Fluid Mechanics Indian Institute of Technology, Kanpur Prof. Viswanathan Shankar Department of chemical Engineering Lecture No. # 02 Welcome to this second lecture on this course on fluid mechanics, designed for chemical engineering undergraduate students. In the 1st lecture, I laid out the motivations as to why fluid mechanics is very important in chemical process industries by showing various examples. (Refer Slide Time: 00:39) For example, we will try to show, that fluid mechanics in chemical process industries. It can come in various forms, so there are some cases in which the role of fluid mechanics is direct, so let me say direct role, as in the case of pumping of fluids, that is there in all process industries; secondly, you have pumping and transportation. Secondly, you have flow measurement. Thirdly, we saw, that mixing an agitation of reactors in chemical reactors. Fourthly, we saw, that the design of packed and fluidized beds. These are some examples where fluid mechanics plays a direct role in the design of chemical process equipment, as well as, various unit operations, that involve in detail the nature of fluid flow.
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Fluid Mechanics
Indian Institute of Technology, Kanpur
Prof. Viswanathan Shankar
Department of chemical Engineering
Lecture No. # 02
Welcome to this second lecture on this course on fluid mechanics, designed for chemical
engineering undergraduate students. In the 1st lecture, I laid out the motivations as to
why fluid mechanics is very important in chemical process industries by showing various
examples.
(Refer Slide Time: 00:39)
For example, we will try to show, that fluid mechanics in chemical process industries. It
can come in various forms, so there are some cases in which the role of fluid mechanics
is direct, so let me say direct role, as in the case of pumping of fluids, that is there in all
process industries; secondly, you have pumping and transportation. Secondly, you have
flow measurement. Thirdly, we saw, that mixing an agitation of reactors in chemical
reactors. Fourthly, we saw, that the design of packed and fluidized beds. These are some
examples where fluid mechanics plays a direct role in the design of chemical process
equipment, as well as, various unit operations, that involve in detail the nature of fluid
flow.
There are cases where fluid mechanics is important, but plays an indirect role where the
goal is not fluid for per say, in the sense, that there are, there are some other unit
operations, that are happening. For example, heat transfer in heat exchanger equipment
or for example, you could have a bubble column reactor, where reaction is happening
between the gas phase and liquid phase there.
The role of fluid mechanics is important, but it is slightly indirect because there, the role
of the fluid is to bring the reactant from a place to a point of interest. For example, if you
have a catalyst particle, we saw in the last lecture, and you, this could be, for example, a
catalyst particle in a packed bed reactor.
If you take an individual catalyst particle, you have fluid flow around it like this. So, the
role of fluid flow is to bring the reactant from this point close to the surface, so that
reaction can take place. Here, the detailed nature of flow is very important and if the
flow is slightly different, for example, like, so if there are recirculating zones in the end
of the cylinder or, or surface, so this really determines whether the product is taken away
and how fast the product is taken away as compared to this case. So, the detailed nature
of flow is important in most unit operations; is important in most unit operations.
The fundamental reason is that in chemical industry most of the operations are carried
out with fluid as the carrying medium, that is, that is primarily because handling fluids
and pumping fluids is easier and mixing fluids is easier and diffusion rates are much
faster in a fluid. So, for these reasons, for these fundamental reasons, most processing
happens typically in the fluid phase, even though the final product need not be in the
fluid form. Final product could be a powder of a pharmaceutical, but the processing itself
happens largely in the fluid phase.
So, fluid mechanics, as we saw in the last lecture and as I am reviewing here, plays the
fundamental role in many chemical processing industries and equipment.
(Refer Slide Time: 04:53)
And we saw, that there are two ways in which we will analyze fluid mechanics problems,
one is the macro-level approach and the other is a micro-level approach. The macro level
approach will involve questions, like what is the power required to mix a fluid in a tank
using an impeller, or what is the pumping cost, that is required to move fluid from one
destination to another. These are macro-scale, macro level approach questions because it
is not required, as we will see, as we go long, to know the detailed flow, that is
happening in the mixing tank, or for example, in the pipe. To answer these questions,
also having detailed information will not hurt, but it is not necessary to have detailed
information.
And we will also see that in engineering problems, it is not often possible to have
detailed information about flow fluids. So, there are cases where we can live with or we
can use the macro level approaches successfully in engineering design, whereas micro
level approach will involve detailed structure of the flow. For example, we saw the
example in case of heat exchanging equipment, where you have hot fluid and cold fluid
flowing in two adjacent pipes, for example, concentric pipes and the nature of heat
transfer will be crucially dependent on whether the hot fluid flows parallelly or it flows
like so; whether there are secondary recirculating regions, which will enhance heat
transfer across the stream lines. So, there are cases where detailed structure of flow has
an impact on the many processes in, in chemical process industries.
So, we will in this course discuss both, macro level approaches, as well as, micro level
approaches in equal measure. And both have their own successes and both have their
own limitations, as we will have opportunity to point out all through this course.
There is another important approach, that, that sort of complements the, these two
approaches, that is, the third approach, which complements the macro and micro level
approaches. This is experimentation, experimental observation. This is because it is not
often possible to analyze all problems, that occur in engineering applications using a
fundamental approach, either microscopic or macro level approaches. In many cases we
have to do systematic experiments to understand a given process equipment, for
example, like a packed bed or a fluidized bed and so on, where it is not really possible to
understand everything from first principles. So, experiments play a major role in
engineering design, especially in process industries.
And here we will show, that by judicious use of dimensional analysis, experiments can
be made much more, doing experiments can be made in a very rational way and we can
collect data and present them in a very, very economical way. And dimensional analysis
has also very, very important applications in scale up of process equipment, as we will
have opportunities to discuss later. So, this is roughly the, these are the kind of
approaches, that we are going to take as, as we go long in this course, but as an engineer
it is important to have a balance mix of all three.
So, ideally, we would like to solve all problems as fundamentally as possible, using first
principles approach, that is, the micro-scale approach, where we compute the detailed
flow field everywhere in the flow. But where it is not possible to have such an approach,
we have to settle for a macroscopic approach where we will see, that we need a lot of
experimental input. So, the macroscopic approach and the experimental approach go
hand in hand, where some parts of this analysis can be done using the macro-approach,
but certain inputs are required from experimental data in the macroscopic approach. So,
we will have opportunities to discuss, opportunity to discuss all the three approaches as
we go along.
(Refer Slide Time: 09:51)
So, this brings us to the detailed contents of the course or outline of the course. So,
having motivated what this course is about and why it is relevant to chemical
engineering, it is now the right time to tell you in detail what are the topics that we are
going to cover as we go along.
So, the first topic is continuum approximation. This is the framework in which most
problems in fluid mechanics are addressed or solved. So, continuum approximation and
introduction to what a fluid is, this is the first topic, that we will discuss. Second topic is
fluid statics; before discussing fluid mechanics it is fluid dynamics, that is, the motion of
flow. We will first discuss the case of no-flow, a static fluid and there are several
problems of engineering interest that come within the purview of fluid statics. We will
address them as well.
Then, we will discuss, we will introduce kinematics. Any mechanics, any topic in
mechanics is divided into two aspects, one is kinematics, which relates to description of
motion without reference to what forces, that caused this motion and then the motion
itself, which is driven by certain applied forces. So, we will first discuss kinematics,
introduce kinematics and the notion of kinematics is very, very important in description
of fluid flow.
Then, we will come to integral or what are called macroscopic balances, so of mass,
momentum and energy. So, as I was just pointing out few minutes back, there are two
approaches that are largely taken in addressing fluid flow problems, one is the macro-
scale approach where the detailed flow structure is not required and the integral balances
are one way of addressing such problems using integral balance, using macroscopic
balance of mass, momentum and energy. And then, we will go to differential balances or
microscopic balances of mass, momentum and energy. As the name suggests, integral
balances will involve integrals of various quantities, such as mass, momentum, energy
and how they change in a flow while differential balances will involve differential
equations of these quantities, like mass, momentum and energy. And finally, these
differential equations will be valid at each and every point in the fluid and if you can
solve them, this will be the most, you know, detailed information, that one can have for a
fluid flow.
After we do, do that we will do dimensional analysis and then apply this to pipe flows
and fittings. And then we will do, we will see, that fluid flow is normally characterized
by a single parameter. Once we do dimensional analysis, there is a parameter called
Reynolds number, which will recur throughout this course after we, we are done with the
basics. So, the Reynolds number, when it is small the flow speeds are small; when the
Reynolds number, when it is large the flow speeds are very large. So, when the flow
speeds are very large we will deal with what are called potential flows. These are some
approximations of the full microscopic equations, differential equations of flow.
And we will discuss, that when potential flow fails we have to invoke, what is called,
boundary layer theory. This is a very important topic in fluid mechanics. Once we are
done with this, this roughly concludes the basic aspects of fluid mechanics.
So, then we will go to fluid solid systems, this involves chemical engineering
applications such as settling, sedimentation, and so on. Then, we will proceed to the
analysis of packed beds, fluidized beds and filtration. We will then proceed to mixing an
agitation in chemical, in chemical industries. So, these are some of the primary
applications of fluid mechanics in chemical processing industries.
And then we will find that finally, we will go to slightly fundamental, but advanced
topics, which are unique to chemical, chemical industries. One is usually the flows, that
we encounter in chemical industries, are not very simple. For example, the flow will not
happen at a very slow pace, it will happen at a very rapid flow rate. In such cases the
flow will become turbulent, so we will give a brief introduction to turbulence and derive
some basic equations of turbulent flows, so that will be the next part.
And finally, we will discuss non-Newtonian flows; I will discuss what these are as we go
along. Simple fluids like water and air called Newtonian fluids because they behave in a
particular way, whereas many complex fluids that are, many fluids, that are encountered
in chemical industry, for example they may be slurries or suspensions of one particle in
another or dispersions of one liquid in another and so on. These are very complex
systems and the way in which they behave in there flow is very different from how water
and air behave. So, these are non-Newtonian fluids or since they exhibit some elasticity
in additions to viscous effects, they are called viscoelastic fluids. So, we will give a brief
introduction to non-Newtonian fluids.
So, this is the agenda for this course and I have already told you the texts that are
suggested for additional readings. Although all these material will be inherently self-
contained, so I have already mentioned this to you, that the basic parts of this course up
to these will, for example you can follow Fox and McDonald for additional reading or
White. Fluid mechanics for these, in addition to the lecture notes, you can follow
McCabe, Smith and Harriet. For these, you can follow Bird, Stewart and Lightfoot
transport phenomena. So, this is the rough agenda for this course.