Fluid Mechanics in Channel, Pipe and Aerodynamic Design Geometries 2 Volume 3

308 Pages·2018·20.2 MB·English

by  Christina G. Georgantopoulou

Fluid Mechanics in Channel, Pipe and
Aerodynamic Design Geometries 2
...To our family

Depy
Andreas
Nikos
Giannis
Lilian

…as without their support none of this would have ever been possible for us
Engineering, Energy and Architecture Set
coordinated by
Lazaros E. Mavromatidis
Volume 3
Fluid Mechanics in Channel,
Pipe and Aerodynamic
Design Geometries 2

Christina G. Georgantopoulou
George A. Georgantopoulos
First published 2018 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
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ISTE Ltd John Wiley & Sons, Inc.
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© ISTE Ltd 2018
The rights of Christina G. Georgantopoulou and George A. Georgantopoulos to be identified as the
authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents
Act 1988.
Library of Congress Control Number: 2018932756

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-140-6
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Chapter 1. Pipe Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Calculation of pipe networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3. Problem-solving methodology for pipe networks . . . . . . . . . . . . . . . . . 10
1.4. Overall approach for the network calculation . . . . . . . . . . . . . . . . . . . 12
1.5. The Hazen–Williams equation for network analysis . . . . . . . . . . . . . . . 13
1.6. Hazen–Williams and Darcy–Weisbach identity . . . . . . . . . . . . . . . . . . 15
1.7. Hardy–Cross method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.8. Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.9. Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.10. Problems with solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.11. Problems to be solved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 2. Open Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2. Non-dimensional parameters in open channels . . . . . . . . . . . . . . . . . . 58
2.3. Open channel types of flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4. Open channels’ geometrical shapes . . . . . . . . . . . . . . . . . . . . . . . . 61
2.4.1. Channels of rectangular cross-sectional area . . . . . . . . . . . . . . . . . 61
2.4.2. Channels of trapezoidal cross-sectional area . . . . . . . . . . . . . . . . . 62
2.4.3. Channels of circular cross-sectional area . . . . . . . . . . . . . . . . . . . 63
2.5. The hydraulic jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.6. Calculation of the depth flow after the hydraulic jump . . . . . . . . . . . . . . 65
2.7. Velocity distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.8. Velocity distribution at the vertical level . . . . . . . . . . . . . . . . . . . . . 68
2.9. Uniform flow in open channel equations – Chezy type . . . . . . . . . . . . . 70
vi Fluid Mechanics 2
2.10. Best hydraulic cross-sectional area . . . . . . . . . . . . . . . . . . . . . . . . 75
2.11. Specific flow energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.12. Channels of rectangular cross-sectional area . . . . . . . . . . . . . . . . . . . 80
2.13. Open channels’ more adequate cross-sectional areas . . . . . . . . . . . . . . 83
2.13.1. Rectangular cross-sectional area . . . . . . . . . . . . . . . . . . . . . . . 83
2.13.2. Trapezoidal cross-sectional area . . . . . . . . . . . . . . . . . . . . . . . 85
2.14. Non-uniform flow in open channels . . . . . . . . . . . . . . . . . . . . . . . 88
2.15. Channels of non-rectangular cross-section area . . . . . . . . . . . . . . . . . 90
2.16. Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2.16.1. Channels of rectangular cross-sectional area formulae . . . . . . . . . . . 93
2.16.2. Channels of trapezoidal cross-section formulae . . . . . . . . . . . . . . 93
2.16.3. Channels of circular cross-sectional area formulae . . . . . . . . . . . . . 94
2.16.4. Channels of rectangular cross-sectional area formulae . . . . . . . . . . . 99
2.16.5. Channels of non-rectangular cross-sectional area formulae . . . . . . . . 100
2.17. Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2.18. Problems with solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
2.19. Problems to be solved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Chapter 3. Boundary Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.2. Laminar incompressible boundary layer . . . . . . . . . . . . . . . . . . . . . . 120
3.3. Characteristic values of the boundary layer . . . . . . . . . . . . . . . . . . . . 125
3.3.1. Thickness δ of the boundary layer . . . . . . . . . . . . . . . . . . . . . . . 125
3.3.2. The thickness displacement δ′ . . . . . . . . . . . . . . . . . . . . . . . . 126
1
3.4. Flow types in the boundary layer . . . . . . . . . . . . . . . . . . . . . . . . . . 127
3.5. Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.6. Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.7. Problems with solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.8. Problems to be solved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Chapter 4. Flow Around Solid Bodies . . . . . . . . . . . . . . . . . . . . . . . . 147
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.2. Geometrical characteristics of an airfoil . . . . . . . . . . . . . . . . . . . . . . 148
4.3. Kutta–Joukowski equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.4. Aerodynamic paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
4.5. Pressure distribution in an airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.6. Lift curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.7. Drag force and drag coefficient curve . . . . . . . . . . . . . . . . . . . . . . . 158
4.7.1. Drag of skin friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.7.2. Form drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
4.7.3. Induced drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Contents vii
4.8. Parameters that influence the drag coefficient C . . . . . . . . . . . . . . . . . 163
D
4.8.1. Dependence of C on the body’s shape . . . . . . . . . . . . . . . . . . . . 163
D
4.8.2. Dependence of C on relative roughness . . . . . . . . . . . . . . . . . . . 165
D
4.8.3. Dependence of C on the Reynolds number . . . . . . . . . . . . . . . . . 170
D
4.9. External flow around industrial solid bodies . . . . . . . . . . . . . . . . . . . 177
4.9.1. Car’s motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
4.9.2. Surface vessel’s motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
4.9.3. Wind flow in ground constructions . . . . . . . . . . . . . . . . . . . . . . 179
4.9.4. Airplane’s motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
4.10. Drag in fluid drops and gas bubbles in creeping flow . . . . . . . . . . . . . . 190
4.11. Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
4.12. Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
4.13. Problems with solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
4.14. Problems to be solved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Appendix 1. Symbols and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Appendix 2. Tables and Diagrams of Natural Values . . . . . . . . . . . . . . 219
Appendix 3. Symbols and Basic Conversion Factors . . . . . . . . . . . . . . 237
Appendix 4. International Standard Atmosphere, SI Units . . . . . . . . . . 239
Appendix 5. International Standard Atmosphere, in BS . . . . . . . . . . . . 251
Appendix 6. NACA Airfoils’ Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 259
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289