on a solid element
it will not deform to certain extent and say
when it reaches the elastic limit it is starting
to deform as in this figure.
What are the major differences between say
fluids including liquids and gases and solids?
So in fluids we deal with continuous streams
of fluid without begin or end. So for example
if we consider the watering this bottle, so
you can see it can continuous from one end
to another so that we have to analyze by using
the continuant concept. But as far as store
is concerned, mainly we will be using say
include the elements when we are applying
a force like this a point force is applied
for load is applied here.
So what is happening particular, say include
the elements in solids so that is the major
difference between solid and fluids and you
can see that in say in fluids the molecules
are usually place or usually spaced so that
it is tatting to flow by just applying some
shear force.
But as far as, so it is concerned the molecules
are densely packed so that the deformation
takes place only after certain limit say elastic
limit and as far as full disk concerns intermolecular
forces are smaller than for solid that is
why the fluid is trying to flow by applying
a small shear stress.
But as far as the solid is concerned, here
is large intermolecular cohesive forces and
hence you have to apply large shear stress
large force to make it some deformation and
as far as fluid is concerned fluid deforms
continuously when acted on by shearing forces
but solid will not the deform continuously.
So these are the major difference differences
between the solids and fluids. So, even though
we are using the fundamental principles of
mechanics in fluid mechanics, so this differences
we have to consider in the development of
all theories and when we are applying this
theories we have to take here all this differences
between the solids and fluids since we will
using most of the time the fundamental principles
developed in mechanics.
Now we discuss the fundamental definitions
in fluid mechanics. So, first we will discuss
what we say system. So as you can see in the
slide a system is predetermined identifiable
mass of fluid say here you can see a cylinder
and there is a piston and what is existing
the fluid liquid or gases are existing in
this system.
Say for example, here if you consider a bottle
of water so the system what is existing the
volume existing in this say one liter of water
including here in this case water and air
so this is the system so system approach is
very important in fluid mechanics since fluid
is always trying to deform with respect to
shear force or shear stress and trying to
flow.
So generally all the analysis will be for
a particular system that means the particular
say volume in a piston as shown in this slide
or are what is shown in this bottle of water
say that means with in this space which is
predefined space what is happening in between
that is will be generally discussing. So this
is called a system approach in fluid mechanics
then another important definition is the control
volume.
Say control volume as you can see in this
slide a control volume is a finite region
in space and has definite volume. So here
you can see a pipe so here between section
1 and section 2. So, the fluid existing that
volume that is control volume, so that we
are considering so what is happening in this
is the major analysis which will do, so this
is the control volume approach used in fluid
mechanics. So say here if you consider a pipe
like this so when the pipe flow is there between
one sections to another, what is happening
so that is the control volume approach.
So now as in mechanics and all branches of
science and engineering in fluid mechanics
also the fundamental quantities like length,
the dimension of which is L and unit is m
and other dimensions like mass the dimension
is M, unit is kilogram and a time say in unit
in second and force unit is Newton and temperature
unit is degree centigrade in the system international
units.
So these are the fundamental quantities used
in fluid mechanics and based up on this fundamental
quantities we will be deriving the secondary
dimensions say for velocity or acceleration
or force or other say other type of quantities
like viscosity and say the acceleration and
all this quantities will be derived based
upon the fundamental quantities of mass, length,
time and the temperature unit degree centigrade.
So generally when we derive this fundamental
quantity we will be using continuum concept.
Since the fluid is say as I mention the flow
is continuous are the molecules are very much
say we detect the continuum approach, so all
the fluid behavior is based up on the continuum
concepts and theories are derived base upon
that and as far as coordinate system is concerned
generally in all this lectures we will be
using Cartesian or cylindrical and intrinsic
coordinate system and then say as I mention
the other units will be derived based up on
the secondary dimensions will be derived based
up on the primary units and in fluid mechanics
we will be using two kinds of approaches or
two kinds of description.
First one is called lagrangian description,
so in the lagrangian description we discuss
the history of the particles exactly, that
means say we study the path of fluid particles
of fixed identity so for example if you consider
a flow say from one section to another we
will be tracking some of the particles and
then what will be happening to that particles
from time to time.
So that is the approach called lagrangian
approach. So, in this approach say the velocity
in xyz direction u can be express a dx by
dt, v can be expresses as dy by dt and w can
be expressed as dz by dt. So similarly the
acceleration can be expressed as ax in x direction
ax is equal to du by dt or that is equal to
d square x by dt square and similarly in y
and z directions. So here in this velocity
and acceleration expressions we can see that
it is mainly what is happening with respect
to time that is what will be analyzing.
So this concept is rarely used in fluid mechanics
due to the various complexities so here you
can see the fluid is moving continuously say
one section to another section so to track
certain particles under then what is happening
with respect to time that kind of analysis
is very difficult in fluid mechanics, but
this lagrangian concept or lagrangian description
is mainly used in solid mechanics. Second
kind of description is called the eulerian
description.
So here what we are doing is we will be analyzing
what is happening between two sections at
a given spatial locations in the flow field
what is happening say for example if we consider
a fluid flow in a bottle like this what is
happening for the pipe flow what will be happening
one section so particular section with respect
to xyz dimensions will be considering and
then what is happening for various fluid particles
at the particular section with respect to
time.
So that the acceleration can be written as
a is equal to the total derivative dv by dt.
So, ax is the acceleration x direction can
be written as du by dt or that is equal to
del u by del t plus u into del u by del x
plus v into del u by del y plus w into del
u by del z, so this concept is very much used
in fluid mechanics.
Since this has got number of advantages since
fluid is moving continuously so in a pipe
flow in a open channel flow so if you consider
a particular section and then what is happening
with respect to space and time what is happening
so that kind of analysis is what will be doing
in this eulerian description and that is very
much used in fluid mechanics.
Now, at the beginning we are discussed, say
a fluid is getting deformed with respect to
shearing forces.
So, shearing forces are very important fluid
mechanics, so when a fluid is in motion shear
stresses are developed if the particles of
the fluid move relative to one another. So
since fluid is moving so you can see that
say with layer there would be shearing stresses
between the fluid say if you consider a section
say between the layers there will be the shearing
forces shear stress will be there.
So the adjacent particles have different velocities
so for example if you consider water flow
in the pipe is consisting of more pipes like
this say the flow is considered say in a pipe
flow so at the pipe wall the velocity will
be zero in this say this solid the pipe say
it is not moving. So that the velocity will
be zero at the pipe wall and then it will
be increasing as we move to watch the centre
of the pipe.
So here in this slide you can see that.
Say here in a pipe flow the water is flow
from left to right. So here since this shearing
force effect say or the nonstick condition
so at the pipe wall here the velocity zero
and the other end also the velocity zero and
you can see the at the center line the velocity
is maximum and you can see there will be a
parabolic profile like this as far as pipe
flow is concerned..
But if you consider say in a uniform flow
like this say if there is no solid wall or
if do not consider the effect of the solid
wall then you can see as in this slide the
velocity is equal in magnitude. So that the
velocity profile is like this slide and that
is called the uniform flow, so some times
in open channel flow we consider this kind
of uniform flow and now we will discuss some
of the important fluid properties, as I mentioned
mass is one of the primary quantity which
is one of the most important properties of
fluid and then another important property
called density.
So density it is the mass per unit volume
and it is expressed as kilogram per meter
cube and another important unit is called
the specific weight which is the weight per
unit volume and that is generally expressed
as gamma is equal to row into g, where row
is the density, g is the acceleration due
to gravity and its unit is Newton per meter
cube. Another important property which will
be using called is specific gravity and it
is the ratio of density of fluid to density
of water and then another property is the
specific volume, it is the reciprocal of the
density and its unit is meter cube per kilogram.
Another important property is called the pressure
the pressure is the normal force per unit
area exerted on a plane surface. So if you
consider say a plain surface like this when
we are applying normal force the force per
unit area is the pressure and its unit is
Newton per meter square and expressed as Pascal.
This pressure can be expressed say like absolute
pressure when we are measuring with respect
to certain edge for local atmosphere pressure
reference is put then we can express as gage
pressure absolute pressure and also vacuum
pressure as differentiated in this slide.
And then another important property is the
bulk modulus of velocity expressed as K, it
is the measure of compressibility of liquids
and unit is same as of pressure. So especially
we are dealing with gases so the compressibility
is very important and also the compressible
fluid compressible liquids this by modulus
of velocity is very important.
The bulk modulus is the change in volume of
a substance as the pressure on it is changed.
Generally these expressions with respect to
this solids and also with respect to liquids
also we can express and another important
fluid property is the viscosity of liquids.
So this property of fluid by virtue of which
offers resistance to shear so this viscosity
has been observed by famous scientist Isaac
Newton and he was answered the cohesion rate
of transfer of molecular momentum are the
predominant cause of viscosity and he was
derived the Newton’s law of viscosity. So
here you can see that if you consider water
so it has got one type of viscosity and if
you consider say other kinds of viscous liquid
say for example here have some honey.
So if you just try to power this honey on
a plate like this you can see that since it
is highly viscous the movement itself is very
slow and then that of shear stress is there
between the layers. So that is the difference
between say viscous fluid and say when the
viscosity is varying just like in a water
and honey.
So Newton with after studying this property,
he derived the fundamentality equation of
Newton law of viscosity which can be expressed
as or he observe that the shear stress is
proportionally to the shear strain the du
by dy and he derived the equation tow is equal
to mu in to du by dy where mu is the coefficient
of viscosity. So here the shear stress is
proportional to the shear strain.
And when he expressed tow is equal to mu into
du by dy tow is equal to mu theta where mu
is the coefficient of viscosity, so it was
already seen here the viscosity coefficient
with respect to honey or with respect to water,
the viscosity is changing and then the fluid
property is also will be changing.
So Newton’s observe say if the change in
shear stress with respect to the shear strain
is linear then that kind of fluid is called
as Newtonian fluid so fluids for which shear
stress is directly proportional to the rate
of shearing strain are designated as Newtonian
fluids and in the case fluid for which the
shearing stress is not linearly related to
the rate of shearing strain are designated
as non Newtonian fluids.
So according to the viscosity, Newton’s
classified mainly the fluids into Newtonian
fluid and non Newtonian fluids. So now in
this slide you can see.
A fluid element like this, so now a shear
stress are shear force is applied here applied
so here we are considering a fluid element
of say delta x size delta x delta y and delta
z and shear force is applied for f in this
direction and the top and a bottom in the
other direction and now if you study with
respect to the shear force the shear strain
we would be considering phi here. So the shear
force is acted on a fluid element.
Now, shear stress can be written as tow is
equal to shears force divided by area A and
deformation due to shear stress is measured
by the size of the angle phi know as the shear
strain.
So if we consider solid, phi is constant for
a fixed shear stress but in fluid phi increases
as the shear stress is applied means the fluid
is flowing. So since the fluid is flowing
this phi increasing and this depends up on
whether it will the variation depends up on
the type of fluid. So if the particle at a
point E in the previous slide moves under
the shear stress to point E and it takes time
t to get there it has moved the distance x.
So we can express shear strain phi is equal
to x by y and write of shear strain can be
written as phi by t which is equal to u by
y and the velocity of particle at E is equal
to x by t is equal to u so that finally we
can write shear stress is equal to constant
multiplied by the shear strain u by y. So
here u by y is the change in velocity with
y so that we can finally here the Newton’s
law of viscosity is expressed as tow is equal
to mu in to du by dy.
The shear stress unit is say here M L to the
power minus 1 T to the power minus 2 and the
unit of coefficient of dynamic viscosity M
L to the power minus 1 T to the power minus
1 and it is expressed as say in poise in system
intention unit and another quantity equal
to kinematic viscosity when we divide the
coefficient of dynamic viscosity mu by the
density row, that quantity is called kinematic
viscosity or mu is equal to kinematic viscosity
mu by row and its unit is L square T to the
power minus 1. So for various liquids like
water, air, the coefficient dynamic viscosity
varies and the shear stress also varies.
Now, with respect to this variation of shearing
stress with the rate of shearing strain we
can classify the fluids in to various categories
so here I show a figure so this figure you
can see here.
The shear stress is plotted here on the x
axis and the right of shear shearing strain
is plotted on the y axis. So in this plot
if the shear stress is varying linearly with
respect to your shearing strain then we get
a straight line like this that there is linear
variation. So, that kind of fluid is called
Newtonian fluid say for example water is Newtonian
fluid and if this variation is not linear.
So here this line can see the various is not
linear so those kind of fluid is called non
Newtonian fluid and then if say the strain,
the right of shearing starts after application
of the efficient quantity of shear stress
like here is up to this point there is no
deformation.
So that kind of fluid is called ideal plastic
and that is after reaching the particular
point it is the variation is linear and then
if the variation is non linear like this then
it is called thixotropic fluid and then again
if the strain is say increasing like this
in this figure say this kind of fluid is called
dilatant fluid and if say the fluid is such
that the shear stress there is not shear strain
only shear stress say if you plot like this
that kind of fluid is called ideal solids
and ideal fluid is totally shearing with respect
to that there is infinite quantity of strain
with respect to shear stress that kind of
fluid is called ideal fluid.
So these definitions will be discussing further
in the coming slides so with respect to the
viscosity we can classified the fluids.
As we already seen in this figure now say
if we classify various liquids say a plastic
fluid in the case of plastic fluid say the
shear stress must reach a certain minimum
value before flow commences. So that we can
write a shear stress tow is equal to A plus
B in to du by dy with power n where A B and
n are some constant and a plastic fluid is
set to be bingham plastic which is neither
a fluid nor a solid when n is equal to 1 in
this relationship say for example
Say toothpaste and tomato ketchup have some
example so this kind of say plastic or bingham
plastic fluid so here you can see when it
is taking this say the toothpaste you can
see how it is behavior. So this kind of fluid
is called bingham plastic fluids and in the
case of as we have seen in the previous figure
the coefficient of viscosity is decreasing
with respect to when the shear is increasing
that kind of fluid is called pseudo plastic
say for example milk and if the mu increases
as the right of shear increases that kind
of fluid is called the dilatants fluid.
For example, paint or the printers ink and
in the case of fluids in which mu decreases
with time for which the shearing are applied
that kind of fluid is called thixotropic fluid
say for example mud gels used in drilling
can be classified as thixotropic fluid and
in the case mu increases with the time for
which shearing forces are applied that kind
of fluid is called rheological fluid and similar
to Newtonian fluids then the time variant
condition but if shear stress changes suddenly
and behave as elastic that kind of fluid is
called viscous elastic.
So as we have seen in this figure with respect
to viscosity the shear stress variation and
shear strain variation, if we plot then as
we have seen say the variations whether it
is linear non linear for whether it is increasing
with respect to shear stress the shear is
strain is increasing or say it is decreasing.
So accordingly we can classify the fluids
and we have seen the definition of these types
of fluid with the examples.
Now we will further discuss some other important
fluid properties, so as I mentioned in the
beginning temperature is of course another
important property so with respect to temperature.
The fluid properties like say viscosity may
change, density may change, so temperature
is also another important fluid property and
then another important property is the surface
tension. So the surface tension is the phenomena
occur due to the unbalanced cohesive forces
acting on different surfaces such as air and
water.
So surface tension it occurs due to the unbalanced
cohesive forces acting on different surfaces
such as air and water. So it is generally
expressed as sigma and then its unit is Newton
per meter. So the intensity of molecular attraction
per unit length along any line of the surface
is the surface tension sigma indicates.
So sigma can be expressed as DF by Dl, where
F is the force and l is the element length.
So due to the surface tension and other properties
there is another important properties in fluid
mechanics called capillary rise.
So this capillary rise occurs as you can see
in the slide, it is due to either cohesion
or due to adhesion. So when we place a small
tube say like a small tube is placed like
this say in water so here it is not observes,
no color here.
So but you can see in this slide if the liquid
is wetting type we can see that there will
be a small rise like this so that is called
capillary rise so this the liquid is you can
see that both surface it is wetting for that
is why due to the cohesion it is a rising
is taking place and that is what is called
capillary rise.
But in the case of non wetting fluids like
say for example mercury so if you take mercury
if you put mercury in a say bottle like this
and then put a small troop then you can see
that it is decrease it is falling down. So
these takes place adhesion of the non wetting
type liquid it will be going down so that
is the capillary falling so there can be capillary
rise or capillary fall based upon say depending
upon the type of liquid due to cohesion or
due to adhesion.
So this capillary rise or fall we can derive
as h is equal to 2 sigma cos theta by gamma
into R, where gamma is the specific wait and
R is the radius of the two which we have seen
in the previous slide and then another important
property is called vapor pressure. So the
vapor pressure takes place when a liquid in
a closed container say if there is some space
smaller space is there the pressure will develop
in the space and as a result of vapor that
is formed by escaping molecules.
So this presser is called the vapor pressure
and then when equilibrium is reached, so that
the number of molecules leaving the surface
is equal to the number entering vapor is said
to be saturated pressure exerted on liquid
surface. So this vapor pressure is say especially
the fluid contains in say both deals are in
pipes.
This vapor pressure is also very important.
This is some of the important fluid properties
and definitions which will be used in this
course. So we have seen some of the important
properties of fluids and then say some definition
are we have seen now as I mentioned earlier
say due to the fluid property like viscosity
and then other important property say no slip
condition of viscous fluid is an important
property is especially boundary conditions
which will be using.
So you can see that when fluid is flowing
say in a pipe like this or in a open channel
flow say the solid is say it is not moving
that means on the container on which the fluid
is say this pipe or the channel where the
fluid is contained so the solid is not moving
but only the fluid is moving.
At the solid surface where the fluid is moving
so at the bottom we have seen the case of
pipe flow at the bottom and at the top prefer
of the pipe the velocity is zero that since
the pipe is not moving. So the velocity the
pipe material which is zero and then the velocity
of the fluid at that point there is the contact
between the solid and fluid. So that velocity
due to the viscous effects that will be tending
to 0, so this no slip condition occurs due
to the relative velocity between the solid
surface and the adjacent fluid particles is
0.
So, fluid element in the solid surface has
zero viscosity. So here you can see in this
slide when the fluid is trying to move as
you can see in this say animation.
So it is trying to when it is moving say when
it is touching this solid surface it is say
there is the velocity zero and then say this
no slip conditions takes place. Now, based
upon this various fundamental properties,
now we will discuss the basic flow analysis
techniques.
So as I mentioned most of the fundamental
principles or theories used in mechanics are
also very much valid in fluid mechanics only
with certain changes as I mention a fluid
is deforming or the variations with respect
to solids. So that variations we have to consider
so some of the important analysis techniques
we will discuss now three basic ways to approach
fluid flow problems are as I mentioned first
one is the control volume or integral analysis.
So that means what is happening in a volume,
we comes a particular volume and what is happening
between or between two sections in that container
or in the volume so that is called the control
volume approach or the integral analysis.
So this approach is very much used in fluid
mechanics and then second approach is called
differential analysis or infinitesimal system
analysis.
So here in this analysis what we are doing
is say with respect to say particular point
say what is the fluid property is important
fluid property is like pressure velocity how
it is varying with respect to say xyz or that
means particular point is concerned. So that
kind of analysis called differential analysis
say del u by del x, del u by del y or del
u by del z so like that what it is happening.
So that is called differential analysis and
the third important approach of fluid analysis
is called the experimental study or the dimensional
analysis. So in the experimental study what
we are doing is we are trying to replicate
the real problem in the laboratory and then
we are trying in a smaller scale and we are
trying to observe what is happening and the
will be making with respect to dimensional
analysis or various other analysis we will
be trying to solve the problem. So that is
the experimental analysis so this are the
three important analysis techniques used in
fluid mechanics first one is the integral
analysis; second one is the differential analysis
and the third one is the dimensional analysis
or the experimental studies.
So in all this cases say we have to see that
the flow satisfy three basic laws of mechanics
and the thermodynamic state relationship and
the associated boundary conditions. The three
basic law mechanics are the equations or the
theories derived based up on the consideration
of mass; consideration of momentum; consideration
of energy.
So, these are the three basic laws of mechanics
based upon which master theories or the fundamental
principles derived and then of course we using
the thermodynamics theories or thermodynamics
equations will also used and then of course
the associated boundary conditions also will
be used in most of the fluid mechanics analysis.
Now we will be discussing the foundations
of flow analysis so as I mentioned.
The important theories of mechanics will be
using for the flow analysis, so five important
foundations of flow analysis are the conservation
of mass based upon which generally in fluid
mechanics we will be derived the continuity
equation and second one is the linear momentum
or the based up on the Newton’s second law
we can derived the momentum equations.
And then third one is the conservation of
energy are from the first law of thermodynamics
we can derived the energy equations and then
we can use this state relationship between
say various fluid properties like a pressure
temperature and density and lastly the appropriate
boundary conditions or say at solid surface
interfaces, inlets and exits. So, based up
on the boundary conditions we will the deriving
the fundamental equations.
In this introductory lecture now we will be
discussing other important aspects that means
as I mentioned fluid is always trying to flow
or the deformation takes place. so flow visualization
is very important in fluid mechanics. So there
are various techniques are used for flow visualization
just like dye smoke or bubble discharge. So
here you can see how we can visualize flow
taking place so here this animation shows
how the flow visualization can be taken place
with respect to dye or smoke and in then another
animation here you can see say with respect
to say here it is a gas burning.
So how it is behaving with respect to say
flow visualization how we can deprecate over
so here in this animation you can see there
is a cubby place and then over say an abstract
is spaced in name flow field and then with
respect to that how it is behaving so here
you can see the flow behave how it is taking
place.
So this say using a dye or a smoke or bubble
we can easily visualize what is happening
so that is one of the important techniques
used in fluid mechanics.
And then we can use surface powder or flakes
or liquid flows so here you can see that say
in this container or if there is in a open
channel the flow is flowing then you can use
some say flakes or some floating material
and then we can see how it is moving.
So that is the way which we can observe how
the fluid movement that is either using surface
or powder or flakes or liquid flows and then
another technique is called floats. As we
have already seen here or neutral or density
neutral floats can be used for the flow visualization
and then also we can use optical techniques
like detect density variations in the particular
say fluids say whether density is varying
from say whether it is constant or it is varying
from one to another one say and then another
technique is called evaporate. Cuttings are
bounded surfaces say how it is behaving so
this is also commonly used in flow visualization
and then another techniques is give me some
fluids it is very easy to get the flow visualization
by additives are bioluminescence and then
another technique is one of the modern technique
called particle image velocity.
We can use some special equipments we can
observe the particle image velocity and then
we can visualize the flow takes place. So
we have seen various flow visualization techniques
so when we are doing theoretical investigations
or sometimes experimentally investigations,
the flow patterns we have to identify the
flow patterns.
So we will be using some general definitions
so we will now discuss some of the general
definitions first one is the stream line So
stream line we can define as a line everywhere
tangent to the velocity vector at a given
instant. So here in this slide you can see
that flow direction is this way and then say
this is the stream line so the fluid particle
the velocity is here.
So if you draw a line like this so this are
called the stream lines so stream line as
such there are no lines but this concept can
be used for say to identify how the fluid
flow is taking place and then say especially
in theoretical analysis we can use this stream
lines for the say flow analysis over flow
observation.
And then another important definition of line
is called path line. So it is actually the
path traversed by a given fluid particle say
with respect to time so here you can see initially
the particle position is here and then with
respect to say time say how it is traversing
so here you can see it is traversing like
this. So the flow direction this particular
case is like this but the fluid particle how
it is traversing. So the path line is also
used in fluid mechanics very much.
And then another important line which is the
definition which is called streak line So
streak line is the locus of particles that
pass through a prescribed point So, here you
can see in this animation say it is the streak
line is shown here.
So it is the locus of particle that pass through
a prescribed points so here you can see how
it is obvious streak line is defined in this
animation and then another definition is another
line is in fluid mechanics time line it is
a set of fluid that forms a line at a given
instance.
