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introduction to fluid mechanics.pdf

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    Front Matter
    About the Authors
    Preface
    List of Symbols
    Table of Contents
    Index
    Front Matter
    Table of Contents
    1. History of Fluid Mechanics
    1.1 Fluid Mechanics in Everyday Life
    1.2 The Beginning of Fluid Mechanics
    Index
    Front Matter
    Table of Contents
    2. Characteristics of a Fluid
    2.1 Fluid
    2.2 Units and Dimensions
    2.3 Density, Specific Gravity and Specific Volume
    2.4 Viscosity
    2.5 Surface Tension
    2.6 Compressibility
    2.7 Characteristics of a Perfect Gas
    2.8 Problems
    Index
    Front Matter
    Table of Contents
    3. Fluid Statics
    3.1 Pressure
    3.2 Forces Acting on the Vessel of Liquid
    3.3 Why Does a Ship Float?
    3.4 Relatively Stationary State
    3.5 Problems
    Index
    Front Matter
    Table of Contents
    4. Fundamentals of Flow
    4.1 Streamline and Stream Tube
    4.2 Steady Flow and Unsteady Flow
    4.3 Three-Dimensional, Two-Dimensional and One-Dimensional Flow
    4.4 Laminar Flow and Turbulent Flow
    4.5 Reynolds Number
    4.6 Incompressible and Compressible Fluids
    4.7 Rotation and Spinning of a Liquid
    4.8 Circulation
    4.9 Problems
    Index
    Front Matter
    Table of Contents
    5. One-Dimensional Flow: Mechanism for Conservation of Flow Properties
    5.1 Continuity Equation
    5.2 Conservation of Energy
    5.3 Conservation of Momentum
    5.4 Conservation of Angular Momentum
    5.5 Problems
    Index
    Front Matter
    Table of Contents
    6. Flow of Viscous Fluid
    6.1 Continuity Equation
    6.2 Navier-Stokes Equation
    6.3 Velocity Distribution of Laminar Flow
    6.4 Velocity Distribution of Turbulent Flow
    6.5 Boundary Layer
    6.6 Theory of Lubrication
    6.7 Problems
    Index
    Front Matter
    Table of Contents
    7. Flow in Pipes
    7.1 Flow in the Inlet Region
    7.2 Loss by Pipe Friction
    7.3 Frictional Loss on Pipes Other Than Circular Pipes
    7.4 Various Losses in Pipe Lines
    7.5 Pumping to Higher Levels
    7.6 Problems
    Index
    Front Matter
    Table of Contents
    8. Flow in a Water Channel
    8.1 Flow in an Open Channel with Constant Section and Flow Velocity
    8.2 Best Section Shape of an Open Channel
    8.3 Specific Energy
    8.4 Constant Discharge
    8.5 Constant Specific Energy
    8.6 Constant Water Depth
    8.7 Hydraulic Jump
    8.8 Problems
    Index
    Front Matter
    Table of Contents
    9. Drag and Lift
    9.1 Flows around a Body
    9.2 Forces Acting on a Body
    9.3 The Drag of a Body
    9.4 The Lift of a Body
    9.5 Cavitation
    9.6 Problems
    Index
    Front Matter
    Table of Contents
    10. Dimensional Analysis and Law of Similarity
    10.1 Dimensional Analysis
    10.2 Buckingham's pi Theorem
    10.3 Application Examples of Dimensional Analysis
    10.4 Law of Similarity
    10.5 Problems
    Index
    Front Matter
    Table of Contents
    11. Measurement of Flow Velocity and Flow Rate
    11.1 Measurement of Flow Velocity
    11.2 Measurement of Flow Discharge
    11.3 Problems
    Index
    Front Matter
    Table of Contents
    12. Flow of an Ideal Fluid
    12.1 Euler's Equation of Motion
    12.2 Velocity Potential
    12.3 Stream Function
    12.4 Complex Potential
    12.5 Example of Potential Flow
    12.6 Conformal Mapping
    12.7 Problems
    Index
    Front Matter
    Table of Contents
    13. Flow of a Compressible Fluid
    13.1 Thermodynamical Characteristics
    13.2 Sonic Velocity
    13.3 Mach Number
    13.4 Basic Equations for One-Dimensional Compressible Flow
    13.5 Isentropic Flow
    13.6 Shock Waves
    13.7 Fanno Flow and Rayleigh Flow
    13.8 Problems
    Index
    Front Matter
    Table of Contents
    14. Unsteady Flow
    14.1 Vibration of Liquid Column in U-Tube
    14.2 Propagation of Pressure in Pipe Line
    14.3 Transitional Change in Flow Quantity in a Pipe Line
    14.4 Velocity of Pressure Wave in a Pipe Line
    14.5 Water Hammer
    14.6 Problems
    Index
    Front Matter
    Table of Contents
    15. Computational Fluid Dynamics
    15.1 Finite Difference Method
    15.2 Finite Volume Method
    15.3 Finite Element Method
    15.4 Boundary Element Method
    Color Plates 1 - 3
    Index
    Front Matter
    Table of Contents
    16. Flow Visualisation
    16.1 Classification of Techniques
    16.2 Experimental Visualization Methods
    16.3 Computer-Aided Visualization Methods
    Color Plates 4 - 6
    Color Plates 7 - 9
    Color Plates 10 - 14
    Index
    Front Matter
    Table of Contents
    Answers to Problems
    Index
    Front Matter
    Table of Contents
    Index
    A
    B
    C
    D
    E
    F
    G
    H
    I
    J
    K
    L
    M
    N
    O
    P
    R
    S
    T
    U
    V
    W
    Z
    Introduction to Fluid Mechanics Y. NAKAYAMA Former Professor, Tokai University, Japan UKEditor R. F. BOUCHER Principal and ViceChancellor, UMIST, UK K E I N E M A N N OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI
    Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd a member of the Reed Elsevier plc group A This book is translated from Ryutai-no-Rikigaku (in Japanese) Published by YOKENDO CO. LTD 5-30-1 5, Hongo, Bunkyo-ku, Tokyo 11 3-0033, Japan 0 1998 by Yasuki Nakayama First published in English in Great Britain by Arnold 1999 Reprinted with revisions by Butterworth-Heinemann 2000 0 Y. Nakayama and R. F. Boucher 1999 All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England WlP 9HE. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publishers Whilst the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the publisher can accept any legal responsibility or liability for any errors or omissions that may be made. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress ISBN 0 340 67649 3 Commissioning Editor: Matthew Flynn Production Editor: Liz Gooster Production Controller: Sarah Kett Cover design: Terry Griffiths Typeset in 10/ 12 pt Times by AFS Image Setters Ltd, Glasgow Printed and bound in Great Britain by MPG, Bodmin, Cornwall
    About the authors Professor Yasuki Nskayama graduated from Waseda University and received his doctorate in mechanical engineering from the same university. He joined the National Railway Research Institute and conducted many research investigations in the area of fluid mechanics. He then became a Professor of Tokai University, Japan, where he taught and researched fluid mechanics and visualisation. He later became President of the Future Technology Research Institute, Japan. Professor Nakayama has received many distinctions and awards for his outstanding research. He has been a Visiting Professor of Southampton University, UK, President of The Visualisation Society of Japan, and Director of The Japan Society of Mechanical Engineers. He has published 10 books and more than 150 research papers. Professor Robert Boucher FEng studied mechanical engineering in London and at Nottingham University. He has held posts in the electricity industry and at the Universities of Nottingham, Belfast, Sheffield and at UMIST, where he is Principal & Vice-Chancellor. His research interests, published in over 120 papers, include flow measurement and visualisation, fluid transients and network simulation, magnetic separation, industrial ventilation and oil drilling technology.
    Preface This book was written as a textbook or guidebook on fluid mechanics for students or junior engineers studying mechanical or civil engineering. The recent progress in the science of visualisation and computational fluid dynamics is astounding. In this book, effort has been made to introduce students /engineers to fluid mechanics by making explanations easy to understand, including recent information and comparing the theories with actual phenomena. Fluid mechanics has hitherto been divided into ‘hydraulics’, dealing with the experimental side, and ‘hydrodynamics’, dealing with the theoretical side. In recent years, however, both have merged into an inseparable single science. A great deal was contributed by developments in the science of visualisation and by the progress in computational fluid dynamics using advances in computers. This book is written from this point of view. The following features are included in the book 1. Many illustrations, photographs and items of interest are presented for easy reading. 2. Portrait sketches of 17 selected pioneers who contributed to the development of fluid mechanics are inserted, together with brief descriptions of their achievements in the field. 3. Related major books and papers are presented in footnotes to facilitate advanced study. chapter topic. 4. Exercises appear at the ends of chapters to test understanding of the 5. Special emphasis is placed on flow visualisation and computational fluid dynamics by including 14 colour plates to assist understanding. Books and papers by senior scholars throughout the world are referenced, with special acknowledgements to some of them. Among these, Professor R. F. Boucher, one of my oldest friends, assumed the role of editor of the English edition and made numerous revisions and additions by checking the book minutely during his busy time as Principal and Vice-Chancellor of UMIST. Another is Professor K. Kanayama of Musashino Academia Musicae who made many suggestions as my private language adviser. In
    x Preface addition, Mr Matthew Flynn and Dr Liz Gooster of Arnold took much trouble over the tedious editing work. I take this opportunity to offer my deepest appreciation to them all. Yasuki Nakayama
    List of symbols area area (relatively small), velocity of sound width of channel width, thickness coefficient of discharge coefficient of contraction drag coefficient frictional drag coefficient lift coefficient moment coefficient coefficient of velocity integration constant, coefficient of Pitot tube, flow velocity coefficient specific heat at constant pressure specific heat at constant volume diameter, drag friction drag pressure drag, form drag diameter specific energy internal energy force Froude number coefficient of friction gravitational acceleration head head, clearance, loss of head, depth, enthalpy geometrical moment of inertia slope moment of inertia bulk modulus interference factor cavitation number length, power, lift
    xii List of symbols mass flow rate, mass (relatively small), strength of doublet, hydraulic mean depth polytropic exponent total pressure pressure stagnation pressure, total pressure, atmospheric pressure static pressure total pressure pressure unaffected by body, static pressure volumetric flow rate discharge quantity per unit time, quantity of heat per unit mass gas constant radius (at any position) radius specific gravity, entropy, wetted perimeter tension, absolute temperature, torque, thrust, period time velocity unaffected by body velocity (x-direction), peripheral velocity volume specific volume, mean velocity, velocity (y-direction), absolute velocity friction velocity velocity (z-direction), relative velocity acceleration, angle, coefficient of discharge compressibility I length, mixing length M mass, Mach number m n P p po ps pt pm Q q R Re Reynolds number r ro s T t U u V u v, W weight w w(z) complex potential ct /3 I' circulation, strength of vortex y 6 6* i vorticity q efficiency 6 angle, momentum thickness ratio of specific heat K i friction coefficient of pipe p p v p z 4 I) w specific weight boundary layer thickness displacement thickness coefficient of viscosity, dynamic viscosity kinematic viscosity, angle velocity potential shear stress angle, velocity potential stream function angular velocity
    History of fluid mechanics There is air around us, and there are rivers and seas near us. ‘The flow of a river never ceases to go past, nevertheless it is not the same water as before. Bubbles floating along on the stagnant water now vanish and then develop but have never remained.’ So stated Chohmei Kamo, the famous thirteenth- century essayist of Japan, in the prologue of Hohjohki, his collection of essays. In this way, the air and the water of rivers and seas are always moving. Such a movement of gas or liquid (collectively called ‘fluid’) is called the ‘flow’, and the study of this is ‘fluid mechanics’. While the flow of the air and the water of rivers and seas are flows of our concern, so also are the flows of water, sewage and gas in pipes, in irrigation canals, and around rockets, aircraft, express trains, automobiles and boats. And so too is the resistance which acts on such flows. Throwing baseballs and hitting golf balls are all acts of flow. Furthermore, the movement of people on the platform of a railway station or at the intersection of streets can be regarded as forms of flow. In a wider sense, the movement of social phenomena, information or history could be regarded as a flow, too. In this way, we are in so close a relationship to flow that the ‘fluid mechanics’ which studies flow is really a very familiar thing to us. The science of flow has been classified into hydraulics, which developed from experimental studies, and hydrodynamics, which developed through theoretical studies. In recent years, however, both have merged into the single discipline called fluid mechanics. Hydraulics developed as a purely empirical science with practical techniques beginning in prehistoric times. As our ancestors settled to engage in farming and their hamlets developed into villages, the continuous supply of a proper quantity of water and the transport of essential food and
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