Giới thiệu, nội dung môn học Cung cấp các kiến thức cơ bản về các qui luật cân bằng và chuyển động của lưu chất, về sự tương tác của lưu chất với các vật thể chuyển động trong lưu chất hoặc với các thành bao quanh. Ứng dụng các qui luật để tính toán các bài toán cơ bản của lưu chất. Thực hành trong phòng thí nghiệm để hiểu rõ các hiện tượng và các nguyên lý cơ bản của cơ lưu chất. Cơ Học Lưu chất là môn kỹ thuật cơ sở cho tất cả các ngành kỹ sư. Môn học nhằm trang bị cho sinh viên những kiến thức cơ bản về các quy luật cân bằng, chuyển động của lưu chất cũng như về sự tương tác của lưu chất với các vật thể di chuyển trong lưu chất hoặc với các thành rắn bao quanh. Môn học này đồng thời cũng trang bị cho sinh viên các phương pháp giải quyết những bài toán ứng dụng cơ bản trong các ngành kỹ thuật: Xây dựng, Thủy lợi, Cấp thoát nước, Hệ thống điện, Cơ khí, Hoá, Tự động thủy khí, Hàng không, Địa Chất - Dầu khí, Môi trường. Bên cạnh đó, sinh viên sẽ thực hiện các thí nghiệm để hiểu rõ các nguyên lý và các hiện tượng cơ bản của cơ lưu chất, làm quen với các thiết bị đo đạc dòng chảy trong phòng thí nghiệm. Ch 1: Mở đầu - Thông tin Thầy/Cô và các vấn đề liên quan đến việc dạy, học và thi - Giới thiệu môn học - Tính chất lưu chất Ch 2:Tĩnh học lưu chất - Các khái niệm về áp suất - Phương trình cơ bản tĩnh học - Tính toán áp suát - Tính toán áp lực lên thành phẳng Ch 2:Tĩnh học lưu chất (tiếp theo) - Tính toán áp lực lên thành cong. - Cân bằng vật trong lưu chất Ch 3: Động lực học lưu chất - Các khái niệm về chuyển động của lưu chất - Phương trình liên tục và các ứng dụng - Phương trình năng lượng Ch 3: Động lực học lưu chất (tiếp theo) - Các ứng dụng phương trình - Phương trình động lượng và các ứng dụng Thực hành -Thí nghiệm : Thủy tĩnh Ch 4: Dòng chảy đều trong ống - Các trạng thái chảy - Phương trình cơ bản và cấu trúc dòng chảy trong ống - Tổn thất năng lượng cục bộ và đường dài trong ống Thực hành -Thí nghiệm : Reynold Ch 4 : Dòng chảy đều trong ống (tiếp theo) - Các bài toán về dòng chảy trong ống : Thực hành – thí nghiệm: Phương trình năng lượng Ch 5: Dòng chảy đều trong kênh hở - Đặc tính dòng đều trong kênh - Tính toán độ sâu, vận tốc và lưu lượng - Thiết kế kênh Thực hành -Thí nghiệm : Dòng chảy qua lỗ Ch 6: Dòng chảy thế và lực nâng lực cản - Khái niệm dòng chảy thế và các định nghĩa hàm thế, hàm dòng. - Hàm thế hàm dòng các chuyển động thế cơ bản - Chồng chập các chuyển động thế và các ứng dụng Thực hành -Thí nghiệm : Mất năng trong ống Ch 6: Dòng chảy thế và lực nâng lực cản (tiếp theo) - Khái niệm về lực nâng lực cản - Đặc trưng dòng chảy bao quanh một vật - Lực cản do ma sát - Lực cản do áp suất - Thí dụ tính toán lực cản - Lực nâng : phân bố áp suất trên bề mặt và dòng chảy xoáy. - Các ví dụ tính toán lực nâng Thực hành -Thí nghiệm : Đo lưu lượng - Đo lưu lượng nước bằng bờ tràn mỏng, bằng ống Ventuary - Đo lưu lượng khí bằng qua lỗ thành mỏng Thí nghiệm – thực hành Thảo luận bài tập về dòng chảy trong ống Thí nghiệm – thực hành Thảo luận bài tập về dòng chảy đều trong ống Thí nghiệm – thực hành Thảo luận bài tập về dòng chảy đều trong kênh hở Thí nghiệm – thực hành Thảo luận bài tập về thế lưu – lực nâng và lực cản Thí nghiệm – thực hành Thảo luận tất cả bài tập trong các chương Kết quả cần đạt được Hiểu được các tính chất vật lý của lưu chất L.O.1.1 – Hiểu các tính chất vật lý của lưu chất như khối lượng, trọng lượng, tính nhớt, tính nén, tính mao dẫn. L.O.1.2 – Ứng dụng công thức Newton tính toán ma sát trên các bề mặt chuyển động. Hiểu được các phương trình cơ bản của lưu chất bao gồm phương trình tĩnh học, phương trình liên tục, phương trình năng lượng và phương trình động lượng L.O.2.1 – Hiểu các bản chất vật lý của phương trình L.O.2.2 – Điều kiện ứng dụng các phương trình Cách ứng dụng các phương trình cơ bản trong các bài toán thực tế L.O.3.1 – Tính toán áp suất và áp lực ở trạng thái tĩnh L.O.3.2 – Tính toán áp suất, vận tốc, năng lượng của dòng chảy lưu chất trong các bài toán thực tế Tính toán dòng chảy trong ống L.O.4.1 – Phân tích cấu trúc dòng chảy trong ống L.O.4.2 – Tính toán các tổn thất năng lượng trong ống L.O.4.3 – Tính toán các yếu tố dòng chảy trong ống (áp suất, vận tốc, năng lượng) Tính toán dòng chảy đều trong kênh hở L.O.5.1 – Đặc tính dòng chảy trong kênh L.O.5.2 – Tính toán độ sâu, vận tốc, lưu lượng dòng chảy trong kênh L.O.5.3 – Thiết kế kênh Dòng chảy thế và lực nâng lực cản L.O.6.1 – Khái niệm dòng chảy thế và hàm dòng hàm thế các chuyển động thế cơ bản L.O.6.2 – Ứng dụng các chuyển động thế L.O.6.3 – Khái niệm về lực nâng lực cản và đặc tính dòng chảy bao quanh vật L.O.6.4 Các công thức tính lực nâng và lực cản Thí nghiệm phân tích các ứng dụng của phương trình cơ bản lưu chất L.O.7.1 – Thí nghiệm phân tích các phương trình cơ bản của lưu chất. L.O.7.2 – Thí nghiệm phân tích dòng chảy trong ống, dòng chảy qua lỗ vòi L.O.7.3 – Thí nghiệm các thiết bị đo áp suất, lưu tốc, lưu lượng Khả năng thảo luận và phân tích các vấn đề liên quan đến cơ lưu chất L.O.8.1 – Hợp đồng nhóm thí nghiệm L.O.8.2 – Cách trình bày thuyết minh, báo cáo thí nghiệm L.O.8.3 – Cách lập luận dựa trên các kiến thức cơ bản để phân tích các vấn đề liên quan đến lưu chất. Tài liệu tham khảo [1] Nguyễn Ngọc Ẩn, Nguyễn Thị Bảy, Lê Song Giang, Huỳnh Công Hoài, Nguyễn Thị Phương. Giáo trình Cơ Lưu Chất . ĐH Bách Khoa, Năm 1998 [2] Nguyễn Ngọc Ẩn, Nguyễn Thị Bảy, Nguyễn Khắc Dũng, Lê Song Giang, Huỳnh Công Hoài, Nguyễn Thị Phương, Hồ Xuân Thịnh, Nguyễn Quốc Ý. Bài tập Cơ Lưu Chất. ĐH Bách Khoa, Năm 2011. Sách tham khảo: [1] Hoàng văn Quý và Nguyễn Cảnh Cầm. Thủy lực 1. NXB Giáo dục, 1973. [2] Nguyễn hữu Chí, Nguyễn hữu Dy, Phùng văn Khương, Bài tập Cơ học Chất lỏng ứng dụng. NXB Giáo Dục 1998 [3] Bruce R. Munson, Donald F.bYoung, Theodore H.Okiishi. E-book: Fundamentals of fluid mechanics. John Wiley & Sons Inc. 2006 [4] Subramanya.K. Theory and application of fluid mechanics. Mc.Graw - Hill 1993 Giáo trình/Textbook Cơ Lưu Chất - Ts Nguyễn Thị Bảy.Pdf Cơ Học Chất Lưu (Hoàng Bá Chư).Pdf Introduction To Fluid Mechanics_Robert W.For, Alan T. Mc_Donald.Pdf Cơ Ứng Dụng Cơ Lý Thuyết Sức Bền Vật Liệu
SIXTH EDITION ntroducti FLUID MECHANIC! Robert W Fox Alan T McDonald Philip J Pritchard T a b l e d S I Units a n d P r e f i x e s SI Symbol Formula meter kilogram second kelvin radian m kg s K rad — — — — — joule newton watt pascal joule J N W Pa J N-m kg • m/s J/s N/m N•m SI Units Quantity Unit SI base units: Length Mass Time Temperature Plane angle Energy Force Power Pressure Work SI supplementary unit: SI derived units: SI prefixes Multiplication Factor 12 000 000 000 000 = 10 000 000 000 = 10" 000 000 = 10 000 = 10 0.01 = io~ 0.001 = 10" 0.000 001 = 10" 0.000 000 001 = 10 0.000 000 000 001 = 10" 3 12 " Source: ASTM Standard for Metric Practice E - , 1997 To be avoided where possible b 2 Prefix SI Symbol tera giga mega kilo centi* mi Hi micro nana pico T G M k c m n P Table G.2 C o n v e r s i o n F a c t o r s a n d Definitions Fundamental Dimension English Unit Exact SI Value Approximate SI Value Length Mass Temperature in lbm 1°F 0.0254 m 0.453 592 37 kg 5/9 K — 0.454 kg — Definitions: Acceleration of gravity: Energy: Length: Power: Pressure: Temperature: K Viscosity: g = 9.8066 m/s ( = 32.174 ft/s ) Btu (British thermal unit) • amount of energy required to raise the temperature of lbm of water 1°F (1 Btu = 778.2 ft • lbf) kilocalorie = amount of energy required to raise the temperature of kg of water K ( l kcal = 4187 J) mile = 5280 ft; nautical mile = 6076.1 ft = 1852 m (exact) horsepower ^ 550 ft • lbf/s bar = 10 Pa degree Fahrenheit, 7V = | T c + 32 (where TQ is degrees Celsius) degree Rankine, R = 7p + 459.67 Kelvin, 7/ = T + 273.15 (exact) Poise = 0.1 kg/(m • s) Stoke ^ 0.0001 m /s gal = 231 in (1 ft = 7.48 gal) C Volume: 3 Useful Conversion Factors: lbf = 4.448 N lbf/in = 6895 Pa Btu = 1055 J hp = 746 W = 2545 Btu/hr kW = 3413 Btu/hr quart = 0.000946 m = 0.946 liter kcal = 3.968 Btu INTRODUCTION TO FLUID MECHANICS SIXTH EDITION R O B E R T W F O X Purdue Univefeity A L A N T M C D O N A L D Purdue University P H I L I P J P R I T C H A R D Manhattan College www.k-t-dra.com 5-t-dra G r u p o k-t-dra • G r u p o k-t-dra Diagonal 85A No 26-05 Polo Club • Fax: (571] 2! 87629 Tefefonos: 2570B95 • 6358137 «AA 93825 • Bogota DC Colombia • e-mail: lnfo@M-dra.com medellin@k-t-dra.com • Tel.: 3426194 • Medellin J O H N W I L E Y & S O N S , INC 13S422 On the Cover + Aerodynamics in action at speeds of 0 miles per hour! The cover photo shows the Formula Ferrari cars of World Driving Champion Michael Schumacher and his teammate Rubens Barrichello at the United States Grand Prix on September 29, 2002 The location is the road circuit of the Indianapolis Motor Speedway in Indianapolis, Indiana Similar Ferrari 1-2 finishes were seen at many racetracks throughout 2002 All modern racing cars use aerodynamic downforce (negative lift) to improve traction without adding significant weight to the car Using high downforce allows high cornering speeds on the twisting, turning road courses typical of Formula races The maximum downforce can exceed twice the weight of the car at 0 miles per hour straightaway speeds! Of course high downforce also causes high drag, which reduces straightaway speed, so a compromise is needed + The photo clearly shows some features of Schumacher's Ferrari Notable is the extensive use of aerodynamic devices designed to develop and control downforce The Ferrari's front wings are two-element designs They are made as large, and placed as far forward on the chassis, as the rules allow The rear wing appears to be a three-element design The rear wing also is made as large as the rules allow; it is placed as far rearward on the chassis as possible The side-mounted engine-cooling radiators are located in housings faired smoothly on the outside to minimize drag The radiator housings are designed with careful flow management inside to maximize the flow of cooling air Also visible are fairings to direct hot air from the radiators around the rear tires, and at the front of the car, cool air toward the brakes Details of underbody airflow management, commonly called "ground effects," are not so easily seen Airflow under the car is routed carefully, using diffusers designed to the limits of the rules, to develop the most negative pressure, and cause it to act over the largest possible area under the car, to develop additional downforce ACQUISITIONS EDITOR Wayne Anderson ASSOCIATE EDITOR Jennifer Welter MARKETING MANAGER Katherine Hepburn SENIOR PRODUCTION EDITOR Patricia McFadden SENIOR DESIGNER Madelyn Lesure PHOTO EDITOR Lisa Gee PRODUCTION MANAGEMENT SERVICES COVER PHOTO: © Wayne P Johnson Ingrao Associates This book was set in Times Roman by Progressive Information Technologies and printed and bound by RR Donneley and Sons The cover was printed by Lehigh Press, Inc This book is printed on acid-free paper © Copyright 2004© John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470 Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, E-Mail: PERMREQ@WTLEY.COM To order books please call l(800)-225-5945 ISBN 0-471-20231-2 WIE ISBN 0-471-37653-1 Printed in the United States of America 10 The cover photograph originally appeared in the January 2003 edition of Road & Track It is used by permission of the publisher, Hachette Filipacchi Media U.S., Inc PREFACE This text was written for an introductory course in fluid mechanics Our approach to the subject, as in previous editions, emphasizes the physical concepts of fluid mechanics and methods of analysis that begin from basic principles The primary objective of this book is to help users develop an orderly approach to problem solv ing Thus we always start from governing equations, state assumptions clearly, and try to relate mathematical results to corresponding physical behavior We emphasize the use of control volumes to maintain a practical problem-solving approach that is also theoretically inclusive This approach is illustrated by 116 example problems in the text Solutions to the example problems have been prepared to illustrate good solution technique and to explain difficult points of theory Example problems are set apart in format from the text so they are easy to identify and follow Forty-five example problems include Excel workbooks on the accompanying CD-ROM, making them useful for "What if?" analyses by students or by the instructor during class Additional important information about the text and our procedures is given in the "Note to Students" section on page of the printed text We urge you to study this section carefully and to integrate the suggested procedures into your problem solving and results-presentation approaches SI units are used in about 70 percent of both example and end-of-chapter prob lems English Engineering units are retained in the remaining problems to provide experience with this traditional system and to highlight conversions among unit sys tems that may be derived from fundamentals Complete explanations presented in the text, together with numerous detailed examples, make this book understandable for students This frees the instructor to de part from conventional lecture teaching methods Classroom time can be used to bring in outside material, expand upon special topics (such as non-Newtonian flow, boundary-layer flow, lift and drag, or experimental methods), solve example prob lems, or explain difficult points of assigned homework problems In addition, the 45 example problem Excel workbooks are useful for presenting a variety of fluid me chanics phenomena, especially the effects produced when varying input parameters Thus each class period can be used in the manner most appropriate to meet student needs The material has been selected carefully to include a broad range of topics suitable for a one- or two-semester course at the junior or senior level We assume a background in rigid-body dynamics and mathematics through differential equations A background in thermodynamics is desirable for studying compressible flow More advanced material, not typically covered in a first course, has been moved to the CD There the advanced material is available to interested users of the book; on the CD it does not interrupt the topic flow of the printed text iii iV PREFACE Material in the printed text has been organized into broad topic areas: • • • • • • • • Introductory concepts, scope of fluid mechanics, and fluid statics (Chapters 1, 2, and 3) Development and application of control volume forms of basic equations (Chapter 4) Development and application of differential forms of basic equations (Chapters and 6) Dimensional analysis and correlation of experimental data (Chapter 7) Applications for internal viscous incompressible flows (Chapter 8) Applications for external viscous incompressible flows (Chapter 9) Analysis of fluid machinery and system applications (Chapter 10) Analysis and applications of one- and two-dimensional compressible flows (Chapters 11 and 12) Chapter deals with analysis using both finite and differential control volumes The Bernoulli equation is derived (in an optional sub-section of Section 4-4) as an example application of the basic equations to a differential control volume Being able to use the Bernoulli equation in Chapter allows us to include more challenging problems dealing with the momentum equation for finite control volumes Another derivation of the Bernoulli equation is presented in Chapter 6, where it is obtained by integrating Euler's equation along a streamline If an instructor chooses to delay introducing the Bernoulli equation, the challenging problems from Chapter may be assigned during study of Chapter This edition incorporates a number of significant changes In Chapter 7, the dis cussion of non-dimensionalizing the governing equations to obtain dimensionless pa rameters is moved to the beginning of the chapter Chapter incorporates pumps into the discussion of energy considerations in pipe flow The discussion of multiple-path pipe systems is expanded and illustrated with an interactive Excel workbook Chapter 10 has been restructured to include separate sub-topics on machines for doing work on, and machines for extracting work from, a fluid Chapter 12 has been completely restructured so that the basic equations for one-dimensional compressible flow are derived once, and then applied to each special case (isentropic flow, nozzle flow, Fanno line flow, Rayleigh line flow, and normal shocks) Finally, a new section on oblique shocks and expansion waves is included We have made a major effort to improve clarity of writing in this edition Pro fessor Philip J Pritchard of Manhattan College, has joined the Fox-McDonald team as co-author Professor Pritchard reviewed the entire manuscript in detail to clarify and improve discussions, added numerous physical examples, and prepared the Excel workbooks that accompany 45 example problems and over 300 end-of-chapter prob lems His contributions have been extraordinary The sixth edition includes 1315 end-of-chapter problems Many problems have been combined and contain multiple parts Most have been structured so that all parts need not be assigned at once, and almost 25 percent of sub-parts have been designed to explore "What if?" questions About 300 problems are new or modified for this edition, and many include a component best suited for analysis using a spreadsheet A CD icon in the margin identifies these problems Many of these problems have been designed so the com puter component provides a parametric investigation of a single-point solution, to fa cilitate and encourage students in their attempts to perform "What if?" experimenta tion The Excel workbooks prepared by Professor Pritchard aid this process significantly A new Appendix H, "A Brief Review of Microsoft Excel," also has been added to the CD PREFACE V We have included many open-ended problems Some are thought-provoking questions intended to test understanding of fundamental concepts, and some require creative thought, synthesis, and/or narrative discussion We hope these problems will inspire each instructor to develop and use more open-ended problems The Solutions Manual for the sixth edition continues the tradition established by Fox and McDonald: It contains a complete, detailed solution for each of the 1315 homework problems Each solution is prepared in the same systematic way as the example problem solutions in the printed text Each solution begins from gov erning equations, clearly states assumptions, reduces governing equations to com puting equations, obtains an algebraic result, and finally substitutes numerical val ues to calculate a quantitative answer Solutions may be reproduced for classroom or library use, eliminating the labor of problem solving for the instructor who adopts the text Problems in each chapter are arranged by topic, and within each topic they generally increase in complexity or difficulty This makes it easy for the instructor to assign homework problems at the appropriate difficulty level for each section of the book The Solutions Manual is available in CD form directly from the publisher upon request after the text is adopted Go to the text's website at www wiley.com/college/fox to request access to the password-protected online version, or to www.wiley.com/college to find your local Wiley representative and request the So lutions Manual in C D form Where appropriate, we have used open-ended design problems in place of tradi tional laboratory experiments For those who not have complete laboratory facili ties, students could be assigned to work in teams to solve these problems Design problems encourage students to spend more time exploring applications of fluid me chanics principles to the design of devices and systems In the sixth edition, design problems are included with the end-of-chapter problems The presentation of flow functions for compressible flow in Appendix E has been expanded to include data for oblique shocks and expansion waves Expanded forms of each table in this appendix can be printed from the associated Excel work books, including tables for ideal gases other than air Many worthwhile videos are available to demonstrate and clarify basic princi ples of fluid mechanics These are referenced in the text where their use would be ap propriate and are also identified by supplier in Appendix C When students finish the fluid mechanics course, we expect them to be able to apply the governing equations to a variety of problems, including those they have not encountered previously In the sixth edition we particularly emphasize physical con cepts throughout to help students model the variety of phenomena that occur in real fluid flow situations We minimize use of "magic formulas" and emphasize the sys tematic and fundamental approach to problem solving By following this format, we believe students develop confidence in their ability to apply the material and find they can reason out solutions to rather challenging problems The book is well suited for independent study by students or practicing engi neers Its readability and clear examples help to build confidence Answers to many quantitative problems are provided at the back of the printed text We recognize that no single approach can satisfy all needs, and we are grateful to the many students and faculty whose comments have helped us improve upon ear lier editions of this book We especially thank our reviewers for the sixth edition: Mark A Cappelli of Stanford University, Edward M Gates of California State Poly technic University (Pomona), Jay M Khodadadi of Auburn University, Tim Lee of VJ PREFACE McGill University, and S A Sherif of University of Florida We look forward to con tinued interactions with these and other colleagues who use the book We appreciate the unstinting support of our wives, Beryl, Tania, and Penelope They are keenly aware of all the hours that went into this effort! We welcome suggestions and/or criticisms from interested users of this book Robert W Fox Alan T McDonald Philip J Pritchard April 2003 ^ CONTENTS CHAPTER INTRODUCTION 1-1 1-2 1-3 1-4 1-5 1-6 Si 1-7 CHAPTER FUNDAMENTAL CONCEPTS 2-1 2-2 2-3 2-4 2-5 2-6 2-7 iCHAPTER /1 Note to Students / l Definition of a Fluid /3 Scope of Fluid Mechanics /4 Basic Equations /4 Methods of Analysis 15 System and Control Volume /5 Differential versus Integral Approach Methods of Description /8 Dimensions and Units /TO Systems of Dimensions /11 Systems of Units / l l Preferred Systems of Units /13 Summary /13 Problems /13 /17 Fluid as a Continuum /17 Velocity Field /19 One-, Two-, and Three- Dimensional Flows /20 Timelines, Pathlines, Streaklines, and Streamlines /21 Stress Field /24 Viscosity /26 Newtonian Fluid /28 Non-Newtonian Fluids /30 Surface Tension /32 Description and Classification of Fluid Motion /35 Viscous and Inviscid Flows /35 Laminar and Turbulent Flows /38 Compressible and Incompressible Flows /39 Internal and External Flows /40 Summary /42 References /42 Problems /42 F L U I D STATICS 3-1 3-2 3-3 /8 /52 The Basic Equation of Fluid Statics /52 The Standard Atmosphere /56 Pressure Variation in a Static Fluid /57 Incompressible Liquids: Manometers /57 Gases /63 vii 13S422 776 ANSWERS TO SELECTED PROBLEMS 11.10 m = 36.7 kg/s; T = 572 K; V = 11.11 11.12 11.14 11.15 11.16 11.23 11.24 11.25 11.26 4.75 m/s; W = 23 MW TJ = 65% Ar = 828 s M = 0.533, 1.08 M = 0.776; V = 269 m/s c = 299 m/s; V = 987 m/s; V/V = 1.41 V = 761 m/s; a = 27.0° V = 642 m/s V = 6320 ft/s A/ = 1.19; V = 804 ft/s; /te/* = 9.84 x 10 m V = 493 m/s; A/ = 0.398 s V = 515 m/s;f = 6.16 s t = 8.51 s Ax = 3920 ft / « 48.5 s M = 0.141,0.314,0.441 M = 0.925; V = 274 m/s Ap/p = 48.5%; No po = 546 kPa; T = 466 K; / J - h = 178kJ/kg po = 126, I28kPa(abs) M = 0.801; V = 236 m/s; T = 245 K c = 295 m/s; V = 649 m/s; a = 27.0°; T = 426 K Ap = 8.67 kPa; V = 195 m/s; V = 205 m/s a = - m / s ; p = 191 kPa (abs); T = 346 K T = 394 °F; p = 85.4 psia; m = 145 lbm/s Yes; No V = 890 m/s; 7/ = 677 K; p = 212 kPa V = 987 m/s; p = 125 kPa; Po = 31.6 kPa; T = 707 K T , = Toj = 20.6 °C; p = 1.01 MPa; Po = 189 kPa; s - s, '= 480 kJ/kg • K T = 539 ° C ; T = - ° C ; Q = - kW; p = 593 kPa; Po = 657 k P a ; s - s = - kJ/kg • K = 344 K; p = 223, 145 kPa (abs); s - s = 0.124 kJ/(kg- K) SQ/^w = 63.0Btu/lbm; Poj = 56.5 psia T = 445 K; p = 57.5, 46.7 kPa (abs); s - , = 59.6 J/(kg • K) T = 2900, 1870 °R; Po = 100, 4.57 psia; s - J , = 0.107 Btu/(lbm- °R) b 11.27 11.28 11.29 11.30 11.31 11.34 11.35 11.36 11.37 0 11.38 11.39 11.40 0 11.41 11.43 x 0 11.44 11.45 11.46 11.47 0 0 0 11.48 0 | 11.49 0l 02 | 11.50 11.51 11.52 0 t 11.53 t 11.54 Ap = 48.2 kPa 11.55 r* = 260 K, p* == 24.7 MPa (abs); v* = 252 m/s n.56 r* = 1500 K,p* = 2.44 MPa (abs); = 2280 m/s 11.57 r* - 2730 K,p* = 25.4 MPa (abs); v* = 1030 m/s n.58 r* = 2390 °R, p* = 79.2 kPa (abs); = 2400 ft/s C h a p t e r 12 12.1 V = 2620 ft/s; M = 1.36; m = 1.76 lbm/s 12.2 V = 1660 ft/s; A/ = 0.787; m = 0.274 lbm/s 12.3 A/ = 1.35 12.4 p = 93.8 kPa 12.5 M = 1.20 12.6 M = 1.20 12.7 V= 475 m/s; A = 0.315 m 12.8 M = 1.75; m = 27.2 kg/s; A = m ; p = 55.0 kPa 12.10 m = 8.50 kg/s 12.11 p, = 33 psia; M, = 0.90; V, = 1060 ft/s 12.12 p, = 166 kPa 12.13 p = 150kPa; M = 0.6; A, = 0.0421 m ; m = 18.9 kg/s 12.14 m = 0.548 kg/s 12.15 A = 1.94 X - m 12.16 p = k P a ; m = 1.92 kg/s 12.17 po = 818 kPa; p = 432 kPa; T = - °C; V = 302 m/s 12.18 po ^ 191 kPa; m = 1.28 kg/s 12.19 m = 0.0107 lbm/s 12.20 / = 68.4 s; As = 0.0739 Btu/(lbm -°R) 12.21 R = 1560 N (to the left) 12.22 To = 188°C; AA = - percent: p = 188 kPa; V = 393 m/s 12.23 p = 687 kPa (abs); m = 0.0921 kg/s; a = 1.62 m/s 12.24 po'= 988 kPa; p = 522 kPa; T = 58.7 °C; V, = 365 m/s, a = 1.25 m/s 12.25 m = 2.73 lbm/s; a = 99.8 ft/s 12.26 /?, = 304 lbf, tension 12.27 A = 0.0340 m ; V = 424 m/s 12.28 A, = 0.377 in 12.29 f = 23.6 s 12.30 M, = 1.00; p = 381 kPa;p, = 191 kPa; T ~ 288 K 2 2 2 e t e X rf e e r/t 2 2 f ANSWERS TO SELECTED PROBLEMS 12.31 / = 23.5 s; As = 161 J/(kg- K) 12.32 m = 0.440 lbm/s 12.33 p = 115 psia; m = 1.53 lbm/s; A, = 0.593 in 12.34 p = 125 kPa (abs); m = 0.401 kg/s 12.35 A = 2.99 in ; m = 3.74 lbm/s 12.36 V = 1300 m/s; m = 87.4 kg/s 12.37 A = 8.86 X ' m , 1.50 X " m 12.38 m = 3.57 lbm/s 12.39 /?, = 950 N 12.40 m = 39.4 lbm/s; F , = 9750 Ibf 12.41 p = 88.3 kPa (abs); m = 0.499 kg/s; X", = 1030 N 12.42 m = 32.4 kg/s; A = 0.167 m ; A,/A, = 19.4 12.43 p, = 2740 psia; m = 0.0437 lbm/s; Thrust = 1.97 Ibf; 36 percent; A = 7.52 X - in 12.44 po = 5600 psia 12.45 m = 0.0726 kg/s; p < 33.5 kPa (abs) 12.46 M = 0.20;rit= 3.19 X 10 kg/s; p = 47.9 kPa (abs) 12.47 p = 18.5 psia; V= 1040 ft/s 12.48 p = 477 kPa (abs); As = 49.5 J/(kg- K) 12.49 m = 0.00321 kg/s; p = 33.8 kPa (abs); As = 314 J/(kg • K) 12.50 m = 0.0192 kg/s; F* = 244 K; p* = 53.4, 13.6 kPa (abs) 12.51 T = 468 K; F = 60 N; As = 149 J/(kg- K) 12.52 F = 822 Ibf 12.53 p , = 56.6 psia; T = 433°R; p = 27.8 psia; m = 0.0316 lbm/s 12.54 T = 238 K; p = 26.1 kPa (abs); As = 172 J/(kg • K) 12.55 M = 0.15; T = 246 K , p = 25.6 kPa; L = 8.41 m 12.56 L = 1.27 m 12.57 F = 459 K; L = 34.5 m 12.58 L = 18.8 ft 12.63 / = 0.0122; Ap = 13.0 psi 12.64 L = 0.405 m 12.66 p = 191 kPa (abs); L = 5.02 m; As = 326 J/(kg • K) 12.67 M = 0.25; Added 12.68 p = 153 psia 12.69 M = 0.452; L = 603 ft 12.70 Ap = 16.6, 18.2, 18.1 psia 12.71 Q = 1.84 X 10 ft /day 12.72 SQ/dm = 145 kJ/kg; Ap = 405 kPa 2 e e 0 12.73 12.74 12.75 12.76 777 8Q/dm = 243 Btu/lbm 8Q/dm = 449 kJ/kg; As = 0.892 kJ/(kg • K) Q = l l l k W ; p , - p = 1.30MPa 8Q/dm = 18kJ/kg; As = 53.2 J/(kg • K); Ap = 2.0 kPa 12.77 V = 1520 ft/s; T = 2310 °R; Q = 740 Btu/s 12.78 p = 209 psia; Q = 2270 Btu/s; m/ = 0.126 lbm/s 12.79 80/rfm = 330 Btu/lbm; Ap = - psia 12.80 V = 866 m/s; p = 46.4 kPa; Af = 1.96; 8Q/dm = 156U/kg 12.81 M = 0.50; T = 1560 K; Q = 1.86 MI/s 12.82 Ap = - 2 kPa; Sg/dm = 447 kJ/kg; Ai- = 889 J/(kg • K) 12.83 8Qldm = 17.0 kJ/kg; F = 318 K; p - 46.3 kPa; p = 87.7 kPa 12.84 M= l.O;p = 48.8 kPa; Ap = - kPa 12.85 Q = 5.16 X 10 Btu/s 12.86 8Q/dm = 313 Btu/lbm; Ap -= - psia 12.87 T = 764 K; m = 0.0215 kg/s; A,7A, = 4.23 12.88 F = 966 K; M = 0.60; 5«2/dw = 343 kJ/kg; Fraction = 0.616 12.91 M = 1.74; p = 4.49 psia 12.93 V = 536 m/s 12.94 po = 7.22 psia; F = 954 °R 12.95 p = 0.359 lbm/ft ; A/ - 0.701 12.96 V = 247 m/s; F = 670 K; As = 315 J/(kg -K) 12.97 p = 28.1, 85.7 psia 12.98 T= 520 K ; p = 1.29 MPa 12.99 V = 257 m/s; M = 0.493; Ap = - kPa 12.100 V = 255 m/s; Ap = 473, 842 kPa 12.101 F = 426 K; po = 207,130 kPa 12.102 M = 2.48; V = 2420 ft/s; p = 24.3 psia; Po = 29.1 psia 12.103 T= 414 K ; p = k P a ; p = 57.9 kPa 12.104 M - 0.545; p = 514 kPa; p = 629 kPa; A = 0.111 m 12.105 A = 2.32 ft ; As = 0.0423 Bru/lbm -°R) 12.106 Ap = - psi; As = 0.0591 Btu/(lbm -°R) 12.107 M = 2.20; p = 178 kPa; V = 568 m/s 12.108 T = 533 K; Ap = 37.4 kPa; As = 30.0 I/(kg • K); po = 116 kPa 0 0 0 0 2 0 0 2 0 s 778 12.109 12.110 12.111 12.112 12.113 12.114 12.115 12.116 12.117 ANSWERS TO SELECTED PROBLEMS V = 265, 279 m/s p = 33.4 kPa; V= 162 m/s M= 1.45; m= 0.808 lbm/s M = 0.701; p = 167 kPa; As = 20.9 J/(kg • K) M = 1.92; p = 89.4, 58.6, 14.5 psia Af = 2.94; po = 3.39 MPa; p = 3.35, 1.00 MPa, 101 kPa p = 301 kPa p = 46.7 psia; A = 1.52 in ; m = 2.55 lbm/s p = 587 kPa;A, = 756 mm ; A = 448 m A/ = 1.50 33.4743 kPa p = 66.6 psia p = 301 kPa(abs) 2 12.118 12.119 12.120 12.121 12.122 12.123 b a [ m 12.125 M = 0.475; p = 361 kPa; r = 400 K; A, = 118 mm ; ^ ^i = - kJ/(kg • K); M = 0.377 12.127 M = 2.14 12.128 V = 2140 ft/s; As = 0.0388 Btu/(lbm-°R) 12.129 M = 2.06; p = 93.4 kPa; = 3.72°; Normal shock: A/ = 0.547; p = 411 kPa; B = 27° 12.130 B = 19.5° - 90° 12.131 6= 25°; B = 46.7°; M = 1.56 12.132 B = 66.2°; p /p, = 6.06 12.133 M = 1.42; V = 484 m/s 12.136 F^/w = 138 kN/m 12.137 FJw = 183 kN/m 12.138 pi = k P a ; p = 15.9 kPa 12.141 po = 1317 kPa,p = 497 kPa; Po = k P a , p = 571 kPa 12.142 FJw = 64.3 kN/m; D = 13.7 kN/m 12.144 C = 0.0177 0 _ t 2 2 2 D INDEX Absolute metric (system of units), 12 Absolute pressure, 56 Absolute viscosity, 28 Acceleration: for rotating control volume, S-13 conservation of mass, 109 first law of thermodynamics, 150 Newton's second law (linear momentum), for control volume moving with constant velocity, 134 for control volume with arbitrary acceleration, S-7 for control volume with rectilinear acceleration, 137 for differential control volume, 129 for nonaccelerating control volume, 116 convective, 199 gravitational, 11 local, 199 of particle in velocity field, 197, 199 cylindrical coordinates, 200 rectangular coordinates, 200 Accelerometer, 100 Adiabatic flow, see Fanno-line flow Adiabatic process, 592 Adverse pressure gradient, , , 430 Aging of pipes, 341 Anemometer: second law of thermodynamics, 151 Basic laws for system, 102 angular-momentum principle, 103 conservation of mass, 102 first law of thermodynamics, 103 Newton's second law (linear momentum), 103 differential form, 212 second law of thermodynamics, 104 Basic pressure-height relation, 55 Bearing, journal, 318 Bernoulli equation, 132,237 Laser Doppler, 382 thermal, 382 Angle of attack, 448 Angular deformation, 197,203, 207 Angular-momentum principle, 103, 145 applications, 243 cautions on use of, 248 interpretation as an energy equation, 249 irrotational flow, S-21 restrictions on use of, 238 unsteady flow, S-18 Bingham plastic, 31 Blasius' solution, S-39 Blower, 488, 548 Body force, 24 Borda mouthpiece, 268 Boundary layer, , fixed control volume, 145 rotating control volume, S-13 Apparent viscosity, 31 Apparent shear stress, 330 Archimedes' principle, 81 Area, centroid of, 69 second moment of, 70 product of inertia of, 71 Area ratio, 343 isentropic flow, 628 Aspect ratio: airfoil, 453 flat plate, 438 rectangular duct, 348 Atmosphere: isothermal, 66 standard, 56 Average velocity, 110, 311 displacement thickness, 412 effect of pressure gradient on, 430 flat plate, 411 integral thicknesses, 413 laminar: approximate solution, 422 exact solution, S-39 momentum integral equation for, 415, 420 momentum-flux profiles, 432 momentum thickness, 413 separation, 430 shape factor, 432 thickness, 412 transition, 411 turbulent, 426 velocity profiles, 432 Barometer, 64 Barotropic fluid, 40 Barrels, U.S petroleum industry, 353, 405 Basic equation of fluid statics, 52 Basic equations for control volume, 102 angular-momentum principle, for inertial control volume, 145 779 780 INDEX Boundary-layer: control, 455, 461 thicknesses, 412 British gravitational (system of units), 12 Buckingham Pi theorem, 277 Bulk (compressibility) modulus, 40, 599, 718 Buoyancy force, 80 Camber, 448 Capillary effect, 33, 282 Capillary viscometer, 327 Cavitation, 40, 524 Cavitation number, 285, 560 Center of pressure, 68, 69 Choking, 632, 638, 646, 661, S-48, S-49 Chord, 448 Circulation, 205, S-38 Coanda effect, 160 Compressible flow, 40, 589, 617 basic equations for, 617 ideal gas, 620 flow functions for computation of, 744 Compressor, 488, 548 Concentric-cylinder viscometer, 48 Confidence limit, 757 ConicaJ diffuser, 344 Conservation: of energy, see First law of thermodynamics of mass, 102, 109, 184 cylindrical coordinates, 189 rectangular coordinates, 184 Consistency index, 31 Contact angle, 32, 720 Continuity, see Conservation of mass Continuity equation, differentia] form, 184 cylindrical coordinates, 189 rectangular coordinates, 184 Continuum, 17 Contraction coefficient, 268, 396 Control surface, Control volume, deformable, 108 rate of work done by, 151 Convective acceleration, 199 Converging-diverging nozzle, see Nozzle Converging nozzle, see Nozzle Conversion factors, 762 Creeping flow, 387 Critical conditions, compressible flow, 610 Critical flow in open ohannel, 285 Critical pressure ratio, 610, 632 Critical Reynolds number, see TransiUon Critical speed: compressible flow, 611 Curl, 204, S-22 Cylinder: drag coefficient, 441 inviscid flow around, S-33, S-35 D'Alembert paradox, 35, S-33 Deformation: angular, 197, 203, 207 linear, 197,209 rate of, 27, 208 Del operator: cylindrical coordinates, 190, S-2, S-22 rectangular coordinates, 54, 186 Density, 17 Density field, 18 Derivative, substantial, 199 Design conditions, see Nozzle Differential equation, nondimensionalizing, 273 Diffuser, 343, , 8 , optimum geometries, 344 pressure recovery in, 344 supersonic, S-46 Dilatant, 31 Dilation, volume, 210 Dimension, 10 Dimensional homogeneity, 11 Dimensional matrix, 282 Dimensions of flow field, 20 Discharge coefficient, 371 flow nozzle, 374 orifice plate, 373 venturi meter, 376 Displacement thickness, 412 Disturbance thickness, see Boundary layer Doppler effect, 382, 602 Doublet, S-28 strength of, S-28 Downwash, 453 Draft tube, 490, 513 Drag, 35,410, 433 form, 38, 454 friction, 434, 438 parasite, 460 pressure, 38, 437, 438 profile, 454 Drag coefficient, 293, 434 airfoil, 454 complete aircraft, 455 cylinder, 441 rotating, 464 flat plate normal to flow, 438 flat plate parallel to flow, 434 golf balls 462 induced, 453 selected objects, 439 sphere, 439, 480 spinning, 461 streamlined strut, 445 supersonic airfoil, 696 vehicle, 293 Dynamic pressure, 239, 240 Dynamic similarity, 286 Dynamic viscosity, 28 Dyne, 12 Efficiency: hydraulic turbine, 502 propeller, 558, 586 propulsive, 557 pump, 295,501 windmill, 567 Elementary plane flows, see Potential flow theory End-plate, 455 Energy equation, for pipe flow, 334 See also First law of thermodynamics Energy grade line, , , 364 English Engineering (system of units), 12 Enthalpy, 153,590 Entrance length, 312 Entropy, 591 Equation of state, 5, 620 ideal gas, 5, 589 Equations of motion, see Navier-Stokes equations Equivalent length, 342 bends, 346 fittings and valves, 346 miter bends, 346 Euler equations, 215, 232 along streamline, 234 cylindrical coordinates, 233 normal to streamline, 235 rectangular coordinates, 233 streamline coordinates, 234 Eulerian method of description, 10, 201 Euler number, 285 Euler turbomachine equation, 491 Experimental uncertainty 2, 755 Extensive property, 104 External flow, , Fan, 488, 542 "laws." 297, 545 selection procedure, 735 specific speed, 546 Fanno-line flow, 643, 645 basic equations for, 644 choking length, 653, S-49 effects on properties, 646 flow functions for computation of, 649, 746 normal shock formation in, S-49 Ts diagram, 646 Field representation, 18 First law of thermodynamics, 103, 150 Fittings, losses in, see Head loss, in valves and fittings Flap 455 Flat plate, flow over, 411 Float-type flow meter, 380 Row behavior index, 31 Flow coefficient, 296, 372 flow nozzle 374, 375 orifice plate, 374 turbomachine, 514 Row field, dimensions of, 20 Row measurement, 369 internal flow, 370 direct methods, 369 linear flow meters, 380 electromagnetic, 381 float-type, 380 rotameter, 380 turbine, 380 ultrasonic, 382 vortex shedding, 380 restriction flow meters, 370 flow nozzle, 374 laminar flow element, 376 orifice plate, 373 venturi, 376 traversing methods, 382 laser Doppler anemometer, 382 thermal anemometer, 382 Flow meter, see Flow measurement Row nozzle, 374 Row visualization, , Ruid, Ruid machinery 487 dynamic, see Turbomachine fan, 488 performance characteristics, 502 positive displacement, 487 propeller, 489 pump, 488 turbine, 489 Ruid particle, 19 Ruid properties 716 Fluid statics: basic equation of, 52 pressure-height relation 55 Ruid system, 347, 528 Force: body, 24 buoyancy, 81 compressibility 284 drag, 433 gravity, 284 hydrostatic, 67 on curved submerged surface, 76 on plane submerged surface, 67 inertia, 282 lift, 433, 447 pressure, 53, 284, 433 shear, 433 surface, 24, 433 surface tension, 32, 33, 284 viscous, 284 Forced vortex, 206 Francis turbine, 490, 513 Free surface, S-3, S-5 Free vortex, 206, S-28 Friction drag, see Drag Friction factor, 336, 338, 339 Darcy, 338 782 INDEX Friction factor (continued) data correlation for, 339, 340 Fanning, 338, 396 laminar flow, 340 smooth pipe correlation, 341 Frictionless flow: compressible adiabatic, see Isentropic flow compressible with heat transfer, see Rayleigh-line flow incompressible, 232 Friction velocity, 302, 331 Froude number, 285 Froude speed of advance, 304 Fully developed flow, 311 Hydraulic grade line, 255, 361, 364 Hydraulic jump, 190 Hydraulic power, 501, 502 Hydraulic systems, 67 Hydraulic turbine, 490, 561 Hydrometer, 97 Hydrostatic force, 67 on curved submerged surfaces, 76 on plane submerged surfaces, 68 Hydrostatic pressure distribution, 69, 121 Hypersonic flow, 600 laminar, 312 turbulent, 330 Fully rough flow regime, 339, 341 Ice, 717 Ideal fluid, S-22 Ideal gas, 5, 589 Lmpeller, 488 Incomplete similarity, 289 Incompressible flow, 40, 106, 187, 192 Incompressible fluid, 57 Induced drag, 453 Inertia! control volume, 116, 134 Inertial coordinate system, 116, 137 Intensive property, 104 Internal energy, 590 Internal flow, , Inviscid flow, 36, 232 Irreversible process, 592 Irrotational flow 205, S-20 Irrotarionality condition, S-20 Irrotational vortex, 207, S-28 Isentropic expansion waves, 690 basic equations for, 691 on an airfoil, 694 Prandtl-Meyer expansion function, 693, 754 isentropic flow, 621 basic equations for, 621 ideal gas, 621 in converging-diverging nozzle, 637 in converging nozzle, 631 effect of area variation on 621, 623 flow functions for computation of, 627, 744 in hs plane, 622 reference conditions for, 625 Isentropic process, 592 Isentropic stagnation properties, 602 for ideal gas, 603, 606 Isothermal flow, S-44 „ H Gage pressure, 56 Gas constant: ideal gas equation of state, 5, 590, 726 universal, , Geometric similarity, 286 Gibbs equations, 592 Grade line 254 energy, 255, 361,364 hydraulic, 5 , , Gradient, 54 Gravity, acceleration of, I Guide vanes, 490 Head, 254, 336, 493 gross, 509,513 pump, , , net, 509,513 shutoff, 500 Head coefficient, 296, 514 Head loss, 335 in diffusers, 345 in enlargements and contractions, 343 in exits, 342 in gradual contractions, 344 in inlets, 343 major, 329, 336 minor, 329, 341 in miter bends, 346 in nozzles, 344 permanent, 377 in pipe bends, 346 in pipe entrances, 343 in pipes, 336 in sudden area changes, 343 total, 336 in valves and fittings, 346 Head loss coefficient, 341 Heat transfer, sign convention for, 104, 150 Hydraulic accumulator, 163 Hydraulic diameter, 348, 650 let pump, 163 Journal bearing, 318 Kaplan turbine, 490, 513 KilogTam force, 577 Kinematic similarity, 286 Kinematics of fluid motion, 197 Kinematic viscosity, 28 Kinetic energy coefficient, 335 Kinetic energy ratio, 309 INDEX Lagrangian method of description, 8, 201 Laminar boundary layer, 422, S-39 flat plate approximate solution, 422 flat plate, exact solution, S-39 Laminar flow, 39, 310 between parallel plates, 312 both plates stationary, 312 one plate moving, 318 in pipe, 324 Laminar flow element (LFE), 376 Laplace's equation, S-23 Lapse rate, 613 Lift, , 3 , 4 Lift coefficient, 448 airfoil, 450 rotating cylinder, 464 spinning golf ball, 462 spinning sphere, 461 supersonic airfoil, 696 Lift/drag ratio, 452 Linear deformation, 197, 209 Linear momentum, see Newton's second law of motion Local acceleration, 199 Loss, major and minor, see Head loss Loss coefficient, see Head loss Lubricating oil, 724, 725 Mach angle, 602 Mach cone, 601 Mach number, 40, 286,596 Magnus effect, 463 Major loss, see Head loss Manometer, 57 capillary effect in, 33 multiple liquid, 62 reservoir, 59 sensitivity, 59 U-tube, 58 Material derivative, 199 Mean line, 448 Measurement, flow, see Flow measurement Mechanical energy, 252, 335 Mechanical flow meter, see Flow measurement Mechanical power, 492 Meniscus, 33, 282 Meridional, 514 Meter, flow, see Flow measurement Methods of description: Eulerian 10,201 Lagrangian, 8, 201 Metric horsepower, 577 Mile, nautical, 763 Minor loss, see Head loss Minor loss coefficient, see Head loss coefficient Model studies, 286 Model test facilities, 299 Modulus of elasticity, 40 Molecular mass, 590, 726 Momentum: angular, see Angular-momentum principle coefficient, 394 linear, see Newton's second law of motion Momentum equation: differential form, 211 for control volume moving with constant velocity, 134 for control volume with arbitrary acceleration, S-7 for control volume with rectilinear acceleration, 137 for differential control volume, 129 for inertial control volume, 116 for inviscid flow, 232 Momentum flux, 117 Momentum integral equation, 415,420 for zero pressure gradient flow, 421 Momentum thickness, 413 Moody diagram, 339 National Transonic Facility (NTF), 299, 613 Nautical mile, 763 Navier-Stokes equations, 213 cylindrical coordinates, 730 rectangular coordinates, 214 Net positive suction head, 524 Network, pipe, 364 Newton, 12 Newtonian fluid, 28, 213 Newton's second law of motion, 103 Noncircular duct, 348 Noninertial reference frame 131, S-7 Non-Newtonian fluid 28, 30 apparent viscosity, 31 consistency index, 31 flow behavior index 31 power-law model, 31 pseudoplastic, 31 rheopectic, 32 thixotropic, 32 time-dependent, 32 viscoelastic, 32 Normal shock, 669 basic equations for, 670 effects on properties, 672 flow functions for computation of, 672, 750 supersonic channel flow with, 678, S-46 Ts diagram, 671, 672 Normal stress, 25, 145, 214 No-slip condition, 3, 37, 311 Nozzle, , choked flow in 632, 638 converging, 624, 631 converging-diverging, 625, 637, 678 design conditions, 639 incompressible flow through, 243 normal shock in, 678 overexpanded, 639 underexpanded, 639 Oblique shock, 680 basic equations for, 681 comparison with normal shock, 684 deflection angle, 687, 753 783 784 INDEX Oblique shock (continued) flow functions for computation of, 684, 752 on an anfoil, 688 shock angle, 687 One-dimensional flow, 20 Open-channel flow, 41 Orifice, reentrant, 268 Orifice plate, 373 Overexpanded nozzle, 639 Particle derivative, 199 Pascal, 762 Pathline, 21 Pelton wheel, 509 Permanent head loss, see Head loss Physical properties, 716 Pipe: aging, 341,581 compressible flow in, see Fanno-line flow head loss, see Head loss laminar flow in, 325 noncircular, 348 roughness, 337, 338 standard sizes, 351 turbulent flow in, 330, 337 Pipe systems, 350 networks, 364 pumps in, 347, 529 single-path, 350 Pi theorem, 277 Pitch, 558 Pitot-static tube 241 Pilot tube 241 Planform area, 446, 448 Poise, 28 Polar plot, lift-drag, 452 Potential, velocity, S-22 Potential flow theory, S-23 elementary plane flows, S-25 doublet, S-28 sink, S-25 source, S-25 uniform flow, S-25 vortex, S-28 superposition of elementary plane flows, S-28 Potential function, S-22 Power coefficient 296, 515, 558 Power-law model, non-Newtonian fluid, 31 Power-law velocity profile, 332 Prandtl boundary layer equations, 301, S-39 Pressure, 53 56 absolute, 56 center of, 68, 69 dynamic, 239 240 gage, 56 isentropic stagnation, see Isentropic stagnation properties stagnation, 239, 240 static, 239 thermodynamic, 214, 239 Pressure coefficient, 285, 343 Pressure distribution: airfoil, 446, 451 automobile, 460 converging-diverging nozzle, 637, 678 converging nozzle, 632 cylinder, inviscid flow, S-33, S-35 diffuser, 361,431 entrance length of pipe, 359 sphere, 440 supersonic airfoil, 688, 694, 696 Pressure drag, see Drag Pressure field, 53 Pressure force, 53 Pressure gradient, 54, 431 effect on boundary layer, 430 Pressure recovery coefficient, 343 ideal, 344 Pressure surface, 448 Pressure tap, 240, 373 Primary dimension, 10, 278 Profile, velocity, see Velocity profile Propeller 489, 554 actuator disk, 554 efficiency, 558 pitch, 558 power coefficient, 558 propulsive efficiency, 557 solidity, 557 speed of advance coefficient, 558 thrust coefficient, 558 torque coefficient, 558 Properties, fluid, 716 air, 728 water, 716,727 Propulsive efficiency, 557 Pseudoplastic, 31 Pump, 488,531 in fluid system, 347, 529 "laws," 297, 520 operating point, 529 parallel operation, 538 positive displacement 549 selection procedure, 733 series operation, 537 specific speed, 516 variable-speed operation, 539 Rankine propeller theory, 556 Rale of deformation, 27, 208 Rayleigh-line flow, 657 basic equations for, 658 choking, 661, S-49 effects on properties, 660 flow functions for computation of, 664, 748 maximum heat addition, 661 Ts diagram, 659, 661 Reentrant entrance, 268 Reference frame, noninertial, 131, S-7 INDEX Repeating parameter, 279 Reversible process, 592 Reynolds experiment, 310 Reynolds number, 36, 284 critical, see Transition Reynolds stress, 330 Reynolds transport theorem, 107 Rheopectic, 32 Rigid-body, motion of fluid, S-l Rotation, 197,203 Rotor, turbomachine 489 Roughness, pipe, 337, 338 Runner, turbomachine, 489 Secondary dimension, 11 Secondary flow, 345 Second law of thermodynamics, 104, 157 Separation, 38, 430 Shaft work, 151 Shape factor, velocity profile, 432 Shear rate, 28 Shear stress, 3, 25 distribution in pipe, 329 Shear work, 152 Shock, normal, see Normal shock Shock, oblique, see Oblique shock Shockless entry flow, 493 Shutoff head, 500 Significant figures, Similarity: dynamic, 286 geometric, 286 incomplete, 289 kinematic, 286 rules, 519 Similar velocity profiles, 421, S-39, S-40 Similitude, 275 Sink, S-25 strength of, S-25 Siphon, 244, 402 SI units, 11,762 prefixes, 762 Skin friction coefficient, 423, 427, S-41 Slug, 12 Sluice gate, 125,245 Solidity, 489, 557 Sound, speed of, 596 599 Source, S-25 strength of, S-25 Span, wing, 453 Specific gravity, 18, ] 6, 717, 718 Specific heat: constant pressure, 590, 726 constant volume, 590, 726 Specific heat ratio, 591, 726 Specific speed, 297, 515, 516 546 Specific volume, 153, 590 Specific weight, 19 Speed of advance coefficient, 558 Speed of sound, 596 ideal gas, 599 solid and liquid, 599 Sphere: drag coefficient, 439 flow around, 37 inviscid flow around, 37 pressure distribution, 440 Spin ratio, 461 Stability, 80 Stage, 488 Stagnation enthalpy, 615, 619 Stagnation point, , , S-34, S-36 Stagnation pressure, 239, 240 isentropic see Isentropic stagnation properties Stagnation pressure probe, 241 Stagnation properties, see Isentropic stagnation properties Stagnation state, 602 Stagnation temperature, 606 Stall, wing, 449 Standard atmosphere, 56 properties of, 57 719 Standard cubic foot (of gas), 16 Standard pipe sizes, 351 Suite: equation of, thermodynamic, 590 Static fluid, pressure variation in, 57 Static pressure, 239 Static pressure probe, 240 Static pressure tap, 239 Steady flow, 19, 110, 187, 192 Stoke, 28 Stokes' drag law, 439 Stokes' theorem, 206 STP (standard temperature and pressure), 17, 726 Stieakline, 21 Stream function, 193, 195 Streamline, 21 equation of, 22, 193 Streamline coordinates 233 237 Streamline curvature, 235,459 Streamlining, 38, 445 Stream tube, 250 Stress, 24 components, 26, 214, 730 compressive, 53 normal, 25, 145,214,730 notation, 25 shear, 25 214, 730 sign convention, 26 yield, 31 Stress field, 24 Stresses, Newtonian fluid, 214 Strouhal number, 381, 442 Substantial derivative, 199 Suction surface, 448 Sudden expansion, 343 785 786 INDEX Superposition, of elementary plane flows, S-28 direct method of, S-29 inverse method of, S-33 Surface force, 24 Surface tension, , System, System head curves, 529 System derivative, 104 relation to control volume, 107 Systems: of dimensions, 11 of units, 11 Taylor series expansion, 53, 184, , , 2 , , 417,418,419 Tds equations, 592 Terminal speed, Thermodynamic pressure, see Pressure Thermodynamics, review of, 589 Thixotropic, 32 Three-dimensional flow, 20 Throat, nozzle, 624 Thrust coefficient, 558 Timeline, 21 Torque coefficient, 514, 558 Total head tube 241 Trailing vortex, 452 Transition, 1 , 1 , 4 Translation, 197 Transonic flow, 600 Ts diagram, 595 Turbine, 489 hydraulic, 489, 561 impulse, 489, 509 reaction, 490, 513 specific speed, 516 wind, 566 Turbine flow meter 381 Turbomachine, 487 axial flow, 488 centrifugal, 488 fan, 488 flow coefficient, 296, 514 head coefficient, 296, 514 mixed flow 489 pump, 488 power coefficient, 296, 515 radial flow, 487 scaling laws for, 296 specific speed, 297, 515 stage, 488 torque coefficient, 514 Turbulent boundary layer, approximate solution for flat plate, 426 Turbulent flow, 39, 310 Turbulent pipe flow, 329 fluctuating velocity, 330 mean velocity, 330 shear stress distribution, 330 velocity profile, 331 buffer layer, 332 logarithmic, 331 power-law, 332 velocity defect, 332 viscous sublayer, 331 wall layer, 330 Two-dimensional flow, 20 Uncertainty, experimental, 2, 755 Underexpanded nozzle, 639 Uniform flow at a section, 20, 111 Uniform flow field, 21 Units, 11,762 Universal gas constant, 590, 726 Unsteady Bernoulli equation, S-18 Unsteady flow, 20 Vapor pressure, 40 Vector, differentiation of, 190, 199 Velocity diagram, 493 Velocity field, 19 Velocity measurement, see Flow measurement Velocity of approach factor, 372 Velocity potential, S-22 Velocity profile, 37 in pipe flow, laminar, 326 turbulent, 331 Vena contracta, 342 361, 370 Venturi flowmeter, 376 Videotapes, fluid mechanics, 731 Viscoelastic, 32 Viscometer: capillary, 327 concentric cylinder, 48, 219 cone-and-plate, 49 Viscosity, 27, 28 absolute (or dynamic), 28, 722 apparent, 31 kinematic, 28, 723 physical nature of, 720 Viscous flow, 36 Viscous sublayer, 331 Visualization, flow, 21, 292 Volume dilation, 210 Volume flow rate, 110 Vortex: forced, 206 free, 206, S-27 irrotational, 207, S-28 strength of, S-28 trailing, 442, 452 Vortex shedding, 306, 442, 452 Vorticity, 205 cylindrical coordinates, 205 Wake, 38,410 Wall shear stress, 329, 423, 427, S-41 Water hammer, 40, 304 Water, properties of, 716,727, 728 Weber number, 285 Weight, 13 Weir, 302 Wetted area, 434 Wetted perimeter, 348, 650 Windmill, 565 Wind tunnel, 293, 299 supersonic, S-47 Wind turbine, 566 efficiency, 567 Winglet, 455 Wing loading, 453 Wing span, 453 Work, rate of, 151 shaft, 151 shear, 152 sign convention for, 104, 151 Yield stress, 31 Zone: of action, 602 of silence, 602 56 810 4 56 810 Reynolds -4-4- i I Biblioteca UPB 0.05 0.04 0.03 0.02 0.015 0.01 0.008 0.006 a; 0.004 O k_ Q) _> 0.002 4—1 a> err 0.001 0.0008 0.0006 0.0004 0.0002 0.0001 0.000,05 0.000,01 8 138422 Re = ^ -g- = 0.000,001 ^ - = 0.000,005 A proven problem-solving approach in Fluid Mechanics now integrated with Excel\ Fox, McDonald & Pritchard provide abalanced approach to fluid mechanics that arms students with a proven problem-solving methodology Students willlearn to adopt an orderly approach to solving problems • Providing afresh look, new co-author PhilipJ Pritchard, of Manhattan College, has clarified and improved descriptions and explanations throughout the book • The text emphasizes the controlvolume concept to provide apractical problem solving approach that is theoretically inclusive • 116 detailedexample problems illustrate important concepts;each problem is solved in complete detail to demonstrate good solution procedure • e x a m p l e p r o b l e m s h a v e a s s o c i a t e d Excel w o r k b o o k s t h a t e n a b l e s t u d e n t s t o p e r f o r m " W h a t i f ? " scenarios when studying the examples; many of the workbooks can be modified to solve end-of-chapter problems • S t u d e n t s c a n u s e Excel t o v a r y p r o b l e m p a r a m e t e r s t o g a i n i n s i g h t i n t o t h e b e h a v i o r o f c o m p l e x solutions • 1315 end-of-chapterproblems, withvarying degrees of difficulty, provide the opportunityto practice building problem-solving skills • The CD accompanying the textincludes; specialand/or advanced topicsections forfurther study t h a t a r e n o t i n c l u d e d i n t h e p r i n t e d t e x t , e x a m p l e p r o b l e m w o r k b o o k s i n Excel, a n d " A B r i e f R e v i e w o f M i c r o s o f t Excer ( a n i n t r o d u c t i o n t o Excets b a s i c f e a t u r e s , a n d s u c h a d v a n c e d f e a t u r e s a s Solver and macros) ©WILEY www.wiley.com/collcgc/fox ... Pritchard April 2003 ^ CONTENTS CHAPTER INTRODUCTION 1-1 1-2 1-3 1-4 1-5 1-6 Si 1-7 CHAPTER FUNDAMENTAL CONCEPTS 2-1 2-2 2-3 2-4 2-5 2-6 2-7 iCHAPTER /1 Note to Students / l Definition of a Fluid... 13S422 VMi CONTENTS 3-4 3-5 *3.6 • 3-7 3-8 CHAPTER B A S I C E Q U A T I O N S IN I N T E G R A L F O R M FOR A C O N T R O L V O L U M E /99 4-1 4-2 4-3 4-4 4-5 • 4-6 * 4-7 4-8 4-9 4-1 0 CHAPTER Hydraulic... /376 8-1 1 Linear flow Meters /380 8-1 2 Traversing Methods /382 8-1 3 Summary /383 References /383 Problems /385 CHAPTER EXTERNAL INCOMPRESSIBLE VISCOUS FLOW 9-1 9-2 • 9-3 9-4 9-5 9-6 9-7 9-8 9-9 /409