Fundamentals of Momentum,

1 Fundamentals of Momentum, Heat, and Mass Transfer5th EditionFundamentals of Momentum, Heat, and Mass Transfer5thEditionJames R. WeltyDepartment of Mechanical EngineeringCharles E. WicksDepartment of Chemical EngineeringRobert E. WilsonDepartment of Mechanical EngineeringGregory L. RorrerDepartment of Chemical EngineeringOregon State UniversityJohn Wiley & Sons, PUBLISHERD aniel SayreACQUISITIONS EDITORJ ennifer WelterMARKETING MANAGERC hristopher RuelCREATIVE DIRECTORH arry NolanDESIGNERM ichael St. MartineSENIOR MEDIA EDITORL auren SapiraSENIOR PRODUCTION EDITORP atricia McFaddenPRODUCTION MANAGEMENT SERVICES Thomson DigitalThis book was set in by Thomson Digital and printed and bound by Hamilton Printing. The cover wasprinted by Lehigh Press, book is printed on acid free paper. 1 Copyright#2008 John Wiley & Sons, Inc. All rights reserved.

2 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 StatesCopyright Act, without either the prior written permission of the Publisher, or authorization through payment of theappropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923,website Requests to the Publisher for permission should be addressed to the PermissionsDepartment, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website order books or for customer service please, call 1-800-CALL WILEY (225-5945).ISBN-13 978-0470128688 Printed in the United States of America10987654321 Preface to the 5thEditionThe first edition ofFundamentals of Momentum, Heat, and Mass Transfer,published in1969, was written to become a part of what was then known as the engineering sciencecore of most engineering curricula.

3 Indeed, requirements for ABET accreditation havestipulated that a significant part of all curricula must be devoted to fundamental emphasis on engineering science has continued over the intervening years, but thedegree of emphasis has diminished as new subjects and technologies have entered theworld of engineering education. Nonetheless, the subjects of momentum transfer (fluidmechanics), heat transfer, and mass transfer remain, at least in part, important componentsof all engineering curricula. It is in this context that we now present the fifth in computing capability have been astonishing since 1969. At that time, thepocket calculator was quite new and not generally in the hands of engineering editions of this book included increasingly sophisticated solution techniques astechnology advanced. Now, more than 30 years since the first edition, computer competencyamong students is a fait accompli and many homework assignments are completed usingcomputer software that takes care of most mathematical complexity, and a good deal ofphysical insight.

4 We do not judge the appropriateness of such approaches, but they surelyoccur and will do so more frequently as software becomes more readily available, moresophisticated, and easier to this edition, we still include some examples and problems that are posed in Englishunits, but a large portion of the quantitative work presented is now in SI units. This isconsistent with most of the current generation of engineering textbooks. There are still somesubdisciplines in the thermal/fluid sciences that use English units conventionally, so itremains necessary for students to have some familiarity with pounds, mass, slugs, feet, psi,and so forth. Perhaps a fifth edition, if it materializes, will finally be entirely , the original three authors (W3), welcome Dr. Greg Rorrer to our team. Greg is amember of the faculty of the Chemical Engineering Department at Oregon State Universitywith expertise in biochemical engineering.

5 He has had a significant influence on thisedition s sections on mass transfer, both in the text and in the problem sets at the end ofChapters 24 through 31. This edition is unquestionably strengthened by his contributions,and we anticipate his continued presence on our writing are gratified that the use of this book has continued at a significant level since thefirst edition appeared some 30 years ago. It is our continuing belief that the transportphenomena remain essential parts of the foundation of engineering education and the modifications and modernization of this fourth edition, it is our hope thatFundamentals of Momentum, Heat, and Mass Transferwill continue to be an essentialpart of students educational , WeltyMarch RorrervThis page intentionally left blank Contents1. Introduction to Momentum Fluids and the Properties at a Point-to-Point Variation of Properties in a Surface Tension112.

6 Fluid Pressure Variation in a Static Uniform Rectilinear Forces on Submerged Closure253. Description of a Fluid in Fundamental Physical Fluid-Flow Fields: lagrangian and eulerian Steady and Unsteady Systems and Control Volumes324. Conservation of Mass: Control-Volume Integral Specific Forms of the Integral Closure395. Newton s Second Law of Motion: Control-Volume Integral Relation for Linear Applications of the Integral Expression for Linear Integral Relation for Moment of Applications to Pumps and Closure576. Conservation of Energy: Control-Volume Integral Relation for the Conservation of Applications of the Integral The Bernoulli Closure767. Shear Stress in Laminar Newton s Viscosity Non-Newtonian Shear Stress in Multidimensional Laminar Flows of a Newtonian Closure908.

7 Analysis of a Differential Fluid Element in Laminar Fully Developed Laminar Flow in a Circular Conduit of ConstantCross Laminar Flow of a Newtonian Fluid Down an Inclined-Plane Closure979. Differential Equations of Fluid The Differential Continuity Navier-Stokes Bernoulli s Closure11110. Inviscid Fluid Fluid Rotation at a The Stream Inviscid, Irrotational Flow about an Infinite Irrotational Flow, the Velocity Total Head in Irrotational Utilization of Potential Potential Flow Analysis Simple Plane Flow Potential Flow Analysis Closure12311. Dimensional Analysis and Dimensional Analysis of Governing Differential The Buckingham Geometric, Kinematic, and Dynamic Model Closure13412. Viscous Reynolds s The Boundary-Layer The Boundary-Layer Blasius s Solution for the Laminar Boundary Layer on a Flat Flow with a Pressure von Ka rma n Momentum Integral Description of Turbulent Shearing The Mixing-Length Velocity Distribution from the Mixing-Length The Universal Velocity Further Empirical Relations for Turbulent The Turbulent Boundary Layer on a Flat Factors Affecting the Transition From Laminar to Turbulent Closure16513.

8 Flow in Closed Dimensional Analysis of Conduit Friction Factors for Fully Developed Laminar, Turbulent,and Transition Flow in Circular Friction Factor and Head-Loss Determination for Pipe Pipe-Flow Friction Factors for Flow in the Entrance to a Circular Closure18214. Fluid Centrifugal Scaling Laws for Pumps and Axial and Mixed Flow Pump Closure19715. Fundamentals of Heat Thermal Combined Mechanisms of Heat Closure21316. Differential Equations of Heat The General Differential Equation for Energy Special Forms of the Differential Energy Commonly Encountered Boundary Closure222 Contentsix17. Steady-State One-Dimensional One-Dimensional Conduction with Internal Generation of Heat Transfer from Extended Two- and Three-Dimensional Closure24618.

9 Unsteady-State Analytical Temperature-Time Charts for Simple Geometric Numerical Methods for Transient Conduction An Integral Method for One-Dimensional Unsteady Closure27019. Convective Heat Fundamental Considerations in Convective Heat Significant Parameters in Convective Heat Dimensional Analysis of Convective Energy Exact Analysis of the Laminar Boundary Approximate Integral Analysis of the Thermal Boundary Energy- and Momentum-Transfer Turbulent Flow Closure29320. Convective Heat-Transfer Natural Forced Convection for Internal Forced Convection for External Closure31821. Boiling and Closure33422. Heat-Transfer Types of Heat Single-Pass Heat-Exchanger Analysis: The Log-Mean Crossflow and Shell-and-Tube Heat-Exchanger The Number-of-Transfer-Units (NTU) Method of Heat-ExchangerAnalysis and Additional Considerations in Heat-Exchanger Closure356xContents23.

10 Radiation Heat Nature of Thermal The Intensity of Planck s Law of Stefan-Boltzmann Emissivity and Absorptivity of Solid Radiant Heat Transfer Between Black Radiant Exchange in Black Radiant Exchange in Reradiating Surfaces Radiant Heat Transfer Between Gray Radiation from The Radiation Heat-Transfer Closure39324. Fundamentals of Mass Molecular Mass The Diffusion Convective Mass Closure42925. Differential Equations of Mass The Differential Equation for Mass Special Forms of the Differential Mass-Transfer Commonly Encountered Boundary Steps for Modeling Processes Involving Closure44826. Steady-State Molecular One-Dimensional Mass Transfer Independent of Chemical One-Dimensional Systems Associated with Chemical Two- and Three-Dimensional Simultaneous Momentum, Heat, and Mass Closure48827.