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THE SCIENCE AND ART OFFLUID MECHANICS EXPERIMENTATION
(ELECTRONIC LECTURES ONME332 FLUID MECHANICS LABORATORY)
Mihir Sen
Department of Aerospace and Mechanical EngineeringUniversity of Notre Dame
Notre Dame, IN 46556
December 27, 2002
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Contents
Preface 3
Welcome 5
The laboratory 9
Design of the experiments 14
A theoretician looks at the Fluids Laboratory 21
Limitations in our knowledge and methods 27
Goodbye 32
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Preface
Spring, 1999.
These are electronic lectures1 for ME332 Fluid Mechanics Laboratory, a course
typically taken by juniors. The laboratory nature of the course means that you,
the students, learn mainly by doing, and I would prefer that you spend the mostproductive time of the day working in the laboratory, discussing with your peers,
analyzing your data, or writing the report. But, in being engaged in these essential
day-to-day activities, there is a danger that you may miss the bigger picture and not
really understand why you are taking this course in the first place, what relation it
has to the professional engineers task, or what you are supposed to be learning. Since
classroom lectures would mean additional time that the average student just does not
have, these electronic lectures are a substitute. They have the main advantage that
they can be read in a more leisurely fashion and in a more relaxed frame of mind;
you can wait till your more urgent tasks are done.
The purpose of these lectures is not to discuss specific experiments; the Notes are
meant for that. They are not intended to be a substitute for a textbook either. Rather,
they are designed to provide you the tools for the interpretation of experimental
results. Though in this sense they may help you with the reports, they are not meant
to have a direct relation with the actual experiments that you will do, but will provide
an overall philosophical umbrella you will be working under.
The chapters will be written as the semester goes along, much in the manner of a
newspaper or magazine column. Since my intention is to substitute actual lectures,I hope you will find the writing style to be informal. The lectures will be placed on
1The word lecture is used in its older sense; it comes from the Latin legere which means to read,
but has now more commonly come to mean a discourse.
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the Web for you to access from your dorm room or any other place where there is a
computer with browser. It will be updated to grow as the chapters are written, and
will ultimately contain all the lectures.
One of the advantages of the written word is that you may go back and re-readwhatever catches your eye. It often happens that with time a paragraph or phrase
takes on a different meaning. Another is that I can request colleagues on the faculty
for their input without making intolerable demands on their schedules. I have done
so, and from time to time you will find a guest lecture by someone else on some aspect
of the subject that they are interested in. I thank them for their contributions. You
will notice that though we share a common interest in fluid mechanics and agree on
most of the technical details, our overall perspectives may differ. We are all involved
in fluid mechanics, but each is on a different path.
If you find errors in the text, or would like to discuss some issues that have been
raised, please feel free to do so. An e-mail or a personal visit is always welcome.
Mihir Sen
Copyright c by M. Sen, 1999
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Welcome
Spring, 1999.
A belated welcome to ME332 Fluid Mechanics Laboratory and this semester. As
classes begin, you have many questions about how it will turn out, whether it will
be a lot or work or difficult. These are legitimate questions from your perspective,but I have no concrete answers to give you. Moreover, reducing the acquisition of
knowledge and skills to a certain number of hours spent per week is not the place to
begin the discussion, I feel. The place I should start, perhaps, is by explaining what
I feel this course should give you. If you know what it is you are supposed to be
learning, you may be better able to allocate your time and be more efficient in your
learning.
First, why is fluid mechanics included in a mechanical engineering curriculum?
The answer to this is quite simple: it is part and parcel of what people expect of
mechanical engineering and mechanical engineers. There was a time, maybe several
decades ago, when all engineers took all the basic engineering sciences like thermody-
namics, electrical technology, metallurgy, and sometimes even fluid mechanics. Over
the last twenty years the curriculum has gradually been narrowed and more focused
and few engineering disciplines require it now, among those being mechanical, civil,
chemical and aerospace engineering, though perhaps under different names. There
are a number of reasons for that, not the least of which is the explosion in knowledge.
It is obvious that as time goes on, the amount of knowledge, if one could quantify
it (computer scientists like to use bits, but it seems to me to be an overly simplifiedunit for this purpose) one must find that it can only grow with each generation. True
some skills are lost as artisans pass away and few can, for example, make clay pottery
as well as our ancestors did. But knowledge, as represented by facts and figures, must
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be an integral in time up to the current moment. I have often wondered what the
mechanical engineering curriculum will look like in a hundred years. The only thing
I can be sure of is that it will look nothing like what it is today. For instance, take
a look at what it was a hundred years ago (at Notre Dame we celebrated 100 yearsof mechanical engineering a decade or so ago). Geometry, mensuration, trigonometry
and surveying figured among the advanced mathematical topics that were covered.
And for good reason; that was what the engineer would actually use. Fluid mechanics
was also taught, but was very empirical. There were many rules of thumb given and
practical advice imparted. The twentieth century has been a technological century;
and that has affected the engineering curriculum greatly. It was recognized, maybe
about fifty years ago, that teaching only what the student would immediately use
upon graduation was short-sighted; there had to be a way of teaching for the future.
From this evolved an emphasis on the engineering sciences, like the ones that were
mentioned before. The logic was that with the basic engineering sciences in hand, one
could deal with whatever the future would bring; though the applications change, the
laws of thermodynamics, for example, are immutable and the machines of the future
would have to satisfy them. Of course, this was not satisfactory to all. Engineering
technology was spun off as a separate degree program in many schools to prepare
students who wanted to work with the technology of the day. Also, shouldnt engi-
neers also be able to work with current technology? In any case, how do you design
a machine knowing only Newtons laws and the laws of thermodynamics? Surely youmust be taught how to apply them. As a result, it seems to me, the pendulum has
begun to swing the other way. You are in the middle of a period of change, but then,
isnt any generation? The bottom line is that, at the moment, fluid mechanics is still
part of the thermal sciences as taught to mechanical and other engineers.
Now the issue of focused learning vs. a broad education. Why do you need to learn
fluid mechanics when it is entirely possible that you may pass your entire working life
without using it. On the one extreme, it is possible to provide an education on only
what you will use. This presupposes of course that you know exactly what you willuse, but more importantly, it will confine you to the use of only that knowledge. On
the other extreme, a liberal education gives you a broad preparation with a profound
knowledge of nothing but the ability to learn later on anything that you need. The
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path that you are going through is in the middle; you learn fluid mechanics but you do
not learn to design multi-stage radial gas compressors, for instance. The hope is that,
if you need to, you can learn to do so. You have the basic knowledge, the technical
language skills to be able to read and understand the literature, and the analyticalskills to be able to apply it. In the end you will find that gas compressors work under
the same physical principles you have been using in other problems in class, nothing
new there. But what if you never work with anything related to fluid mechanics, is
the time spent on it then wasted? The answer again is no. If all you learn from a
fluid mechanics class is fluid mechanics, then perhaps the time is indeed wasted. But
if you learn how to analyze a problem in general, represent it in mathematical form,
solve the mathematics, and then interpret the results physically, it will help you in
many different ways. This is similar to saying that you are better off learning to add
any set of numbers, even though in life you will have to actually add only specific
sets. You do not a priori know what numbers they will be, and in any case it is far
easier to learn the general technique of addition than only specific examples. The
use of examples to help in learning the general principle should not be confused with
knowing only those examples. Once you have the analytical skills developed by fluid
mechanics and similar courses, you will be able to apply the skills to whatever comes
up.
Next, why a fluid mechanics laboratory? The answer to this is more difficult.
Given that fluid mechanics is important, isnt it enough to have it in a theory class?
You learn how a fluid behaves, how it flows, and how to calculate things about it.
This is related to an even deeper question: do you really need to have multiple objects
around you to be able to learn to add? It is impossible to tell since we always have
objects around us. Would an alien race, for example, that didnt have any discover
arithmetic? In principle it is possible, and in principle it is possible for you to learn
all that you need to know from a book. The human mind, of course, is capable of very
abstract thought and can distinguish between the statement that 2 + 3 = 5 and that
two apples and three apples together make five apples. In a similar fashion, losses inpipelines, to cite one simple example, can be learned through equations, but would
they have the same physical feel? That is, would you know, really know what it means,
long after the formulas are forgotten? I would argue, and I believe that most of you
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would agree, that a hands-on laboratory experience reinforces, at the very least, book
learning. But then, what about a laboratory for every course? Shouldnt dynamics
have one, and thermodynamics, and all the others? An experiment with hockey
pucks sliding across an air table can help explain the conservation of momentumduring collision; a p V T-cell can make thermodynamics more vivid. How would
we fit these into the curriculum? Obviously we couldnt, even though faculty often
wonder if laboratories in their favorite subjects should be included. There has to
be a balance; traditionally a fluid mechanics laboratory is included in a mechanical
engineering curriculum. In our case, we have designed this to be the third in a 3-
course series: Measurements Laboratory, Solids Mechanics Laboratory, and this. The
courses have been designed to be a continuum, and to teach a related set of concepts.
So, the current course is not meant merely to confirm what you have seen in the
fluid mechanics class, in fact it would miss the point entirely if this were the case.
Moreover, one can argue that if the student were to take only one course in fluid
mechanics, a laboratory course rather than theory should be the one. If children were
left with enough apples and oranges, they would ultimately figure out the rules of
arithmetic; the knowledge would be very firm, but too slow in coming. We are in a
rush, we would like the student to know so many things in a four-year period, and
so we put all that in the theory classes. But the point still remains that the theory
has been developed to solve certain real-life problems involving fluids, and unless you
see what they are, the knowledge is abstract. It may be, and I see a certain practicaladvantage to this, that the laboratory should come before the theory. After all the
purpose of the theory is to explain the problems that you will need to solve, instead
of those that canbe solved.
I have tried to give a perspective on the role that fluid mechanics plays in an
engineering curriculum as I see it, but there is much more to be said. In future
lectures I will give you my perspective on what I hope you will be learning this
semester.
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The laboratory
Spring, 1999.
By now you have had some experience with a couple of complete cycles of the
laboratory, you are familiar with the experiments themselves and with data analysis
and report writing. This is a good time to discuss the objectives behind the course,and what you are expected to learn from it.
Fluid mechanics is, of course, the central topic. So what is it about fluid mechanics
that you learn from a laboratory that is different from a book? Before I get into that,
let me first discuss what I hope you will learn this semester that is not related to fluid
mechanics, at least it is not exclusive to fluid mechanics. Put a different way, if fluid
mechanics were all you learned from this laboratory, the time is not well spent.
This laboratory, as I have mentioned before, is the third in a series of three
laboratory-based courses in mechanical engineering, following those on Measurements
and Solid Mechanics. The sequence is designed in the following manner. The experi-
mental experience in the first is in a controlled environment; you are more or less told
what to do and what results to obtain, and how to manipulate and interpret the data.
It is, after all, the first engineering laboratory experience for you. The second revolves
around solid mechanics, but the organization of the laboratory is such as to put a
greater burden on you. You work under the supervision of a graduate student, but
you have to depend on your own resources to read the written material to figure out
how to process the data appropriately. The third course, this one, takes the process
one step farther; you have some guidance in terms of written material, but it is upto you to decide what exactly to do, how to do it and what to make of the results.
Moreover, there is a minimum that you can do, or you can be creative and do more
than that. This is not the end of the series; in the senior year you will have Senior
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Design in which you are set free and have only your own wits, imagination and the
knowledge you have gained in the program, to design and construct a machine that
will fulfill a given goal. Soon thereafter, of course, you may have to prove your ability
for independent and creative thought and action in the context of a working life.
To instill independence and creativity is really the purpose behind education. If
all you have when you leave is a collection of facts and figures, it will be difficult, in
the long run, to put that information to use in any practical fashion. Besides, it will
soon be obsolete. If, however, you learn how to find information and how to use it,
that process will never go out of style. In this course you are given a minimum of
information, but you have at hand a basic knowledge of fluid mechanics as well as the
textbook itself. This is much like how it is going to be in the real world. You have
to figure out what to do in the laboratory. You will determine what measurements torecord, and how to process the data. This is the procedure behind every experiment,
large or small, simple or complicated. You may find, in the beginning, that when you
sit down to do the calculations you do not have all the data that you need. In this
case you will have to go back again and get what you need. This is also how it is
often done in real life, though it is not a recommended procedure. By the time the
semester is over you will have learned to think and plan ahead, and make sure that
you have noted all the information you will need before you leave the laboratory.
Knowledge gained from a laboratory course is, in a certain sense, real. The calcu-
lations themselves are no different from what you do in a theory class. The difference,
however, lies in that you have a physical system in front of you. Your measurements
correspond to some quantity in this system. For most people, this helps make the ab-
stract concrete. You think of the pressure not simply as a symbol p, but as a physical
quantity that can be represented by a symbol, p, x or any other. There is a difference
between reality and our representation of it, and engineering is a discipline that is
based on reality. Mathematics is often used as a model or surrogate for reality. It is
certainly easier to manipulate equations to determine numbers than it is to make an
experiment every time we wanted to know how a certain design would turn out, butwe must not confuse the model with reality.
Another important aspect to learning in the laboratory environment relates to
skills that you acquire on the use of tools. These skills, along with others such as
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writing ability and computer literacy, will also be valuable in an engineering career.
Generally speaking, current engineering programs do not really give you any exposure
to the use of machinery for manufacture, which would have been good, but to a
limited extent to the use of measuring instruments. You have used them before inthe previous laboratory courses, and any further experience that you get with them is
beneficial. Each instrument is different and its operation has to be learned separately.
When you come across any new device, it will take you some time to become familiar
with it to the point that you know exactly what it is doing. However, having used
similar instruments will give you the confidence to handle most anything new. Most
of the instruments that you see in the laboratory are off the shelf items of general
use, and you will become familiar with the practical aspects of characteristics such as
sensitivity, offset and range. Along with the instruments themselves, you also learn
to use modern techniques of data acquisition and processing. Computer use in the
laboratory has become very common over the last ten years, and an ability to work
with them is a necessary skill in most experimental work. Because of time constraints
your exposure to these tools is necessarily partial; the computer programs are set up
for you to use, although in a working environment you may be responsible not only
for choosing the hardware appropriate for the job, but also writing the software to do
it. You will also use computerized tools for data analysis, processing images, drawing
graphs, and writing reports. The point to be remembered in all these items is not
the specific tool that you learn to use but the fact that you have to learn by yourself,by asking other people or from the manuals. Again, it is not what you learn but how
you learn it that will be the most useful skill in the long run. If you can do it once,
you can do it again when required to do so in the future. Along with knowledge,
skills should not be frozen but must move with the times.
Reading the recommended reading material and making sense from it is another
part of the learning process. There may be many instances in what you see and
do in the laboratory that you need to read up upon. That is fine; if you dont know
something, at least you know how to find the information. But finding the informationis also not enough, you must be able to understand it and to use it. This is where
your previous education comes in. Someone without the appropriate education in
the field can read the same material but not understand it at all. There is not only
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technical jargon to be overcome but also a body of knowledge is needed that is simple
for you but not for the other person. This is what you will have to do in the future
in situations for which you are not completely prepared.
Writing is another important ability that you are practicing. Engineers are often
taken to task for their poor skills in this regard, even though writing and presentation
skills are very important in many of the careers that engineers pursue. There are
several reasons why writing is the often the preferred mode of communication: before
you can write something down you have to really understand what you are going
to say; what you write will stay around for some time and can be passed on and
read by many who are not initial recipients of the information. There have often
been discussions within the faculty as to where the writing skill is learned, and it
invariably comes down to the practice of report writing. Of course, reports are notexclusive to the laboratories but, unlike in a theory class, they are the main vehicle
of student expression in a laboratory course. What must you learn about writing
and from writing? That it is important to express yourself clearly and concisely in a
language that free from grammatical, spelling and other errors. It is often said that
mathematics and graphics are the twin languages of the engineer. Use them well,
but use them appropriately within a context of a text. Writing is an art, and like all
arts cannot be taught. You have to see examples of it to see what is good and what
should be avoided, and you have to practice it again and again.
And yes, you will also learn about fluid mechanics. In the laboratory you will
come across phenomena that you will observe or measure that merited only a passing
reference in the theory class, if that. The reason is that not all fluid mechanical
phenomena can be calculated and dissected from a theoretical perspective, but that
does not make them any less important. It is also important to get a feeling for the
quantities that you measure. How fast must a water flow really be before it turns
turbulent? What kind of pressure drop can you expect in an elbow or other fitting as
compared to a straight pipe? Another important aspect is to know the limitations of
theory. Practical engineering applications of fluid mechanics is heavily dependent onthe use of empirically obtained coefficients and factors. It is often not obvious to a
beginner in the subject what these are, and how much one should trust the values that
one obtains from handbooks. In many cases you will find values and numbers that
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are different from those commonly accepted in the literature. When that happens,
does it mean that you are wrong and that the books are right? Not necessarily. Your
measurements may be exact but the setup of the experiment maybe different from
that in the literature. As a practicing engineer you may have to adapt an idealizedsolution or piece of information to a situation that is similar but not identical.
Of course all measurements have errors, but how large are they and are they
important? A laboratory exercise gives you some feeling for the order of magnitude
of the errors you may have in any calculation derived from the measurement. You
may find that for a given phenomenon, a 25% error is good, 5% excellent, and 1%
impossible to get, while for another 5, 1 and 0.2 may be the corresponding numbers.
It all depends on the phenomenon that you are measuring. To be able to use the
results of a theoretical calculation in a design, for example, is very important to know
the accuracy of the numbers that you calculate. In fact you may be called upon to
make predictions in situations in which there is no exact procedure to do so and a
guesstimate is all that can be done. Engineers have to build and not everything
they build is completely understood in all its details. Theoretical calculations, on
the other hand, sometimes give the impression that something can be calculated to
a large number of significant figures. This is not true if the calculation is based on
some experimental quantity. In this connection, a common rule of thumb is to use
numbers up to three significant figures only (except if it starts with 1 in which case
four significant figures is all right); after all it indicates an accuracy of better than1%, which is pretty good. In fact, after doing the experiments you will appreciate
how good an error of only 1% really is.
So you see there is much more to the laboratory than getting numbers and cal-
culating results. Most of the times you will not be aware that you are learning
something. But if you spend time in the laboratory and think about the apparatus
and what you are doing while you are doing it, you will gain the experience and skills
that will serve you well in the future.
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Design of the experiments
This chapter has been written with the help of Rod McClain.
Spring, 1999.
Working with the experiments, you may wonder why they are designed exactlythe way they are. Another reason to know is that in the future, it may happen that
some of you may be required by your job to not only work with experiments, but
also design them. In this lecture I will try to give you some background on how the
experiments you see came to be that way. Like all design, this is a creative process
with no unique answer, and every semester we actually come up with slightly different
results. There are several people involved the process: Mr. Rod McClain, Professional
Specialist, is in overall charge of the lab, Mr. Chuck Klein, Machinist, does whatever
milling, cutting, and drilling is needed in the machine shop, and Mr. Kevin Peters,
Technician, helps to put the experiments together and set up the computers.The first step in the process is to select the experiments. Some of the most
important criteria for this are the following.
Safety: The experiments must be, above all else, as safe as we can make them.
Water and electricity do not mix well, and a fluids lab must have both. The ex-
periments are designed so that these two are well separated. Moving machinery
is mostly kept out of the way.
Simplicity of operation: By looking at the experimental apparatus, an observershould be able to figure out how to start it, which way the fluids flow, and what
is happening in the experiment. In conjunction with safety, this means that the
pumps should be separated from the measurement area but easily visible. A
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very complex piece of machinery or piping would be hard to understand in a
short time.
Simplicity in manufacture and assembly: We usually have only a couple of
weeks to put together the experiments. Even though instructional use of the
Departments machine shop is given first priority, often there is need of an
additional tool that takes time to get, or there is a breakdown of equipment
that slows down the process. Apparatus that is complicated to construct is
sometimes planned and built over several years. For example, the water tables,
which are simple to use, are fabricated in a relatively complicated manner which
includes the cutting, heating, bending, and joining of transparent material.
Simple to maintain: Most operational problems should be simple to fix during
use. The students are extremely careful with what they do in the laboratory,
fully justifying the trust that has been put on them. However, normal wear and
tear has to take place. This is especially important for equipment that has been
in use for a long time. Sometimes maintenance is not possible and we have to
adapt to a loss in the middle of experiments. Last year a turbine flow meter
that had been in use for ten years simply decided that it had enough, and we
had to retire that experiment.
Expense: We have a fixed budget to work with. Some major items are purchased
slowly over the years to replace those that are worn out or obsolete. We have
recently bought new Windows-based computers to replace some old Macs, but
we need more in the future.
Robustness: The experiments must be able to take the wear and tear from
ninety students a week without frequent breakdowns. We have also found that
working with fluids other than air or water tends to be very messy.
Variety: Some experiments should explain basic principles and a fundamental
understanding of fluid mechanics, and others should parallel the use of fluidmechanics in industry. Similarly, some measurements should be manual and
others computerized. This way you can see the advantages and disadvantages
of both.
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New experiments: We usually put in some new experiments every semester and
upgrade others. If we ourselves dont take an interest in the experiments, we
cannot expect the students to do so either.
The following is the procedure that we use to put together the experiments.
Selection: Rod McClain and I get together, perhaps several times a week, be-
ginning a couple of months before the experiments are due to be operational.
We have a long list of possible experiments and ideas from which to choose.
We discuss what the experiments will be, what relation they have to the real
life use of instrumentation and fluid mechanics, what basic principles they il-
lustrate, whether they preserve an adequate balance between what can truly be
calculated from theory and what cannot, as well as a balance between experi-
ments using air and those using water. The experiments, furthermore, should
be simple enough to be easily understood at a glance so that it isnt a black
box.
Design: We first sketch some options on the blackboard, and then decide on
the ones we will do this semester. Rod McClain then designs the apparatus
in terms of dimensions, pump sizes, measuring instruments, and mechanical
assembly. Often the initial idea undergoes a substantial change for the better.
This process is a combination of machine design and fluid mechanics. The
design should be such as to be easily manufactured and assembled. The fluid
mechanics calculations are essentially a reverse of what you do after you have
taken the data. In order to estimate the various quantities, he looks up values
of friction factors and flow coefficients reported in the literature so that he
can determine reasonable flow rates and pressure drops. Then he can choose
from standard piping sizes, pump catalogs, and electronic instruments so that
the outputs that you actually measure, the voltage going to a multimeter for
instance, are large enough for you to get good data. Often the requirements
are conflictive, we have to make choices, and a perfect design is not entirelypossible. We also try to use off the shelf equipment and instruments, both for
cost considerations and also because that is what you will probably encounter
in the future.
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Manufacture and assembly: Chuck Klein and Kevin Peters help out in this stage.
Often this part of the process is iterative if there is some error in machining or
in the design. Remember that it is very different having an experiment working
in the blackboard, and actually doing what it is supposed to do on the labfloor. Pipes usually dont leak on the blackboard, for one thing. In this regard,
experience is the best teacher, and I am happy to say that the staff is very
experienced in what they do. Sometimes, when we try new things, the result is
not entirely as expected.
Testing: We run through the experiment ourselves before putting it on line.
Sometimes there are minor modifications to be made even at this late stage.
Instructions: The write-up for an experiment cannot be finalized until the ex-
periment itself is. There are two types of instructions to be given. Some are
general in terms of a schematic of the experiment, the objectives, recommended
readings, and the equations to be used; these are posted on the Web. Others
make sense only with the experiment in front of you, like information on calibra-
tion or how to use the software; so these are posted at the workstation. Some
of the components, especially those hidden from view, also need to labeled. In
the end, you will notice that not every detail is provided, so that you develop
an ability to deduce what you dont know from the information at hand. As
an example, you have to figure out that the valve handle parallel to the pipesignifies an open valve, which you can do by opening one valve and checking
the resulting flow rate in the rotameter.
There are also certain specific comments that we can make regarding each one of
the experiments that you are doing this half-semester.
Unit 1: Hydrostatics
Hydrostatics is one of the few instances in fluid mechanics for which we have
exact mathematical solutions (some laminar flows being another). The experiments
will show that, in spite of this, the experimental results are not perfect and one should
have a healthy respect for the difficulty of getting perfect results.
(a) Piston in cylinder
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This is an experiment that we have used for a number of years. It is simple
but instructive. The interior spring and the process of bringing the piston back to
the same level together enable the linearity of the force-pressure relationship to be
demonstrated without knowledge of the spring characteristics. The piston-cylinderarrangements are off the shelf pneumatic actuators commonly used in control appli-
cations.
(b) Free surface under rotation
Though other measuring techniques, like optical devices, could have been used, we
have opted for simplicity and not necessarily accuracy. Having to shift the origin of
the distance measurements to conform to theoretical results, is also a useful exercise.
In real life you will often find that the information is not in the form you would like
to have; this is a simple example.
Unit 2: Flow visualization
This provides an excellent opportunity for the visual appreciation of the complex-
ity of flow phenomena.
(a) Water table
The experiment itself is simple, but the handling of photographic images is very
modern. In fact what you learn in this regard will hopefully be useful to you in
other applications in the future. In the design of water flow visualization by dye, it isimportant for the water speed to be low enough for the dye not to mix quickly with
the surrounding water, nor sink due to density differences.
(b) Reynoldss experiment
This is a classic experiment. The settling chamber as we have it is not large
enough to do the job well. Furthermore, a vertical tube would have avoided the
effect of descending dye streams due to density differences. We intend to redo this
experiment in the future. Pressure measurement by a manometer illustrates a simple
and accurate method that is to be contrasted to the electronic output of a pressure
transducer used elsewhere.
Unit 3: Flow measurement
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These are a set of basic measuring instruments that are commonly used. One of
the problems is that that the three measuring devices have vastly different pressure
drops. Since we have used a single pressure transducer, there is no way out of having
one of the devices, the total-head tube in this case, with a relatively small reading inthe multimeter. In each device the pressure drop produced had to be matched with
the range of the transducer and the capability of the pump.
(a) Mean velocity
The Venturi was made in the shop (for a cost of $10 as opposed to about $800 for
a purchased item). The main design criterion is that the expansion angle be small to
avoid flow separation; otherwise it would be working as an orifice. Both Venturi and
orifice meters are instruments in common use in industry.
(b) Total-head tube
Unfortunately this is one of the instruments that you cannot see, so a drawing has
to be provided. The total-head tube is more common in air-handling applications; in
fact it is also used in Unit 4(b).
Unit 4: Pipe flow
These are a couple of experiments with air. It is very difficult to have a laminar
flow of air, and the flows here are turbulent.
(a) Entrance effects and losses
We introduce computerized data acquisition that is typical of many modern mea-
suring systems. The software is written so as to display the pressure vs. distance curve
which gives visual meaning to the difference in the behavior between the entrance and
the fully developed regions.
(b) LFE and velocity profile
You get to see what a turbulent velocity profile looks like, and how different it iscompared to a parabolic laminar one.
Unit 5: Minor losses
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These are basic components of many hydraulic systems, widely used but only
empirically understood. These experiments illustrate how the coefficients reported in
the literature are obtained.
(a) Valves
You are introduced to a variety of different valves, each with a different loss
coefficient to opening angle relation. An appreciation of the nonlinearity of this
relation is important, especially for control applications. Valves, particularly globe
and needle valves, are carefully designed to produce a near-linear behavior around
the point of operation.
(b) Fittings
You are introduced to a variety of different fittings.
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A theoretician looks at the Fluids
Laboratory
The guest writer for this lecture is Professor Joseph M. Powers.
Spring, 1999.
When Prof. Sen asked me to make a contribution to this new venture of electronic
lectures, in the old sense of the word lecture, I was somewhat unsure of what to
contribute. Having skimmed through the first few of these lecture has not led to
any grand insights, but has encouraged me to adopt a somewhat informal, stream-of-
consciousness style in giving my comments on fluids lab.
First a bit about myself, as it relates to this topic. I was educated entirely as a
mechanical engineer, obtaining three degrees in this field, with my graduate work fo-
cusing on developing and solving theoretical models for the fluid mechanics of chem-
ically reactive systems. I never had a fluids lab in my undergraduate or graduate
curricula, though there were plenty of courses on fluids theory. We werent short on
lab courses however: there were full courses in solids lab, measurements lab, controls
lab, chemistry lab, physics lab, etc. Fluids just did not happen to make the cut in
the required courses. Thats all immaterial, as Prof. Sen has pointed out in his earlier
lectures, in many ways one important goal of a laboratory course, whatever the sub-
ject matter, is to instill in the student the idea that the theory has some grounding
in empirical physical reality. That is there are many paths to knowledge and under-
standing. Observation is one of them and in many ways is the foundation of Westernscience, at least after the Renaissance. You may recall the dangers of theory not
grounded at some level in empiricism: Aristotle wrote books on physics. He decided
that F = mv. He should have checked. Any rocket he designed would probably
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crash ; even knowing F = ma, about 10% of our rockets dont make it. Anyway,
despite the bulk of my own research being theoretical, I have always been surrounded
by fluid laboratories. At the University of Illinois, my office was next door to half a
dozen screaming supersonic wind tunnels, and my office, save me, was filled with fourscreaming graduate students working on their experiments. I have also worked at a
number of laboratories and in most instances sought and found significant interaction
with my colleagues whose first priority was in the laboratory.
In a recent experience, I shared an office with a physicist who was designing multi-
million dollar experiments involving high speed impact dynamics. He had been doing
this for nearly ten years after an education similar to my own, which focused entirely
on theory. What I saw in him was someone who truly understood the motivation
for why he was doing the experiment and was really able to do excellent detectivework in analyzing why it behaved as it did. I think he achieved success because
he worked at having competence in all areas. First, his work had certain goals,
generally requiring detailed experimental evidence. An example question would be,
if we hit this material really hard (some number would be attached to quantify it),
will this component survive or break? The answer is simply not known beforehand,
and it is going to be very expensive to find out, so he needs to do it right the first
time, no partial credit. Second, he knew how to design and engineer his equipment
to provide definitive answers to those questions. Heres where a lot of creativity
was required. Could one design a simple experiment for a prototype that would
mimic the behavior of the model? Third he knew how to use theoretical analysis to
guide him in designing his experiment. Before any experiment was run, a large finite
element code was exercised to get an idea of what would happen. As with nearly all
theoretical models, their predictions do give some idea of how the system behaves, but
they cannot capture every detail; some of these details can be critically important.
Nevertheless, the theoretical model predictions were able to give very good estimates,
and reassurance that the experiment had a chance to answer the proper question.
Often times, the experiment was re-designed before the actual test in response todisturbing model predictions. After the experimental tests were run, there was a
quite long post-mortem phase which required a lot of analysis of the results. An
important question was always, did it behave in the way we thought it would, and
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if not, why not? What impressed me most was that one skilled person was able to
marshal both experimental and theoretical skill in such a fashion to get at the heart
of some important science/engineering questions. The goal was to get at the truth,
and to use the best set of tools to get the answer. Brains, theory, empiricism: allworked together.
Do they always work together? No. Sometimes I see this as a problem and some-
times not. Working at another laboratory a few years ago, I found myself surrounded
on one worksite by some experimentalists who had little use for theoreticians, and at
a nearby site by theoreticians who had little use for experimentalists. The method of
the experimentalist was to hit a specimen hard and see what happened. Then try it
again, then again. Theyre still hitting things, breaking them, and Im not quite sure
what theyve learned. Their theoretical colleagues in a nearby building stayed busymainly talking with themselves, making tweaks to a code which had fundamental
flaws and have little hope for providing first principles answers for any questions. It
may have some value as an fancy way to do interpolation, but it was not clear that
it was either science or engineering.
At yet another laboratory, I worked with a group that was purely theoretical, and
many of them were making good contributions despite not having a experiment in
sight. What were they up to? In a nutshell, algorithm improvement. There are some
very classical problems that are so well understood theoretically and experimentally
that no one really questions them. Nevertheless, many of these problems may require
a lot of computational resources to accurately simulate with a theoretical model. An
example might be the flow of a low Reynolds number fluid over a sphere. Currently
there is a lot of room for improvements in algorithms for solving well-known equations
of fluid mechanics. At lunch recently, Prof. Bass of the CSE department relayed a
story of a researcher here at Notre Dame who was solving equations which modelled
groundwater flow. A simulation generally took over twenty-four hours. This faculty
member asked a colleague in the CSE department to look at the source code; by
making a few changes in how do loops were structured, what used to run in twenty-four hours then ran in twenty-four minutes! Often times however, it is much more
challenging to increase the efficiency. In fact some of these problems have challenged
some of the best minds of this century. We do not have the best algorithm yet, and
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we are probably not even close to what could be, so there is still lots of work to be
done.
So what does all of this have to do with fluids lab? Im not really sure. I do
know that one goal that I would encourage you to adopt in your education, whichwill continue after university is to do your best to understand why things behave as
they do. Being able to answer such questions will make you a valuable person to your
company and more importantly to your society. Having taught the fluids laboratory
before, I know there are many opportunities to flex your neurons on such matters.
Now most of you will not be spending your lives calculating Strouhal numbers or
measuring friction factors. There may come a time when they might in fact be useful,
but even more useful I think is that fluids lab offers an opportunity to understand
some basic realities of nature which are well grounded in theory, and in that offers
hope that there are other things in nature that we may come to understand. My
hypothesis is that it was the instilled bravado, combined with a knowledge of both
theory and empiricism that was instilled in generations of past engineers, that led us
to Kitty Hawk in 1903 and the Sea of Tranquility in 1969 and many places to come
in future years. It is only with an appreciation of both that we will reach them.
Question from a student
I just read your lecture, in conjunction with continuing work I am doing on a fluids
lab. In the E-Lecture you said, most of us probably will not be calculating Strouhal
numbers and friction factors. While those exact words have not been uttered by
other professors, others have said that we will probably not be doing this specific
task or that specific task. It seems then that we do a lot of things that we will never
do. I write, not to say why dont we do what we will actually do as professionals,
the reasons we do those things is reasonably clear. What, then, does a professional
engineer do in a career? Clearly there are too many things we can do to enumerate,
but generally speaking, what is so different about the work of a professional engineer
and a student engineer? Artificiality, trivia, and simplicity seems to be the core of a
student engineers life, does this go away at the professional level? graduate level? Inclass I have heard three professors recently comment that we will not be doing this
or that ... it just made me wonder. If you have any insight on the subject and/or
know what it is that a real engineer does, please, do tell.
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Professor Powerss answer
Thanks for reading the lecture. To your question, what do real engineers do,
a comprehensive answer is very difficult. They really do an incredible range of tasks
from designing new technology, maintaining existing technology, selling products,
managing personnel and projects, running companies, etc. These tasks usually re-
quire a wide variety of skills, including fundamental knowledge of math, chemistry,
and physics; fundamental knowledge of an engineering discipline, written and oral
communication ability, and broad knowledge of humanistic knowledge.
It really is impossible for any four year educational institution to give each student
detailed preparation for EVERY possible contingency that you may be faced with in
an engineering career. It cannot be done, and it would be foolish to try. What
we can do is focus on some standards which are accepted throughout the engineeringcommunity and educate you for proficiency in those. To some what may seem artificial
and trivial, to others may be a fundamental core principle.
I play the piano, and there is an analogy between piano pedagogy and engineering
pedagogy. I have spent literally hours working on scales and arpeggios. They are not
fun, they are not particularly interesting musically, and certainly most people dont
want to hear them, especially when repeated and repeated. And yet to play Mozart
well, one really must get the discipline which is most easily acquired by doing the
preliminary exercises. I also played basketball in high school. Our practices focused
on calisthenics, drills, and wind sprints; scrimmage was a small part. Without these
however, our game would have suffered. The same analogy holds for figure skaters:
the beauty of Katerina Witts long program would not have been obtained without
the focus in practice on the fundamentals. I think you get the point.
You mention that some professors, including myself, say you probably wont be
doing [this] in your job, That is often a fact, to deny it would be dishonest. That
does not mean there is no value in learning such a task. Another fact is that you will
be doing SOMETHING, who knows what, and that something will probably require
you to know some aspect of engineering VERY well. A visiting faculty told me he washired as a consultant by some former students of his. He was not terribly impressed
with their performance in his fluids class ten years previously, but found working for
GE Gas Turbine Engines had considerably honed their fluids skills so that they were
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completely up to speed with him on most of the issues. These students DID need the
Strouhal number. Another group that should have learned the Strouhal number were
the engineers who designed the Tacoma Narrows Bridge, which collapsed because of
a Strouhal number effect. But it remains a fact that most engineers dont use theStrouhal number.
I remember well two contrasting conversations Ive had with graduates of our pro-
gram. The first was with Jim Weatherbee, ND 74, BSAE, who has piloted several
space shuttle missions. I asked him how much of his undergraduate education he has
had occasion to use. His reply was instant, Ive used all of it. Now, Weatherbee
was an unusually gifted student put into extraordinary circumstances, but that still
made me feel pretty good. I saw another former student, David, in the hallway as
he returned to campus for a football game. David had been in my fluids class, and
graduated with a roughly 2.4 GPA. I asked what he was doing now. Consulting
with a financial firm, was his reply. I asked him how often he got to use the fric-
tion factor and the rest of his engineering fundamentals. His reply was also instant:
Never. I then asked, with so many engineers going to non-traditional jobs, would
he recommend altering our education system to reflect that. Once again, instantly, he
said, Dont change a thing! He said that the problem solving skills, the work ethic,
and the fundamental thinking that an engineering education instills were extremely
valuable to him on his job. His supervisors recognized that, which is why they hired
engineers over seemingly better qualified business majors.I will conclude by reiterating the point I was trying to make in the e-lecture.
Understanding Strouhal numbers and friction factors can be useful, but even more,
understanding them gives evidence that there is a part of nature that we can un-
derstand and hope that there is more that can be understood. This spirit has led
engineers to fly to the moon, win the cold war, and build the internet. Theres more
to build.
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Limitations in our knowledge and
methods
Spring, 1999.
Knowledge in all the sciences is of two kinds: theoretical and empirical. Theformer comes from paper and pencil calculations while the latter is more based on
experimental observations. Fluid mechanics is especially well-placed to exemplify this
separation, as well as their unification and blending for the purposes of practical use.
Theoretical knowledge and methodology can also be of two kinds: analytical in which
closed-form solutions are obtained, and numerical where a computer code must be
used.
All knowledge is, at a fundamental level, empirical. We observe the world around
us and see things always happening a certain way. From this we formulate our basic
laws, examples of which are the laws of motion and those of thermodynamics. There
is no way to provethese laws; it is just the way nature is. Once we accept that, we can
use these laws to build up predictions for more complex situations. We use the tools
provided by mathematics, for instance, to calculate quantities that may be of interest.
One example of this procedure is CFD (Computational Fluid Dynamics) that uses
computational techniques (finite differences, finite elements, spectral methods, panel
methods, etc.) for flow calculations that can be used to help design a fluid machine.
If every fluid problem could be accurately and cheaply solved in this way, there would
be no need for experiments. Unfortunately, this is not so.There is one elementary reason why experimental information is needed: theoret-
ical models are useless without material properties like fluid viscosity, density, etc.
However that is not all; even if all information on properties were well known, not all
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problems are solvable by theoretical means. There are various reasons for this.
Analytical solutions of the differential governing equations are available only for
very few cases, and approximations can be obtained for some more. Even though
wherever closed form expressions for the calculated quantities exist they are
preferable to numerical computations, the range and variety of these solutions
are limited.
Computation may not be possible in a given problem. This is particularly true
for many turbulent flows for which the best that can be done is to replace
the governing equations with its time-averaged analog with plausible models
to take into account turbulence. In any case and in the best of circumstances
these models have free constants which have to be carefully calibrated against
experiments.
The cost of a computation may be too high. This happens if there is a wide
distribution of length or time scales in the problem. For example, if the ratio of
the largest to smallest length scale is of order 10 in a three-dimensional flow, a
computational mesh of at least 101010, i.e. 103, will be needed. Many of the
practical problems in the field involve scale ratios much larger than that which
cannot be solved at a reasonable cost. Such is the case for many laminar flows
and most turbulent ones. The cost of computation is based on the hardware
necessary to run the computational code and the time it takes for it to obtain
results. The hardware can range from a PC or a UNIX-based workstation all
the way up to a supercomputer where an hour of computer time could cost a
thousand dollars.
Computational results may not be obtained in real time. For control purposes,
for instance, it is important to have results in real time so that a stabilizing
signal can be applied.
The items above suggest that it is not always possible or practical to take ourbasic engineering laws and deduce from them analytically or numerically the desired
results. If this is so, why then do we teach or learn the theory? There are several
reasons for this.
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Numerical computations must be first validated against known analytical solu-
tions. If we write a computer code to do a certain job, the first solution that it
must be asked to obtain is one for which we have a known answer. If it can get
that, then there is a chance that it may be right in another problem for whichwe do not have the solution.
A similar situation exists with respect to experiments. If possible, the first time
the apparatus is run, the experimental results must be checked against known
results. These may be in the form of solutions obtained another way or by
previous experimenters. Instruments are often calibrated in this fashion.
For both numerical and experimental techniques, analytical solutions provide
an absolute benchmark against which they can be validated or calibrated and
the order of any error precisely determined.
Analytical solutions provide a physical understanding of the flow from which
much can be obtained. For example, it is known that for laminar flow the drag of
an object is proportional to the flow velocity. Neither numerical nor experimen-
tal techniques will give such precise information. This physical understanding
is often all that is necessary for a successful analysis or design.
What then are the advantages of numerical techniques? Let us summarize.
Numerical methods are of greater reach than analytical methods. For example,
analytical solutions exist for the drag of flow around a sphere for low Reynolds
numbers. This is the Stokes drag relation which is valid only for a Reynolds
number of order unity or below. Numerical methods can provide solutions for
higher Reynolds numbers even in the presence of separation behind the sphere
as long as the flow is laminar.
Numerical methods can be used where no exact or approximate solution is
available.
Once the computational code has been written and verified, it can be used over
and over again with little change. This has led to a number of commercial codes
in the market to solve general problems in fluid mechanics.
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Now we come to the advantages of experiments.
Experiments arereality. This cannot be overemphasized. The approximations
made in all theoretical approaches are not present here. Of course, there maybe other approximations if we are forced to carry out the experiment in a setup
different from the one in which we actually want the answer. The size or some
other factor may be different.
Turbulence is dealt with in a much easier fashion. Using modern tools like the
hot-wire anemometer, laser doppler anemometer, or particle image velocimeter,
detailed spatial and time distributions of the velocity can be obtained.
Parametric variations are sometimes much easier. If, for example, one is inter-
ested in the drag coefficient on a sphere as a function of Reynolds number, one
merely has to run the experiment for measuring the drag force the desired num-
ber of times. Each experiment does not take long. In a numerical method also
the runs have to be repeated many times, but the computational time increases
as the Reynolds number goes up.
One can thus look upon the triad of techniques, analytical, numerical and ex-
perimental, as complementing rather than substituting for each other. Often, if the
prediction is critical, two or three of the approaches will be used, the most common
being the numerical with the experimental. If they confirm each other, one can be
reasonably sure that the results are right. From that point on one can use whichever
method is cheaper to provide an accurate answer.
The last issue that I would like to discuss today is the limitations on our theo-
retical knowledge. If we are to blend theoretical and experimental approaches in real
life, we must be aware where knowledge of one kind ends and the other begins. The
undergraduate-level books often do not make this very clear, I have sometimes dis-
cussed experimental results with students who have assumed that whatever is given
in the textbook is accurate and that his or her experiment must be wrong. To takean example, let us look at the critical Reynolds number of 2300 for transition from
laminar to turbulent flow in a pipe (p. 37 in the book). What the book does not
say is that there is no theoretical basis for this number. All that it represents is an
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average value for a large number of experiments. In fact there is a wide divergence
in the results of these experiments due to entrance conditions and other disturbances
that may be present in the pipe. Some semesters students have obtained values of
1700 and in others 2800. There is nothing wrong in either value; what would bewrong is to discard ones answer which is dependent on what is actually happening
in favor of what the book says. To be fair, it is extremely difficult for you to question
a number provided by a source of certain authority, especially when it uses words
like pipe flow is laminar when Re 2300 . . ., but it is important to bear in mind
that the authority may possibly be wrong. Well not exactly wrong, but there are
complicated arguments that are, for reasons of simplicity, left out of the discussion in
the book. One of the main purposes of the fluid mechanics laboratory is for you to
learn the limitations of theory and the kind of information that can only be obtained
experimentally.
There is another kind of trap that one can get into in not looking at the fine
print in a book. Again, taking the example of Reynolds number, the critical value
of 2300 is only for pipe flow. In fact this is clearly mentioned in the text. However,
I have encountered many instances where the values have been assumed as holding
for all flows internal or external. I wish that fluid mechanics were so simple, but
it is not. The transition of a boundary layer from laminar to turbulent may occur
for a Reynolds number (based on distance from the leading edge) of around 5 105
(p. 413). In this case it turns out that the theory of the onset of turbulence isquite advanced and there is considerable theoretical overlap between theoretical and
experimental results.
The conclusion of this discussion is that neither theoretical nor experimental
knowledge is superior to the other but is merely complementary. One must be careful
to find out which is which, and also be aware of the exact boundaries of our knowl-
edge as well as those of the methods that we use to work with them. Only then can
we apply them appropriately to practical problems. Though here I have used fluid
mechanics as an example, the basic ideas are true for many of the disciplines that
you will see within engineering.
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Goodbye
Spring 2002
In the Spring of 1999 when these lectures were written, I had made some notes
to myself of topics to add in future versions. However, I have not taught the course
since then. Since this is something that I have not done, I leave them for you as ideasto think about.
Unconstrained by reality, what would a dream lab be, what hardware would it
have, and what would the students learn?
Rather than being a science, experimentation is an art with no unique answers.
These is a tendency to think of a lab as being just like a theory course, with the
only difference being that you have to generate the numbers experimentally to
do the homework. It is, however, more than that.
In these electronic lectures I have tried to tell you the reasons behind why we
teach things the way we do, and also what the objectives of this course are. Some
of the goals are tangible and clear while the others are not so. My hope is that
you have learned the tangibles and are well on your way towards the intangibles.
Learning to think, do and write clearly about something will be a lifelong need, and
fluid mechanics is merely an example. What you have learned in this course during
this semester is only a beginning. In the future I hope that you will have the time to
look back and the desire to build on it.
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