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M. Hanif Chaudhry Applied Hydraulic Transients Third Edition Applied Hydraulic Transients M. Hanif Chaudhry Applied Hydraulic Transients Third Edition ISBN 978-1-4614-8537-7 ISBN 978-1-4614-8538-4 (eBook) DOI 10.1007/978-1-4614-8538-4 Springer New York Heidelberg Dordrecht London This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer 1 Download (/download/link/applied-hydraulic-transients-) is part of Springer Science+Business Media (www.springer.com) Library of Congress Control Number: M. Hanif Chaudhry College of Engineering and Computing University of South Carolina of the material is concerned, All materials on our website are shared by users. If you have any questions about copyright issues, please report (/document/report/appliedspecifically the rights 2013947167 Columbia, SC, USA © Author 1979, 1987, 2014 hydraulic-transients-) us to resolve them. We are always happy to assist you. To Shamim 216 APPLIED HYDRAULIC TRANSIENTS || Preface channels in a systematic and comprehensive manner from introduction to advanced level, with an views by m-hanif emphasis on the presentation of efficient and robust computational procedures for analysis and simulation. on Dec 12, 2016 Category: Download: 8 These procedures, based on modern numerical methods, are suitable for machine computations, provide more Report (/document/report/appliedComment: 0 DOCUMENTS accurate results as compared to the available traditional methods and allow the analysis of large and complex hydraulic-transients-) systems. The field of application is very broad and diverse and covers systems, such as hydroelectric power (/category/documents.html) plants, pumped storage schemes, water-supply systems, oil pipelines, cooling-water and industrial piping Comments systems. The book is suitable as a reference for practicing engineers and researchers and as a text for seniorlevel undergraduate and graduates students. Because of diverse nature, the material in each chapter is presented more or less as stand-alone. Practical applications are emphasized throughout by including case Description studies of real-life projects, problems of applied nature and photographs and design criteria. Design charts and Download Applied Hydraulic Transients || empirical formulas are presented in the appendix for approximate analyses and for comparing different alternatives for feasibility studies and preliminary design and for the selection of parameters for detailed Transcript analyses. Solved examples and sample computer programs are included to facilitate learning. SI units are used throughout. However, equivalent values of empirical constant in the Customary English units are provided M. Hanif Chaudhry Applied Hydraulic Transients Third Edition which should allow the use of these units without much difficulty. The general sequence of presentation in this Applied Hydraulic Transients third edition is similar to that in the earlier editions. However, revisions are made throughout for clarity and the M. Hanif Chaudhry Applied Hydraulic Transients Third Edition references are updated. A new chapter on leak and partial blockage detection is added. In each chapter, a ISBN 978-1-4614-8537-7 ISBN 978-1-4614-8538-4 (eBook) DOI 10.1007/978-1-4614-8538-4 Springer New York chapter-opener photograph is included as an illustrative introduction to the chapter. In Chapter 1, the historical Heidelberg Dordrecht London This work is subject to copyright. All rights are reserved by the Publisher, whether background is updated and a section on wave reflection and transmission is added. A new section introduces the whole or part of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on the Applied Hydraulic Transients covers transient flow in closed conduits and in open microfilms or in any other physical way, and transmission or information storage and retrieval, electronic VIII Preface inclusion of unsteady friction in the governing equations in Chapter 2 and the simulation of adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. unsteady friction and the application of higher-order numerical methods are presented in Chapter 3. Coverage Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material of the modeling of pump turbines is expanded in Chapter 5. A new section in Chapter 8 outlines the supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by determination of the functional significance of stenosis in cardiovascular systems. The material in Chapters 10, the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of 11, and 13 is revised and a new Chapter 12 discusses the detection of leaks and partial blockages in pipelines. the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be Design charts and other data are presented in Appendix A and sample computer programs in FORTRAN along obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance with sample input and output data are included in Appendices B through E. I have used Chapters 1 through 5 Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive and 10 as a textbook for a three-credit graduate course on hydraulic transients at Old Dominion University, names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence Washington State University and University of South Carolina. Different chapters or parts thereof may be used of a specific statement, that such names are exempt from the relevant protective laws and regulations and for instructional material for advanced level, specialized courses and workshops. Thanks are extended to therefore free for general use. While the advice and information in this book are believed to be true and accurate British Columbia Hydro and Power Authority and California Department of Water Resources for data and at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility prototype test results on their projects and to my former colleagues, R. E. Johnson for the instrumentation for for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect the prototype tests and R. M. Rockwell and J. Gurney for Figs. 5-11 and 5-29, and G. Vandenburg for Fig. 10to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media 4. Dr. Sam Martin generously provided technical advice, photographs, and figures. Assistance provided by my (www.springer.com) Library of Congress Control Number: M. Hanif Chaudhry College of Engineering and former graduate student, Dr. Elkholy, for the preparation of the manuscript, by Dr. Mohapatra for proofreading Computing University of South Carolina of the material is concerned, specifically the rights 2013947167 Columbia, the final draft, and by Rebecca Wessinger for the preparation of the figures for inclusion in the manuscript is SC, USA © Author 1979, 1987, 2014 thankfully acknowledged. Several individuals from all over the globe were very kind in providing photographs To Shamim and other material; these are acknowledged throughout the book. I am thankful to my family, especially our Preface channels in a systematic and comprehensive manner from introduction to advanced level, with an grandchildren, Aryaan, Amira, and Rohan, for many hours that should have been spent with them but were emphasis on the presentation of efficient and robust computational procedures for analysis and simulation. These required by the preparation of this edition. M. Hanif Chaudhry Columbia, SC, USA procedures, based on modern numerical methods, are suitable for machine computations, provide more accurate Contents 1 BASIC CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1-1 Introduction . . . . . . . . . . results as compared to the available traditional methods and allow the analysis of large and complex systems. The . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1-2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . field of application is very broad and diverse and covers systems, such as hydroelectric power plants, pumped . . . 2 1-3 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1-4 Basic Waterhammer storage schemes, water-supply systems, oil pipelines, cooling-water and industrial piping systems. The book is Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1-5 Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . suitable as a reference for practicing engineers and researchers and as a text for senior-level undergraduate and . . . . . 11 1-6 Wave Reflection and Transmission . . . . . . . . . . . . . . . . . . . . . . . . 15 1-7 Transient Flow Analysis . graduates students. Because of diverse nature, the material in each chapter is presented more or less as stand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1-8 Causes of Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . alone. Practical applications are emphasized throughout by including case studies of real-life projects, problems of . . . 19 1-9 System Design and Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1-10 Accidents and Incidents . applied nature and photographs and design criteria. Design charts and empirical formulas are presented in the . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1-11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . appendix for approximate analyses and for comparing different alternatives for feasibility studies and preliminary . . . . . 26 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References . . . . . . . . . design and for the selection of parameters for detailed analyses. Solved examples and sample computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2 TRANSIENT-FLOW EQUATIONS . . . . . . . . . . . . . . . . programs are included to facilitate learning. SI units are used throughout. However, equivalent values of empirical . . . . . . . 35 2-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2-2 Reynolds Transport constant in the Customary English units are provided which should allow the use of these units without much Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2-3 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . difficulty. The general sequence of presentation in this third edition is similar to that in the earlier editions. . . . . . 39 2-4 Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2-5 General Remarks . . . . . However, revisions are made throughout for clarity and the references are updated. A new chapter on leak and . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2-6 Wave Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . partial blockage detection is added. In each chapter, a chapter-opener photograph is included as an illustrative . . . . 49 2-7 Solution of Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . 54 2-8 Unsteady Friction . . . . . . . introduction to the chapter. In Chapter 1, the historical background is updated and a section on wave reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2-9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and transmission is added. A new section introduces the Applied Hydraulic Transients covers transient flow in . . . 59 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 References . . . . . . . . . . . closed conduits and in open . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3 CHARACTERISTICS AND FINITE-DIFFERENCE VIII Preface inclusion of unsteady friction in the governing equations in Chapter 2 and the simulation of unsteady METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3-1 Introduction . . . . . . . . . . . . . . . friction and the application of higher-order numerical methods are presented in Chapter 3. Coverage of the . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 modeling of pump turbines is expanded in Chapter 5. A new section in Chapter 8 outlines the determination of the X Contents 3-2 Characteristic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3-3 Boundary Conditions . functional significance of stenosis in cardiovascular systems. The material in Chapters 10, 11, and 13 is revised . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3-4 Convergence and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . and a new Chapter 12 discusses the detection of leaks and partial blockages in pipelines. Design charts and other . . . . 82 3-5 Method of Specified Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3-6 Computational Time data are presented in Appendix A and sample computer programs in FORTRAN along with sample input and Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3-7 Unsteady Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . output data are included in Appendices B through E. I have used Chapters 1 through 5 and 10 as a textbook for a . . . . 88 3-8 Explicit Finite-Dierence Method . . . . . . . . . . . . . . . . . . . . . . . . 92 3-9 General Remarks . . . . . . . . . three-credit graduate course on hydraulic transients at Old Dominion University, Washington State University and . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3-10 Implicit Finite-Dierence Method . . . . . . . . . . . . . . . . . . . . . . . . University of South Carolina. Different chapters or parts thereof may be used for instructional material for 98 3-11 Comparison of Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . 100 3-12 Analysis Procedure . . . . . . . advanced level, specialized courses and workshops. Thanks are extended to British Columbia Hydro and Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3-13 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Authority and California Department of Water Resources for data and prototype test results on their projects and . . . 104 3-14 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Problems . . . . . . . . . . . . to my former colleagues, R. E. Johnson for the instrumentation for the prototype tests and R. M. Rockwell and J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gurney for Figs. 5-11 and 5-29, and G. Vandenburg for Fig. 10-4. Dr. Sam Martin generously provided technical . . . . . . . . . . . . . . 110 4 TRANSIENTS IN PUMPING SYSTEMS . . . . . . . . . . . . . . . . . 115 4-1 Introduction . . . . advice, photographs, and figures. Assistance provided by my former graduate student, Dr. Elkholy, for the . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4-2 Pump Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . preparation of the manuscript, by Dr. Mohapatra for proofreading the final draft, and by Rebecca Wessinger for . . . . . . . . . . 116 4-3 Pump Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4-4 Power Failure . the preparation of the figures for inclusion in the manuscript is thankfully acknowledged. Several individuals from . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 4-5 Complex Systems . . . . . . . . . . . . . . . . . . . . . . . . . . all over the globe were very kind in providing photographs and other material; these are acknowledged throughout . . . . . . . . . . . . 133 4-6 Pump Start-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4-7 Design the book. I am thankful to my family, especially our grandchildren, Aryaan, Amira, and Rohan, for many hours that Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4-8 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . should have been spent with them but were required by the preparation of this edition. M. Hanif Chaudhry . . . . . . . . . . . . . . . . . . . 143 4-9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Columbia, SC, USA Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 References . . . . . . . . . . . . . . . . Contents 1 BASIC CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5 TRANSIENTS IN HYDROELECTRIC POWER PLANTS 155 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1-2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5-2 Hydroelectric Power Plant . . . . . . 1-3 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1-4 Basic Waterhammer Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5-3 Conduit System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 . . . . . . . . . . . . . . . . . . . . . 8 1-5 Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1-6 Wave 5-4 Hydraulic Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 5-5 Hydraulic Turbine Governor . . . Reflection and Transmission . . . . . . . . . . . . . . . . . . . . . . . . 15 1-7 Transient Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 5-6 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1-8 Causes of Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1-9 System 175 5-7 Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 5-8 Governing Stability . . . . . . Design and Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1-10 Accidents and Incidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5-9 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1-11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Problems . . . . . . 192 5-10 Pumped-Storage Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 5-11 Pump Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 5-12 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2 TRANSIENT-FLOW EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . 35 2-1 Introduction . . . . . . . . . . 207 5-13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2-2 Reynolds Transport Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2-3 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2-4 Momentum Equation . . . . . . . . . . . . . . . . . . . . . 216 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2-5 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents XI 6 TRANSIENTS IN COOLING-WATER SYSTEMS . . . . . . . . 221 6-1 Introduction . . . . . . . . . . . . . . . 45 2-6 Wave Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2-7 Solution of Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6-2 Cooling-Water Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2-8 Unsteady Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2-9 222 6-3 Causes of Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 6-4 Analysis Procedures . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 6-5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 . . 230 6-6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 Problems . . . . . . . . . . . . . . 3 CHARACTERISTICS AND FINITE-DIFFERENCE METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 . . . . . . . . . . . . 234 7 TRANSIENTS IN LONG OIL PIPELINES . . . . . . . . . . . . . . . 237 7-1 Introduction . . . . . . . . X Contents 3-2 Characteristic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3-3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 7-2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3-4 Convergence and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 7-3 Causes of Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7-4 Methods of 82 3-5 Method of Specified Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3-6 Computational Time Interval . . . . . Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 7-5 Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3-7 Unsteady Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3-8 . . . . . . . . . . . . . . 244 7-6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Problems . . Explicit Finite-Dierence Method . . . . . . . . . . . . . . . . . . . . . . . . 92 3-9 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3-10 Implicit Finite-Dierence Method . . . . . . . . . . . . . . . . . . . . . . . . 98 3-11 . . . . . . . . . . . . . . . . . . . . . . . . 247 8 PERIODIC FLOWS AND RESONANCE . . . . . . . . . . . . . . . . . 249 8-1 Comparison of Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . 100 3-12 Analysis Procedure . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 8-2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3-13 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3-14 . . . . . . . . . . . . . . . . . . . . . . . . . 250 8-3 Development of Periodic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 8Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Problems . . . . . . . . . . . . . . . . . . . . . . . . . 4 Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 8-5 Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 8-6 Transfer Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4 TRANSIENTS IN PUMPING SYSTEMS . . . . . . . . . . . . . . . . . 115 4-1 Introduction . . . . . . . . . . . . . . . . . . . . . 266 8-7 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 8-8 Spatial Variation of . . . . . . . . . . . . . . . . . . . . . . 116 4-2 Pump Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4-3 Pressure and Discharge . . . . . . . . . . . . . . . . 296 8-9 Pressure Nodes and Antinodes . . . . . . . . . . . . . . . . . . . . . Pump Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4-4 Power Failure . . . . . . . . . . . . . . . . . . . . . . . . . . 298 8-10 Resonant Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 8-11 Verification of . . . . . . . . . . . . . . . . . . . . . . 122 4-5 Complex Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4-6 Transfer-Matrix Method . . . . . . . . . . . . . . . . . . . . 304 8-12 Variable-Characteristics Pipeline . . . . . . . . . . . . . . . Pump Start-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4-7 Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 8-13 Stenosis in Human Cardiovascular System . . . . . . . . . . . . . . . . . 316 8-14 Case Study . . . . . . . . . . . . . . . . . . . . . . . . 142 4-8 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4-9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 8-15 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Problems . . . . . . . . . . . . . . . . . . . . . . . . .
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