Jets, Wakes, and Cavities

Jets, Wakes, and Cavities

1st Edition - January 1, 1957

Write a review

  • Authors: Zarantonello Eduardo H., G. Birkhoff
  • eBook ISBN: 9780323162715

Purchase options

Purchase options
DRM-free (PDF)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order

Description

Applied Mathematics and Mechanics, Volume 2: Jets, Wakes, and Cavities provides a systematic discussion of jets, wakes, and cavities. This book focuses on the general aspects of ideal fluid theory and examines the engineering applications of fluid dynamics. Organized into 15 chapters, this volume starts with an overview of the different types of jets and explores the atomization of jets in carburetors in connection with gasoline engine design. This text then emphasizes the formal treatment of special flows and examines the flows that are bounded by flat plates and free streamlines. Other chapters consider the flows that are bounded by the cavity behind a symmetric wedge. This book discusses as well the intuitive momentum and similarity considerations. The final chapter deals with several surprising physical complications. Mathematician, physicists, engineers, and readers interested in the fields of applied mathematics, experimental physics, hydraulics, and aeronautics will find this book extremely useful.

Table of Contents


  • Preface

    List of Reference Abbreviations

    I. Background and Prospectus

    1. Examples of Jets

    2. Wakes and Cavities

    3. Plan of Book

    4. Dimensionless Ratios

    5. Real Wakes

    6. Kinds of Cavitation

    7. Parallel Flow Models

    8. Euler Flows

    9. Free Streamlines

    10. Conservation Laws and Jets

    11. Applications to Cavities

    12. Ideal Plane Flows

    13. General Theorems

    14. Applications

    15. Effective Computation; Generalizations

    16. Viscosity and Turbulence

    17. Other Physical Variables

    II. Circular Sector Hodographs

    1. Introduction

    2. Cavity behind Plate

    3. Detailed Formulas

    4. Cavity behind Wedge

    5. Jet from Funnel

    6. Jet against Plate

    7. Réthy Flows

    8. Applications; Superposition Principle

    9. Partial Fractions

    10. Beta Functions

    III. Simple Flows Past Wedges

    1. Introduction

    2. Simple Flows; Reflection Principle

    3. W-diagrams of "simple" Flows

    4. Impinging Jets

    5. Divided Jets

    6. Physical Applications

    7. Simple Flows Past Wedges

    8. Reentrant Jets

    9. Geometrical Classification of Simple Flows

    10. Flows with Circular Sector Hodograph

    11. Other Examples

    IV. General Theory

    1. Singularities of W(T)

    2. Reflection Principle

    3. Asymptotic Geometry of Free Streamlines

    4. Momentum Equations

    5. Drag and Lift

    6. Moment

    7. Separation Curvature

    8. Inflections of Free Boundaries

    9. Free Stream Surfaces

    10. Variational Principle

    11. Extension to Infinite Stream

    12. Lavrentieff's Theorem

    13. Under-over Theorem

    14. Uniqueness Theorem

    15. Minimum Cavity Drag

    V. Multiple Plates

    1. Parametric Rectangle

    2. Case of M Plates

    3. Annular Sector Hodograph

    4. Method of Reflection

    5. Impinging Jets from Nozzles, I

    6. Perpendicular Plates

    7. Position Integral

    8. U-shaped Obstacles II

    9. Riabouchinsky Flows

    10. Impinging Jets from Nozzles, II

    11. General Formulas

    12. Plate in Jet from Nozzle

    13. Interior Sources and Vortices

    14. Cusped Cavities

    15. Hollow Vortices

    VI. Curved Obstacles

    1. Semicircular Parametrization

    2. The Function Ω(t)

    3. Geometrical Interpretations

    4. Basic Integral Equations

    5. Symmetric Cavities

    6. Brillouin-Villat Separation Condition

    7. Asymmetric Case: Parameter Problem

    8. Analogs of Réthy Flows

    9. Physical Applications

    10. Cusped Cavities

    11. Reentrant Jets

    12. Riabouchinsky Flows

    13. Cascades of Airfoils

    14. Other Examples

    VII. Existence and Uniqueness

    1. Historical Introduction

    2. Nearly Flat Obstacles

    3. Leray's Use of Fixpoint Theory

    4. Parameter Problem

    5. Jacob's Lemma

    6. Convex Obstacles

    7. Method of Continuity

    8. Weinstein's Function

    9. Uniqueness

    10. Variational Method; Symmetrization

    11. The Minimizing Profile

    VIII. Compressibility and Gravity

    1. Hodograph Equations

    2. Chaplygin Equation of State

    3. Flows Past Wedges

    4. Curved Obstacles

    5. Polytropic Equation of State

    6. General Equation of State

    7. Integral Equations

    8. Supersonic Jets

    9. Ultra-Fast Jets

    10. Potential Flows with Gravity

    11. Integral Equation Method

    IX. Effective Computation

    1. General Remarks

    2. Cavity behind a Plate

    3. Jet from a Slot

    4. Incomplete Beta Functions

    5. Parameter Problem

    6. Isobars and Isoclines

    7. Related Methods

    8. Curved Barriers

    9. Theoretical Discussion

    10. Other Methods

    X. Axially Symmetric Flows

    1. Typical Problems

    2. Potential Theory

    3. Axial Source Distributions

    4. Source and Vortex Rings

    5. Integral Equation Approaches

    6. Approximate Methods

    7. Jets from Conical Orifices

    8. Impinging Jets

    9. Underwater Cavities

    10. Swirling Flows

    11. Rising Bubbles in Tubes

    XI. Unsteady Potential Flows

    1. Vapor-Filled Spherical Bubbles

    2. Cavitation in a Variable Pressure Field

    3. Gas-filled Cavities

    4. Transient Cavities behind Missiles

    5. Bubble Migration; Laws of Bjerknes

    6. Cavity Induced Mass

    7. Globule Acceleration

    8. Impact Forces

    9. Impact of Cones and Wedges

    10. Constant Acceleration Coefficient

    11. Stability of Plane Interface

    12. Taylor Instability

    13. Spherical and Cylindrical Bubbles

    14. Helmholtz Instability

    15. Stability of Capillary Jets

    16. Stability of other Configurations

    XII. Steady Viscous Wakes and Jets

    1. Boundary Value Problem

    2. Critical Discussion

    3. Wakes in Creeping Flow

    4. Flow Separation

    5. Asymptotic Wake Structure

    6. Wake Momentum

    7. Oseen Equations

    8. Boundary Layer Approximation

    9. Momentum Theorem

    10. Similarity Hypothesis

    11. Creeping Jets

    12. Inertial Effects

    13. Schlichting's Model

    14. Laminar Plane Jets

    15. Exact Self-Similarity

    XIII. Periodic Wakes

    1. Basic Facts

    2. Karman Model

    3. Shedding of Vorticity

    4. Vorticity and Wake Momentum

    5. Vorticity and Drag

    6. Invariance Theorem

    7. Karman's Stability Argument

    8. Strouhal Number

    9. Miscellaneous Effects

    10. Plate at Zero Incidence

    11. Axially Symmetric Periodic Wakes

    12. Periodic Jets; Edge Tones

    13. Bird Tones

    XIV. Turbulent Wakes and Jets

    1. General Remarks

    2. Flow Separation

    3. Base Underpressure

    4. Wake Structure

    5. Wake Turbulence

    6. Mixing Length Concept

    7. Asymptotic Wake Behavior

    8. Wakes with Hydrodynamical Self-Propulsion

    9. Mixing Zone

    10. Structure of Jets

    11. Mixing Length "Theories"

    12. Further Literature

    XV. Miscellaneous Experimental Facts

    1. General Discussion

    2. Bubbling and Boiling

    3. Tensile Strength of Liquids

    4. Bubble Dynamics

    5. Acoustic Cavitation

    6. Cavitation Damage

    7. Propeller Cavitation

    8. Scale Effects in Water Entry

    9. Bubble Entrainment

    10. Jet Persistence

    11. Atomization of Jets

    12. Other Jet Configurations

    Bibliography

    Plates I-II

    Index

Product details

  • No. of pages: 366
  • Language: English
  • Copyright: © Academic Press 1957
  • Published: January 1, 1957
  • Imprint: Academic Press
  • eBook ISBN: 9780323162715

About the Authors

Zarantonello Eduardo H.

G. Birkhoff

Ratings and Reviews

Write a review

There are currently no reviews for "Jets, Wakes, and Cavities"