Fluid mechanics demystified

Fluid Mechanics

Demystifi ed

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Fluid Mechanics

Demystifi ed

Merle C. Potter, Ph.D.

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ABOUT THE AUTHOR

Merle C. Potter, Ph.D., taught fluid mechanics for 42 years at Michigan Tech, The

University of Michigan, and Michigan State University. He is the author of several

engineering books, including Thermodynamics Demystified. Dr. Potter’s research

has been in theoretical and experimental fluid mechanics and energy analysis of

buildings. He has received several teaching awards including the 2008 American

Society of Mechanical Engineer’s James Harry Potter Gold Medal.

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CONTENTS

Preface xi

CHAPTER 1 The Essentials 1

1.1 Dimensions, Units, and Physical Quantities 2

1.2 Gases and Liquids 5

1.3 Pressure and Temperature 6

1.4 Properties of Fluids 8

1.5 Thermodynamic Properties and Relationships 14

Quiz No. 1 17

Quiz No. 2 19

CHAPTER 2 Fluid Statics 21

2.1 Pressure Variation 21

2.2 Manometers 25

2.3 Forces on Plane and Curved Surfaces 27

2.4 Accelerating Containers 32

Quiz No. 1 37

Quiz No. 2 40

CHAPTER 3 Fluids in Motion 43

3.1 Fluid Motion 44

3.2 Classifi cation of Fluid Flows 50

3.3 Bernoulli’s Equation 56

Quiz No. 1 62

Quiz No. 2 65

CHAPTER 4 The Integral Equations 67

4.1 System-to-Control-Volume Transformation 68

4.2 Continuity Equation 71

4.3 The Energy Equation 73

4.4 The Momentum Equation 78

Quiz No. 1 86

Quiz No. 2 89

CHAPTER 5 The Differential Equations 91

5.1 The Boundary-Value Problem 92

5.2 The Differential Continuity Equation 92

5.3 The Navier-Stokes Equations 97

5.4 The Differential Energy Equation 104

Quiz No. 1 105

Quiz No. 2 106

CHAPTER 6 Dimensional Analysis and Similitude 107

6.1 Dimensional Analysis 108

6.2 Similitude 116

Quiz No. 1 120

Quiz No. 2 122

CHAPTER 7 Internal Flows 125

7.1 Entrance Flow 125

7.2 Laminar Flow in a Pipe 128

7.3 Laminar Flow Between Parallel Plates 133

7.4 Laminar Flow Between Rotating Cylinders 138

7.5 Turbulent Flow in a Pipe 143

7.6 Open Channel Flow 156

Quiz No. 1 159

Quiz No. 2 161

CHAPTER 8 External Flows 163

8.1 Basics 163

8.2 Flow Around Blunt Bodies 165

8.3 Flow Around Airfoils 173

viii Fluid Mechanics Demystifi ed

8.4 Potential Flow 175

8.5 Boundary-Layer Flow 184

Quiz No. 1 198

Quiz No. 2 201

CHAPTER 9 Compressible Flows 203

9.1 Basics 204

9.2 Speed of Sound 205

9.3 Isentropic Nozzle Flow 208

9.4 Normal Shock Waves 214

9.5 Oblique Shock Waves 219

9.6 Expansion Waves 224

Quiz No. 1 227

Quiz No. 2 229

APPENDIX A Units and Conversions 231

APPENDIX B Vector Relationships 235

APPENDIX C Fluid Properties 237

APPENDIX D Compressible Flow Table for Air 245

Final Exams 255

Solutions to Quizzes and Final Exams 265

Index 299

Contents ix

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PREFACE

This book is intended to accompany a text used in that first course in fluid

mechanics that is required in all mechanical engineering and civil engineering

departments, as well as several other departments. It provides a succinct

presentation of the material so that students more easily understand the difficult

parts. Many fluid mechanics texts are very long and it is often difficult to

ferret out the essentials due to the excessive verbiage. This book presents those

essentials.

We have included a derivation of the Navier-Stokes equations with several solved

flows. It is not necessary, however, to include them if the elemental approach is

selected. Either method can be used to study laminar flow in pipes, channels,

between rotating cylinders, and in laminar boundary layer flow.

The basic principles upon which a study of fluid mechanics is based are illustrated

with numerous examples and practice exams that allow students to develop their

problem-solving skills. The solutions to all problems in the practice exams are

included at the end of the book. Examples and problems are presented using SI

metric units.

The practice exams at the end of each chapter contain four-part, multiple-choice

problems similar to those found on national exams, such as the Fundamentals of

Engineering exam (the first of two exams required in the engineering registration

process) or the Graduate Record Exam (required when applying for most graduate

schools). There are also partial-credit practice exams at the end of each chapter.

Engineering courses do not, in general, utilize multiple-choice exams but it is quite

important that students gain experience in taking such exams. This book allows that

experience, if desired. If one correctly answers 50% or more multiple-choice questions

correctly, that is quite good.

The mathematics required is that of other engineering courses except that if the

study of the Navier-Stokes equations is selected then partial differential equations

are encountered. Some vector relations are used but not at a level beyond most

engineering curricula.

If you have comments, suggestions, or corrections or simply want to opine, please

email me at MerleCP@sbcglobal.net. It is impossible to write a book free of errors

but if we’re made aware of them, we can have them corrected in future printings.

So, please send me an email when you discover one.

Merle C. Potter P.E., Ph.D.

xii Preface

Fluid Mechanics

Demystifi ed

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