Fluid Mechanics: An Introduction to the Theory of Fluid Flows

728 Pages·2008·14.96 MB·English

by  Franz Durst

Fluid Mechanics
F. Durst
Fluid Mechanics
An Introduction to the Theory
of Fluid Flows
With347Figuresand13Tables
123
Prof.Dr.Dr.h.c. FranzDurst
FMPTechnologyGmbH
AmWeichselgarten34
91058Erlangen
Germany
[email protected]
English Translation:
Ingeborg Arnold
Fliederstrasse 40
66119Saarbrücken
Germany
[email protected]
ISBN:978-3-540-71342-5 e-ISBN:978-3-540-71343-2
LibraryofCongressControlNumber:2007937409
(cid:1)c 2008Springer-VerlagBerlinHeidelberg
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reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,
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This book is dedicated to my wife Heidi
and my sons Bodo Andr´e and Heiko Brian
and their families
Preface of German Edition
Some readers familiar with fluid mechanics who come across this book may
ask themselves why another textbook on the basics of fluid mechanics has
been written, in view of the fact that the market in this field seems to be
more than saturated. The author is quite conscious of this situation, but he
thinks all the same that this book is justified because it covers areas of fluid
mechanics which have not yet been discussed in existing texts, or only to
some extent, in the way treated here.
Whenlookingatthetextbooksavailableonthemarketthatgiveanintro-
duction into fluid mechanics, one realizes that there is hardly a text among
them that makes use of the entire mathematical knowledge of students and
that specifically shows the relationship between the knowledge obtained in
lectures on the basics of engineering mechanics or physics and modern fluid
mechanics.There has been no efforteither to activate this knowledge for ed-
ucationalpurposes in fluid mechanics.This book therefore attempts to show
specifically the existing relationships betweenthe abovefields, andmoreover
to explainthem ina waythat is understandableto everybody andmakingit
clear that the motions of fluid elements can be described by the same laws
as the movements of solid bodies in engineering mechanics or physics. The
tensor representation is used for describing the basic equations, showing the
advantages that this offers.
Thepresentbookonfluidmechanicsmakesanattempttogiveanintroduc-
tory structured representationof this special subject, which goes far beyond
the potential-theory considerations and the employment of the Bernoulli
equation, that often overburden the representations in fluid mechanics text-
books. The time when potential theory and energy considerations, based on
theBernoulliequation,hadtobethecenterofthefluidmechanicaleducation
ofstudents is gone.The developmentofmodernmeasuringandcomputation
techniques, that took place in the last quarter of the 20th century, up to the
application level, makes detailed fluid-flow investigations possible nowadays,
and for this aim students have to be educated.
vii
viii Preface
Using the basic education obtained in mathematics and physics, the
present book strives at an introduction into fluid mechanics in such a way
thateachchapterissuitedtoprovidethematerialforaone-weekortwo-week
lectures, depending on the educational and knowledge level of the students.
Thestructureofthebookhelpsstudents,whowanttofamiliarizethemselves
with fluid mechanics, to recognize the material which they should study in
addition to the lectures to become acquainted, chapter by chapter, with the
entire field of fluid mechanics. Moreover, the present text is also suited to
study fluid mechanics on one’s own. Each chapter is an introduction into a
subfield of fluid mechanics. Having acquired the substance of one chapter,
it is easier to read more profound books on the same subfield, or to pursue
advanced education by reading conference and journal publications.
In the description of the basic and most important fluid characteristic
for fluid mechanics, the viscosity, much emphasis is given so that its physi-
cal cause is understood clearly. The molecular-causedmomentum transport,
leadingto theτ -terms inthe basic fluidmechanicalequations,is dealtwith
ij
analogously to the molecular-dependent heat conduction and mass diffusion
in fluids. Explaining viscosity by internal “fluid friction” is physically wrong
andisthereforenotdealtwithinthisforminthebook.Thistextismeantto
contributeso thatreadersfamiliarizingthemselveswith fluidmechanicsgain
quick access to this special subject through physically correctly presented
fluid flows.
The present book is based on the lectures given by the author at the
University of Erlangen-Nu¨rnberg as an introduction into fluid mechanics.
Many students have contributed greatly to the compilation of this book by
referring to unclarified points in the lecture manuscripts. I should like to
express my thanks for that. I am also very grateful to the staff of the Fluid
MechanicsChairwhosupportedmeinthecompilationandfinalproof-reading
of the book and without whom the finalization of the book would not have
been possible. My sincere thanks go to Dr.-Ing. C. Bartels, Dipl.-Ing. A.
Schneider, Dipl.-Ing. M. Glu¨ck for their intense reading of the book. I owe
special thanks to Mrs. I.V. Paulus, as without her help the final form of the
book would not have come about.
Erlangen, Franz Durst
February 2006
Preface of English Edition
Fluidmechanicsisastillgrowingsubject,duetoitswideapplicationinengi-
neering, science and medicine. This wide interest makes it necessary to have
a book available that provides an overall introduction into the subject and
covers, at the same time, many of the phenomena that fluid flows show for
different boundary conditions. The present book has been written with this
aim in mind. It gives an overview of fluid flows that occur in our natural
and technical environment. The mathematical and physical background is
providedas a soundbasis to treatfluid flows.Tensor notationis used,andit
is explainedas being the bestwayto expressthe basiclawsthatgovernfluid
motions, i.e. the continuity, the momentum and the energy equations.These
equationsarederivedinthebookinagenerallyapplicablemanner,takingba-
sickinematicsknowledgeoffluidmotionintoaccount.Particularattentionis
giventothe derivationsofthe moleculartransportterms formomentumand
heat. In this way, the generally formulated momentum equations are turned
into the well-known Navier–Stokes equations. These equations are then ap-
plied, in a relatively systematic manner, to provide introductions into fields
such as hydro- and aerostatics, the theory of similarity and the treatment
of engineering flow problems, using the integral form of the basic equations.
Potential flows are treated in an introductory way and so are wave motions
thatoccurinfluid flows.The fundamentalsofgasdynamicsarecovered,and
the treatment of steady and unsteady viscous flows is described. Low and
high Reynolds number flows are treated when they are laminar, but their
transitionto turbulence is alsocovered.Particularattentionis givento flows
that are turbulent, due to their importance in many technical applications.
Their statisticaltreatmentreceivesparticularattention,andanintroduction
into the basics of turbulence modeling is provided. Together with the treat-
mentofnumericalmethods,thepresentbookprovidesthereaderwithagood
foundation to understand the wide field of modern fluid mechanics. In the
finalsections,the treatmentof flowswith heat transferis touchedupon, and
an introduction into fluid-flow measuring techniques is given.
ix
x Preface
On the above basis, the present book provides, in a systematic manner,
introductions to important “subfields of fluid mechanics”, such as wave mo-
tions, gas dynamics, viscous laminar flows, turbulence, heat transfer, etc.
After readershavefamiliarizedthemselveswith these subjects,they willfind
it easy to read more advanced and specialized books on each of the treated
specializedfields.Theywillalsobepreparedtoreadthevastnumberofpubli-
cationsavailableintheliterature,documentingthehighactivityinfluid-flow
research that is still taking place these days. Hence the present book is a
goodintroductionintofluidmechanicsasawhole,ratherthanintooneofits
many subfields.
The present book is a translation of a German edition entitled “Grundla-
genderStro¨mungsmechanik:EineEinfu¨hrungindieTheoriederStro¨mungen
von Fluiden”. The translation was carried out with the support of Ms. Inge
ArnoldofSaarbru¨cken,Germany.Hereffortstopublishthisbookaregreatly
appreciated. The final proof-reading was carried out by Mr. Phil Weston of
Folkestone in England. The author is grateful to Mr. Nishanth Dongari and
Mr.DominikHaspelforalltheireffortsinfinalizingthebook.Verysupportive
help was received in proof-readingdifferent chapters of the book. Especially,
the author would like to thank Dr.-Ing. Michael Breuer, Dr. Stefan Becker
and Prof. Ashutosh Sharma for reading particular chapters. The finalization
of the book was supported by Susanne Braun and Johanna Grasser. Many
students atthe UniversityofErlangen-Nu¨rnbergmadeuseful suggestionsfor
correctionsandimprovementsandcontributedinthis wayto the completion
of the English version of this book. Last but not least, many thanks need to
be given to Ms. Isolina Paulus and Mr. Franz Kaschak. Without their sup-
port,the presentbookwouldhavenotbeenfinalized.The author hopesthat
all these efforts were worthwhile, yielding a book that will find its way into
teachingadvancedfluidmechanicsinengineeringandnaturalsciencecourses
at universities.
March 2008 Franz Durst
Contents
1 Introduction, Importance and Development
of Fluid Mechanics ....................................... 1
1.1 Fluid Flows and their Significance....................... 1
1.2 Sub-Domains of Fluid Mechanics........................ 4
1.3 Historical Developments ............................... 9
References ................................................. 14
2 Mathematical Basics...................................... 15
2.1 Introduction and Definitions............................ 15
2.2 Tensors of Zero Order (Scalars)......................... 16
2.3 Tensors of First Order (Vectors) ........................ 17
2.4 Tensors of Second Order ............................... 21
2.5 Field Variables and Mathematical Operations ............ 23
2.6 Substantial Quantities and Substantial Derivative ......... 26
2.7 Gradient, Divergence, Rotation and Laplace Operators .... 27
2.8 Line, Surface and Volume Integrals...................... 29
2.9 Integral Laws of Stokes and Gauss ...................... 31
2.10 Differential Operators in Curvilinear Orthogonal
Coordinates .......................................... 32
2.11 Complex Numbers .................................... 36
2.11.1 Axiomatic Introduction to Complex Numbers ...... 37
2.11.2 Graphical Representation of Complex Numbers ..... 38
2.11.3 The Gauss Complex Number Plane ............... 39
2.11.4 Trigonometric Representation .................... 39
2.11.5 Stereographic Projection......................... 41
2.11.6 Elementary Function ............................ 42
References ................................................. 47
3 Physical Basics ........................................... 49
3.1 Solids and Fluids ..................................... 49
3.2 Molecular Properties and Quantities of Continuum
Mechanics ........................................... 51
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