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Problems for Biomedical Fluid Mechanics and Transport Phenomena
How does one deal with a moving control volume? What is the best way to make a complex
biological transport problem tractable? Which principles need to be applied to solve a given
problem? How do you know whether your answer makes sense?
This unique resource provides over 200 well-tested biomedical engineering problems that
can be used as classroom and homework assignments, quiz material, and exam questions.
Questions are drawn from a wide range of topics, covering fluid mechanics, mass transfer,
and heat transfer applications. These problems, which are motivated by the philosophy that
mastery of biotransport is learned by practice, will aid students in developing the key skills
of determining which principles to apply and how to apply them.
Each chapter starts with basic problems and progresses to more difficult questions.
Lists of material properties, governing equations, and charts provided in the appendices
make this book a fully self-contained resource. Solutions to problems are provided
online for instructors.
Mark Johnson is Professor of Biomedical Engineering, Mechanical Engineering, and
Ophthalmology at Northwestern University. He has made substantial contributions to the
study of the pathogenesis of glaucoma and of age-related macular degeneration of the retina.
His academic interests include biofluid and biotransport issues, especially those related to
ocular biomechanics.
C. Ross Ethier holds the Lawrence L. Gellerstedt, Jr. Chair in Bioengineering and is a
Georgia Research Alliance Eminent Scholar in Biomechanics and Mechanobiology at
Georgia Tech and Emory University. His academic interests include cell and tissue
biomechanics and mechanobiology. He is co-author of Introductory Biomechanics: From
Cells to Organisms, one of the Cambridge Texts in Biomedical Engineering.
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© in this web service Cambridge University Press
Cambridge University Press
978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
Frontmatter
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CAMBRIDGE TEXTS IN BIOMEDICAL ENGINEERING
Series Editors
W. Mark Saltzman, Yale University
Shu Chien, University of California, San Diego
Series Advisors
Jerry Collins, Alabama A & M University
Robert Malkin, Duke University
Kathy Ferrara, University of California, Davis
Nicholas Peppas, University of Texas, Austin
Roger Kamm, Massachusetts Institute of Technology
Masaaki Sato, Tohoku University, Japan
Christine Schmidt, University of Texas, Austin
George Truskey, Duke University
Douglas Lauffenburger Massachusetts Institute of Technology
Cambridge Texts in Biomedical Engineering provide a forum for high-quality
textbooks targeted at undergraduate and graduate courses in biomedical engineering.
It covers a broad range of biomedical engineering topics from introductory texts to
advanced topics, including biomechanics, physiology, biomedical instrumentation,
imaging, signals and systems, cell engineering, and bioinformatics, as well as other
relevant subjects, with a blending of theory and practice. While aiming primarily at
biomedical engineering students, this series is also suitable for courses in broader
disciplines in engineering, the life sciences and medicine.
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© in this web service Cambridge University Press
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978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
Frontmatter
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Problems for
Biomedical Fluid
Mechanics and
Transport Phenomena
Mark Johnson
Northwestern University, Illinois
C. Ross Ethier
Georgia Institute of Technology and Emory University
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© in this web service Cambridge University Press
Cambridge University Press
978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
Frontmatter
More information
University Printing House, Cambridge CB2 8BS, United Kingdom
Published in the United States of America by Cambridge University Press, New York
Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminating knowledge in the pursuit of
education, learning, and research at the highest international levels of excellence.
www.cambridge.org
Information on this title: www.cambridge.org/9781107037694
© M. Johnson and C. R. Ethier 2014
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2014
Printed and bound in the United States of America
A catalog record for this publication is available from the British Library
ISBN 978-1-107-03769-4 Hardback
Additional resources for this publication at www.cambridge.org/johnsonandethier
Cambridge University Press has no responsibility for the persistence or accuracy of
URLs for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
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© in this web service Cambridge University Press
Cambridge University Press
978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
Frontmatter
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To my wife, son, parents, and family,
and to my mentors, colleagues, and students,
who have all in their own ways contributed to this book
Mark Johnson
To my students, colleagues, and family,
who have all taught me so much.
C. Ross Ethier
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© in this web service Cambridge University Press
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978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
Frontmatter
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“A tremendously valuable resource for bioengineering students and instructors that contains
problems scaling from the molecular to whole body level. Nearly every system in the body is
included, as well as a variety of clinically and industrially relevant situations. The problems
are aimed at instruction in applying basic physical principles in a variety of settings, and
include entertaining topics such as squid swimming, elephant ear heat transfer, whistling to
spread germs, and air friction over a bicyclist. What fun!”
James E. Moore Jr., Imperial College London
“The problems and solutions represent an invaluable resource for instructors. In addition,
the step-by-step procedure described in section 1.3 is a wonderfully insightful reminder of
what students really need to know to be successful in solving fluid mechanics problems.
Instructors would do well to teach this procedure at the beginning and to refer to it
consistently throughout the course.”
M. Keith Sharp, University of Louisville
“A book devoted solely to biologically relevant problems in fluid mechanics and transport is
a very welcome addition to the teaching armamentarium in this area. Problems related to
cardiovascular, respiratory and ocular physiology are emphasized, deriving from the
substantial research expertise of the authors. The problems are very interesting and in many
cases very challenging. They cover a range of difficulty that should be appropriate for both
undergraduate and graduate level courses and more than enough topics to provide
substantial breadth. Overall excellent! Now I’m looking forward to working out my own
solutions and maybe peeking at the solution manual.”
John M. Tarbell, The City College of New York
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© in this web service Cambridge University Press
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978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
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Contents
Preface page ix
1 Problem solving 1
2 Conservation of mass and the Reynolds transport theorem 16
3 Steady and unsteady Bernoulli equation and momentum
conservation 23
4 Viscous flow 36
5 Momentum boundary layers 60
6 Piping systems, friction factors, and drag coefficients 66
7 Problems involving surface tension 70
8 Non-Newtonian blood flow 74
9 Dimensional analysis 80
10 Statistical mechanics 87
11 Steady diffusion and conduction 90
12 Unsteady diffusion and conduction 103
13 Convection of mass and heat 119
14 Concentration and thermal boundary layers 135
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Mark Johnson and C. Ross Ethier
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15 Mass and heat transfer coefficients 142
16 Osmotic pressure 151
Appendix A. Material properties of fluids 156
Appendix B. Transport equations 158
Appendix C. Charts 162
References 169
Permissions 171
viii Contents
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© in this web service Cambridge University Press
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978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
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Preface
This book arose out of a need that frequently faced us, namely coming up with
problems to use as homework in our classes and to use for quizzes. We have found
that many otherwise excellent textbooks in transport phenomena are deficient in
providing challenging but basic problems that teach the students to apply transport
principles and learn the crucial engineering skill of problem solving. A related
challenge is to find such problems that are relevant to biomedical engineering
students.
The problems included here arise from roughly the last 20–30 years of our
collective teaching experiences. Several of our problems have an ancestry in a
basic set of fluid mechanics problems first written by Ascher Shapiro at MIT and
later extended by Ain Sonin, also at MIT. Roger Kamm at MIT also generously
donated some of his problems that are particularly relevant to biomedical transport
phenomena. Thanks are due to Zdravka Cankova and Nirajan Rajkarnikar, who
helped with proof-reading of the text and provided solutions for many of the
problems.
For the most part, the problems in this book do not involve detailed mathematics
or theoretical derivations. Nor do they involve picking a formula to use and then
plugging in numbers to find an answer. Instead, most of the problems presented
require skills in problem solving. That is, much of the challenge in these problems
involves deciding how to approach them and what principle or principles to apply.
Students will need to understand how to pick a control volume, and that multiple
control volumes are necessary for some problems. How does one deal with a
moving control volume? How many principles need to be applied to solve a
given problem? How do you know whether your answer makes sense? Students
who are struggling or stuck on a particular problem will want to know how they
should proceed in such cases. The problems presented here will raise all of these
issues for students.
In the first chapter, we give general principles of problem solving, and present the
Reynolds transport theorem. We also show an example of how we would approach
and solve one problem. However, problem solving is best learned by doing prob-
lems. Seeing someone else solve a problem is not nearly as educational. We hope
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978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
Frontmatter
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that we have provided a wide variety of problems in different areas of transport
phenomena, most at the basic level, that aids in the development of problem-solving
skills for students in these areas. Each chapter of problems is organized such that the
easier problems are at the beginning of the chapter, and then the problems become
progressively harder. The exception to this rule is that heat transfer problems are to
be found at the end of each chapter.
x Preface
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© in this web service Cambridge University Press
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978-1-107-03769-4 - Problems for Biomedical Fluid Mechanics and Transport Phenomena
Mark Johnson and C. Ross Ethier
Frontmatter
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