Patrick F. Dunn, Measurement, Data Analysis, and Sensor Fundamentals for Engineering and Science, 2nd Edition
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11.5.8 Temperature . . . . . . . . . . . . . . . . . . . . . . . 423
11.5.9 Other Properties . . . . . . . . . . . . . . . . . . . . . 424
11.6 Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
11.7 Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . 427
11.8 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 431
11.9 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 431
11.10 Homework Problems . . . . . . . . . . . . . . . . . . . . . . 433
Bibliography 437
12 *Technical Communication 439
12.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 439
12.2 Guidelines for Writing . . . . . . . . . . . . . . . . . . . . . . 440
12.2.1 Writing in General . . . . . . . . . . . . . . . . . . . . 440
12.2.2 Writing Technical Memoranda . . . . . . . . . . . . . 441
12.2.3 Number and Unit Formats . . . . . . . . . . . . . . . 443
12.2.4 Graphical Presentation . . . . . . . . . . . . . . . . . 444
12.3 Technical Memo . . . . . . . . . . . . . . . . . . . . . . . . . 447
12.4 Technical Report . . . . . . . . . . . . . . . . . . . . . . . . . 449
12.5 Oral Technical Presentation . . . . . . . . . . . . . . . . . . 451
12.6 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . 454
12.7 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . 454
12.8 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . 454
Bibliography 457
A Glossary 459
B Symbols 473
C Review Problem Answers 483
Index 485
Preface
This text covers the fundamental tools of experimentation that are currently
used by both engineers and scientists. These include the basics of experimen-
tation (types of experiments, units, and technical reporting), the hardware of
experiments (electronics, measurement system components, system calibra-
tion, and system response), and the methods of data analysis (probability,
statistics, uncertainty analysis, regression and correlation, signal characteri-
zation, and signal analysis). Historical perspectives also are provided in the
text.
This second edition of Measurement and Data Analysis for Engi-
neering and Science follows the original edition published by McGraw-Hill
in 2005. Since its first publication, the text has been used annually by over 30
universities and colleges within the U.S., both at the undergraduate and grad-
uate levels. The second edition has been condensed and reorganized following
the suggestions of students and instructors who have used the first edition.
The second edition differs from the first edition as follows:
• The number of text pages and the cost of the text have been reduced.
• All text material has been updated and corrected.
• The order of the chapters has been changed to reflect the sequence of
topics usually covered in an undergraduate class. Former Chapters 2
and 3 are now Chapters 11 and 12, respectively. Their topics (units
and technical communication) remain vital to the subject. However,
they often can be studied by students without covering the material in
lecture. Former Chapter 6 on measurement systems has been moved up
to Chapter 3. This immediately follows electronics, now Chapter 2.
• Some sections within chapters have been reorganized to make the text
easier to follow as an introductory undergraduate text. Some sections
now are denoted by asterisks, indicating that they typically are not
covered during lecture in an introductory undergraduate course. The
complete text, including the sections denoted by an asterisk, can be
used as an upper-level undergraduate or introductory graduate text.
• Over 150 new problems have been added, bringing the total to over
420 problems. A Problem Topic Summary now is included immediately
before the review and homework problems at the end of each chapter to
guide the instructor and student to specific problems by topic.
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• The text is now complemented by an extensive text web site for students
and instructors (www.nd.edu/∼pdunn/www.text/measurements.html).
Most appendices and some chapter features of the first edition have been
moved to this site. These include unit conversions (formerly Appendix
C), learning objectives (formerly Appendix D), review crossword puzzles
and solutions (formerly at the end of each chapter and Appendix F), dif-
ferential equation derivations (formerly Appendix I), laboratory exercise
descriptions (formerly Appendix H), MATLAB
r
sidebars with M-files
(formerly in each chapter), and homework data files. Instructors who
adopt the text for their course can receive a CD containing the review
problem/homework problem solutions manual, the laboratory exercise
solution manual, and a complete set of slide presentations for lecture
from Taylor & Francis / CRC Press.
Many people contributed to the first edition. They are acknowledged in the
first edition preface (see the text web site). Since then, further contributions
have been made by some of my Notre Dame engineering students, my senior
teaching assistants Dr. Michael Davis and Benjamin Mertz, and my colleagues
Professor Flint Thomas, Dr. Edmundo Corona, Professor Emeritus Raymond
Brach, Dr. Abdelmaged Ibrahim, and Professor David Go. Dr. Eric Matlis and
Mr. Leon Hluchota provided the instruments shown on the cover. Jonathan
Plant also has supported me as the editor of both editions.
Most importantly, each and every member of my family has always been
there with me along the way. This extends from my wife, Carol, who is happy
to see the second edition completed, to my grandson, Eliot, whose curiosity
will make him a great experimentalist.
Patrick F. Dunn
University of Notre Dame
Written while at the University of Notre Dame, Notre Dame, Indiana; the Uni-
versity of Notre Dame London Centre, London, England; and Delft University
of Technology, Delft, The Netherlands.
***********************
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Web: www.mathworks.com
Author
Patrick F. Dunn, Ph.D., P.E., is a professor of aerospace and mechanical
engineering at the University of Notre Dame, where he has been a faculty
member since 1985. Prior to 1985, he was a mechanical engineer at Argonne
National Laboratory from 1976 to 1985 and a postdoctoral fellow at Duke
University from 1974 to 1976. He earned his B.S., M.S., and Ph.D. degrees in
engineering from Purdue University (1970, 1971, and 1974). He is the author
of over 160 scientific journal and refereed symposia publications and a licensed
professional engineer in Indiana and Illinois. He is a Fellow of the American
Society of Mechanical Engineers and an Associate Fellow of the American
Institute of Aeronautics and Astronautics. He is the recipient of departmental,
college, and university teaching awards.
Professor Dunn’s scientific expertise is in fluid mechanics and micropar-
ticle behavior in flows. He is an experimentalist with over 40 years of expe-
rience involving measurement uncertainty. He is the author of the textbook
Measurement and Data Analysis for Engineering and Science (first
edition by McGraw-Hill, 2005; second edition by Taylor & Francis / CRC
Press, 2010), and Uncertainty Analysis for Forensic Science with R.M.
Brach (first and second editions by Lawyers & Judges Publishing Company,
2004 and 2009).
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1
Experiments
CONTENTS
1.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Role of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 The Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Experimental Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Classification of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Problem Topic Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7 Review Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.8 Homework Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
...there is a diminishing return from increased theoretical complexity and ...
in many practical situations the problem is not sufficiently well defined to
merit an elaborate approach. If basic scientific understanding is to be
improved, detailed experiments will be required ...
Graham B. Wallis. 1980. International Journal of Multiphase Flow 6:97.
The lesson is that no matter how plausible a theory seems to be, experiment
gets the final word.
Robert L. Park. 2000. Voodoo Science. New York: Oxford University Press.
Experiments essentially pose questions and seek answers. A good experiment
provides an unambiguous answer to a well-posed question.
Henry N. Pollack. 2003. Uncertain Science ... Uncertain World. Cambridge:
Cambridge University Press.
1.1 Chapter Overview
Experimentation has been part of the human experience ever since its begin-
ning. We are born with highly sophisticated data acquisition and computing
systems ready to experiment with the world around us. We come loaded with
1
2 Measurement and Data Analysis for Engineering and Science
the latest tactile, gustatory, auditory, olfactory, and optical sensor packages.
We also have a central processing unit capable of processing data and perform-
ing highly complex operations at incredible rates with a memory far surpassing
any that we can purchase.
One of our first rudimentary experiments, although not a conscious one,
is to cry and then to observe whether or not a parent will come to the aid
of our discomfort. We change the environment and record the result. We are
active participants in the process. Our view of reality is formed by what we
sense. But what really are experiments? What roles do they play in the process
of understanding the world in which we live? How are they classified? Such
questions are addressed in this chapter.
1.2 Role of Experiments
Perhaps the first question to ask is, “Why do we do experiments?” Some of
my former students have offered the following answers:
“Experiments are the basis of all theoretical predictions. Without experi-
ments, there would be no results, and without any tangible data, there is no
basis for any scientist or engineer to formulate a theory. ... The advancement
of culture and civilization depends on experiments which bring about new
technology... .” (P. Cuadra)
“Making predictions can serve as a guide to what we expect, ... but to
really learn and know what happens in reality, experiments must be done.”
(M. Clark)
“If theory predicted everything exactly, there would be no need for ex-
periments. NASA planners could spend an afternoon drawing up a mission
with their perfect computer models and then launch a flawlessly executed
mission that evening (of course, what would be the point of the mission, since
the perfect models could already predict behavior in space anyway?).” (A.
Manella)
In the most general sense, man seeks to reach a better understanding of
the world. In this quest, man relies upon the collective knowledge of his prede-
cessors and peers. If one understood everything about nature, there would be
no need for experiments. One could predict every outcome (at least for deter-
ministic systems). But that is not the case. Man’s understanding is imperfect.
Man needs to experiment in the world.
So how do experiments play a role in our process of understanding? The
Greeks were the earliest civilization that attempted to gain a better under-
standing of their world through observation and reasoning. Previous civiliza-
tions functioned within their environment by observing its behavior and then
adapting to it. It was the Greeks who first went beyond the stage of sim-
ple observation and attempted to arrive at the underlying physical causes of
Experiments 3
what they observed [1]. Two opposing schools emerged, both of which still
exist but in somewhat different forms. Plato (428-347 B.C.) advanced that
the highest degree of reality was that which men think by reasoning. He be-
lieved that better understanding followed from rational thought alone. This is
called rationalism. On the contrary, Aristotle (384-322 B.C.) believed that
the highest degree of reality is that which man perceives with his senses. He
argued that better understanding came through careful observation. This is
known as empiricism. Empiricism maintains that knowledge originates from
and is limited to concepts developed from sensory experience. Today it is
recognized that both approaches play important roles in advancing scientific
understanding.
There are several different roles that experiments play in the process of
scientific understanding. Harr´e [2], who discusses some of the landmark exper-
iments in science, describes three of the most important roles: inductivism,
fallibilism, and conventionalism. Inductivism is the process whereby the
laws and theories of nature are arrived at based upon the facts gained from the
experiments. In other words, a greater theoretical understanding of nature is
reached through induction. Taking the fallibilistic approach, experiments are
performed to test the validity of a conjecture. The conjecture is rejected if the
experiments show it to be false. The role of experiments in the conventionalis-
tic approach is illustrative. These experiments do not induce laws or disprove
hypotheses but rather show us a more useful or illuminating description of
nature. Testings fall into the category of conventionalistic experiments.
All three of these approaches are elements of the scientific method.
Credit for its formalization often is given to Francis Bacon (1561-1626). The
seeds of experimental science were sown earlier by Roger Bacon (c. 1220-1292),
who was not related to Francis. Roger attempted to incorporate experimental
science into the university curriculum but was prohibited by Pope Clement IV.
He wrote of his findings in secrecy. Roger is considered “the most celebrated
scientist of the Middle Ages.” [3] Francis argued that our understanding of
nature could be increased through a disciplined and orderly approach in an-
swering scientific questions. This approach involved experiments, done in a
systematic and rigorous manner, with the goal of arriving at a broader the-
oretical understanding. Using the approach of Francis Bacon’s time, first the
results of positive experiments and observations are gathered and considered.
A preliminary hypothesis is formed. All rival hypotheses are tested for possible
validity. Hopefully, only one correct hypothesis remains. Today the scientific
method is used mainly to validate a particular hypothesis or to determine
the range of validity of a hypothesis. In the end, it is the constant interplay
between experiment and theory that leads to advancing our understanding, as
illustrated schematically in Figure 1.1. The concept of the real world is devel-
oped from the data acquired through experiment and the theories constructed
to explain the observations. Often new experimental results improve theory
and new theories guide and suggest new experiments. Through this process,
a more refined and realistic concept of the world is developed. Anthony Lewis
4 Measurement and Data Analysis for Engineering and Science
summarizes it well, “The whole ethos of science is that any explanation for
the myriad mysteries in our universe is a theory, subject to challenge and
experiment. That is the scientific method.”
FIGURE 1.1
The interplay between experiment and theory.
Gale [4], in his treatise on science, advances that there are two goals of
science: explanation and understanding, and prediction and control. Science is
not absolute; it evolves. Its modern basis is the experimental method of proof.
Explanation and understanding encompass statements that make causal con-
nections. One example statement is that an increase in the temperature of a
perfect gas under constant volume causes an increase in its pressure. These
usually lead to an algorithm or law that relates the variables involved in
the process under investigation. Prediction and control establish correlations
between variables. For the previous example, these would result in the corre-
lation between pressure and temperature. Science is a process in which false
hypotheses are disproved and, eventually, the true one remains.
1.3 The Experiment
What exactly is an experiment? An experiment is an act in which one phys-
ically intervenes with the process under investigation and records the results.
This is shown schematically in Figure 1.2. Examine this definition more closely.
In an experiment one physically changes in an active manner the process be-
ing studied and then records the results of the change. Thus, computational
Experiments 5
simulations are not experiments. Likewise, sole observation of a process is not
an experiment. An astronomer charting the heavens does not alter the paths of
planetary bodies; he does not perform an experiment, rather he observes. An
anatomist who dissects something does not physically change a process (al-
though he physically may move anatomical parts); again, he observes. Yet, it is
through the interactive process of observation-experimentation-hypothesizing
that understanding advances. All elements of this process are essential. Tradi-
tionally, theory explains existing results and predicts new results; experiments
validate existing theory and gather results for refining theory.
FIGURE 1.2
The experiment.
When conducting an experiment, it is imperative to identify all the vari-
ables involved. Variables are those physical quantities involved in the pro-
cess under investigation that can undergo change during the experiment and
thereby affect the process. They are classified as independent, dependent,
and extraneous. An experimentalist manipulates the independent variable(s)
and records the effect on the dependent variable(s). An extraneous variable
cannot be controlled, but it affects the value of what is measured to some
extent. A controlled experiment is one in which all of the variables in-
volved in the process are identified and can be controlled. In reality, almost
all experiments have extraneous variables and, therefore, strictly are not con-
trolled. This inability to precisely control every variable is the primary source
of experimental uncertainty, which is considered in Chapter 7. The measured
variables are called measurands.
A variable that is either actively or passively fixed throughout the ex-
periment is called a parameter. Sometimes, a parameter can be a specific
function of variables. For example, the Reynolds number, which is a nondi-
mensional number used frequently in fluid mechanics, can be a parameter
in an experiment involving fluid flow. The Reynolds number is defined as
Re = ρUd/µ, where U is the fluid velocity, d is a characteristic length, ρ is
the fluid’s density, and µ is the fluid’s absolute viscosity. Measurements can be
made by conducting a number of experiments for various U, d, ρ, and µ. Then
the data can be organized for certain fixed values of Re, each corresponding
to a different experiment.
Consider for example a fluid flow experiment designed to ascertain whether
or not there is laminar (Poiseuille) flow through a smooth pipe. If lami-
nar flow is present, then theory (conservation of momentum) predicts that
∆p = 8QLµ/(πR
4
), where ∆p is the pressure difference between two locations