# Momentum Transfer in Fluids

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Momentum Transfer in Fluids provides information pertinent to fluid mechanics. This book discusses several topics related to the movement of fluids, including boundary-layer analysis, statistical treatment of turbulence, as well as laminar and turbulent shear-flow. Comprised of seven chapters, this book starts with an overview of the physical nature of momentum and describes the application of this concept to systems of variable weight, which are useful in the prediction of the physical behavior of fluids in motion. This text then explores the fundamental properties and the macroscopic aspects of turbulent flow. Other chapters present the significance and utility of mixing length and other macroscopic turbulence parameters. This book discusses as well the prediction of the velocity and friction as functions of position in the flowing stream. The final chapter deals with the qualitative aspects of boundary flows for compressible and incompressible fluids. This book is a valuable resource for scientists and chemical engineers.

## Table of Contents

Preface

Chapter I. Introduction to momentum transfer

I-1. Fundamental Variables

I-2. Frames of Reference

I-3. Definition of Element of Volume

I-4. Conservation of Momentum

I-5. Pressure Gradient

I-6. Thermodynamics of Flowing Systems

I-7. Stress and Deformation

I-8. Types of Fluid Flow

I-9. Time Averages

I-10. Flow Equation for an Important Special Case

I-11. Flow in a Circular Pipe

Example I

I-12. The Bernoulli Equation

I-13. Flow between Parallel Flat Plates

I-14. Laminar Flow in a Cylindrical Pipe

I-15. Steady, Uniform, Laminar Flow between Parallel Plates

I-16. Dimensionless Parameters

Example 2

Example 3

I-17. Transition from Laminar to Turbulent Flow

I-18. Friction Coefficients

I-19. Smooth and Rough Circular Pipes

Nomenclature

References

Chapter II. Some Simple Properties of Turbulent Flow

II-1. Concepts of Flow

II-2. Temperature Fluctuations

II-3. Transfer of Momentum as a Result of Turbulence

II-4. Measurement of Velocity

II-5. Characteristic Length

II-6. Mixing Length

II-7. Eddy Viscosity

II-8. Dimensionless Relations

II-9. Flow near Boundary

Nomenclature

References

Chapter III. Some Macroscopic Characteristics of Turbulent Flow

III-1. The Similarity Hypothesis

III-2. Idealized Turbulent Flow between Parallel Plates Based on Similarity Hypothesis

III-3. Idealized Turbulent Flow in a Circular Channel — Similarity Hypothesis

III-4. The Momentum Transfer Hypothesis

ΙΙΙ-5. Idealized Turbulent Flow between Parallel Plates — Momentum Transfer Hypothesis

III-6. Transport Characteristics

III-7. The Vorticity Transport Hypothesis

III-8. Simplified Velocity Deficiency Relations

Nomenclature

References

Chapter IV. Velocity Distribution and Friction Factors for Turbulent Flow

IV-1. Velocity Distribution at Boundary in Circular Conduits

IV-2. Transition Region

IV-3. Flow between Parallel Plates

IV-4. Behavior near Center of Channel

IV-5. Bulk Velocities

IV-6. Resistance to Flow

IV-7. Resistance Factor λ

IV-8. Laminar Film Thickness

IV-9. Velocity Distribution in Rough Conduits

IV-10. Friction Factor

IV-11. Experimental Results for Flow in Circular Conduits

Nomenclature

References

Chapter V. General Equations of Fluid Motion

V-1. Equation of Continuity

V-2. Boundary Conditions for the Equation of Continuity

V-3. Acceleration of the Flowing Fluid

V-4. External Forces Acting on a Flowing Fluid

V-5. Forces Acting on the Surface of a Portion of a Flowing Fluid

V-6. Momentum Equations for a Flowing Fluid

V-7. Acceleration of the Flowing Fluid (Continued)

V-8. Evaluation of the Surface Stresses in a Flowing Fluid

V-9. Navier-Stokes Equations

V-10. Navier-Stokes Equations in Cylindrical Coordinates

V-11. Navier-Stokes Equations for Spherical Coordinates

V-12. Dimensionless Form of the Equations of Motion

Example 1

Example 2

V-13. Initial and Boundary Conditions for the Equations of Motion

V-14. Comments on the Solution of the Equations of Motion

V-15. General Discussion of Turbulent Flow

V-16. Reynolds Transformation of the Equations of Motion

Example 3

Nomenclature

References

Chapter VI. Some Properties of Turbulence

VI-1. Measurement of the Physical Nature of Turbulence

VI-2. Correlations

VI-3. Characteristic Properties

VI-4. Kinetic Energy

VI-5. Spectrum of Turbulence

VI-6. Decay of Turbulence

VI-7. Temperature Fluctuations

VI-8. Eddy Viscosities

VI-9. Structure of Turbulent Shear-Flow

Nomenclature

References

Chapter VII. Boundary Layer

VII-1. Steady Uniform Flow

VII-2. Nonuniform, Steady Boundary-Flow

VII-3. Transition

VII-4. Boundary Flows for Incompressible Fluids

VII-5. Navier-Stokes Equations

VII-6. Environmental Conditions

VII-7. Separation

VII-8. Drag on Immersed Bodies

VII-9. Flow along a Flat Plate

Example 1

Example 2

VII-10. Drag

VII-11. Thickness of Boundary Layer

VII-12. Effect of Curvature

VII-13. Flow about Circular Cylinders

Example 3

VII-14. The Momentum Theorem

VII-15. A Polynomial Velocity Distribution

Example 4

VII-16. Estimation of Separation

VII-17. Analysis

VII-18. Turbulent Boundary Layers

VII-19. Effect of Anisotropic Turbulence

VII-20. Minor Correction Terms

VII-21. Effects of Dissipation and Thermal Transfer

VII-22. Temperature Recovery Factors

VII-23. Laminar Flow

VII-24. Slip Flow

VII-25. Turbulent Flow

Nomenclature

References

Appendix I. A derivation of Bernoulli's Equation

Nomenclature

Appendix II. An Introduction to Tensors and the Statistical Theory of Turbulence

AII-1. An Introduction to Tensors

ΑΙΙ-2. Newtonian Stress Tensor

ΑΙΙ-3. Acceleration in Generalized Coordinates

ΑΙΙ-4. Components of Vorticity

ΑΙΙ-5. Navier-Stokes Equation

AII-6. Reynolds Stresses

AII-7. Bernoulli's Equation

AII-8. Definition of Isotropic Turbulence

AII-9. Derivation of the Correlation Tensor for Isotropic Turbulence

AII-10. Correlation Coefficients between the Derivatives of the Velocities

AII-11. Expression of Mean Values by Integrals

AII-12. Correlation between Pressure and Velocity

AII-13. Triple Correlations

AII-14. Propagation of the Correlation

AII-15. Relation between Correlation and Spectral Theories

Nomenclature

References

Appendix III. Constants and Conversion Factors, Dimensions

Nomenclature

References

Appendix IV. Analysis of Potential Flow Across a Cylinder

References

Index

## Product details

- No. of pages: 406
- Language: English
- Copyright: © Academic Press 1956
- Published: January 1, 1956
- Imprint: Academic Press
- eBook ISBN: 9780323151924