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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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