# Fundamentals of Aerodynamits

Size: px
Start display at page:

Transcription

1 Fundamentals of Aerodynamits Fifth Edition in SI Units John D. Anderson, Jr. Curator of Aerodynamics National Air and Space Museum Smithsonian Institution and Professor Emeritus University of Maryland Mc Graw Hill Singapore Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. Louis Bangkok Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal New Delhi Seoul Sydney Taipei Toronto

2 Preface to the Fifth Edition xix PART 1 Fundamental Principles Chapter 1 Aerodynamics: Some Introductory Thoughts Importance of Aerodynamics: Historical Examples Aerodynamics: Classification and Practical Objectives Road Map for This Chapter Some Fundamental Aerodynamic Variables Units Aerodynamic Forces and Moments Center of Pressure Dimensional Analysis: The Buckingham Pi Theorem Flow Similarity Fluid Statics: Buoyancy Force Types of Flow Continuum Versus Free Molecule Flow Inviscid Versus 'Viscous Flow Incompressible Versus Compressible Flows Mach Number Regimes Viscous Flow: Introduction to Boundary Layers Applied Aerodynamics: The Aerodynamic Coefficients Their Magnitudes and Variations Historical Note: The Illusive Center of Pressure Historical Note: Aerodynamic Coefficients Summary Problems 98 Chapter 2 Aerodynamics: Some Fundamental Principles and Equations Introduction and Road Map Review of Vector Relations Some Vector Algebra Typical Orthogonal Coordinate Systems Scalar and Vector Fields Scalar and Vector Products Gradient of a Scalar Field Divergence of a Vector Field Curl of a Vector Field Line Integrals Surface Integrals Volume Integrals Relations Between Line, Surface, and Volume Integrals Summary Models of the Fluid: Control Volumes and Fluid Elements Finite Control Volume Approach 118 xi

3 xii Contents Infinitesimal Fluid Element Approach Molecular Approach Physical Meaning of the Divergente of Velocity Specification of the Flow Field Continuity Equation Momentum Equation An Application of the Momentum Equation: Drag of a Two-Dimensional Body Comment Energy Equation Interim Summary Substantial Derivative Fundamental Equations in Terms of the Substantial Derivative Pathlines, Streamlines, and Streaklines of a Flow Angular Velocity, Vorticity, and Strain Circulation Stream Function Velocity Potential Relationship Between the Stream Function and Velocity Potential How Do We Solve the Equations? Theoretical (Analytical) Solutions Numerical Solutions-Computational Fluid Dynamics (CFD) The Bigger Picture Summary Problems 198 PART 2 Inviscid, Incompressible Flow 201 Chapter 3 Fundamentals of Inviscid, Incompressible Flow Introduction and Road Map Bernoulli's Equation Incompressible Flow in a Duct: The Venturi and Low-Speed Wind Tunnel Pitot Tube: Measurement of Airspeed Pressure Coefficient Condition an Velocity for Incompressible Flow Governing Equation for Irrotational, Incompressible Flow: Laplace's Equation Infinity Boundary Conditions Wall Boundary Conditions Interim Summary Uniform Flow: Our First Elementary Flow Source Flow: Our Second Elementary Flow Combination of a Uniform Flow with a Source and Sink Doublet Flow: Our Third Elementary Flow Nonlifting Flow over a Circular Cylinder Vortex Flow: Our Fourth Elementary Flow Lifting Flow over a Cylinder The Kutta-Joukowski Theorem and the Generation of Lift Nonlifting Flows over Arbitrary Bodies: The Numerical Source Panel Method Applied Aerodynamics: The Flow over a Circular Cylinder-The Real Case Historical Note: Bernoulli and Euler-The Origins of Theoretical Fluid Dynamics Historical Note: d'alembert and His Paradox Summary Problems 309

4 Contents xiii Chapter 4 fhapter 5 Incompressible Flow over Airfoils 313 Incompressible Flow over Finite Wings Introduction Airfoil Nomenclature Airfoil Characteristics Philosophy of Theoretical Solutions for Low-Speed Flow over Airfoils: The Vortex Sheet The Kutta Condition Without Friction Could We Have Lift? Kelvin's Circulation Theorem and the Starting Vortex Classical Thin Airfoil Theory: The Symmetric Airfoil The Cambered Airfoil The Aerodynamic Center: Additional Considerations Lifting Flows over Arbitrary Bodies: The Vortex Panel Numerical Method Modern Low-Speed Airfoils Viscous Flow: Airfoil Drag Estimating Skin-Friction Drag: Laminar Flow Estimating Skin-Friction Drag: Turbulent Flow Transition Flow Separation Comment Applied Aerodynamics: The Flow over an Airfoil-The Real Case Historical Note: Early Airplane Design and the Role of Airfoil Thickness Historical Note: Kutta, Joukowski, and the Circulation Theory of Lift Summary Problems Introduction: Downwash and Induced Drag The Vortex Filament, the Biot-Savart Law, and Helmholtz's Theorems Prandtl's Classical Lifting-Line Theory Elliptical Lift Distribution General Lift Distribution Effect of Aspect Ratio Physical Significance A Numerical Nonlinear Lifting-Line Method The Lifting-Surface Theory and the Vortex Lattice Numerical Method Applied Aerodynamics: The Delta Wing Historical Note: Lanchester and Prandtl-The Early Development of Finite-Wing Theory Historical Note: Prandtl-The Man Summary Problems 484 Chapter 6 Three-Dimensional Incompressible Flow Introduction Three-Dimensional Source Three-Dimensional Doublet Flow over A Sphere Conzment an the Three-Dimensional Relieving Effect General Three-Dimensional Flows: Panel Techniques Applied Aerodynamics: The Flow over a Sphere-The Real Case 497

5 xiv Contents 6.7 Applied Aerodynamics: Airplane Lift and Drag Airplane Lift Airplane Drag Application of Computational Fluid Dynamics for the Calculation of Lift and Drag Summary Problems 512 PART 3 Inviscid, Compressible Flow 513 Chapter 7 Compressible Flow: Some Preliminary Aspects Introduction A Brief Review of Thermodynamics Perfect Gas Internal Energy and Enthalpy First Law of Thermodynamics Entropy and the Second Law of Thermodynamics Isentropic Relations Definition of Compressibility Governing Equations for Inviscid, Compressible Flow Definition of Total (Stagnation) Conditions Some Aspects of Supersonic Flow: Shock Waves Summary Problems 546 Chapter 8 Normal Shock Waves and Related Topics Introduction The Basic Normal Shock Equations Speed of Sound Comments Special Forms of the Energy Equation When Is A Flow Compressible? Calculation of Normal Shock-Wave Properties Comment on the Use of Tables to Solve Compressible Flow Problems Measurement of Velocity in a Compressible Flow Subsonic Compressible Flow Supersonic Flow Summary Problems 599 Chapter 9 Oblique Shock and Expansion Waves Introduction Oblique Shock Relations Supersonic Flow over Wedges and Cones A Comment on Supersonic Lift and Drag Coefficients Shock Interactions and Reflections Detached Shock Wave in Front of a Blunt Body Comment on the Flow Field behind a Curved Shock Wave: Entropy Gradients and Vorticity Prandtl-Meyer Expansion Waves Shock-Expansion Theory: Applications to Supersonic Airfoils A Comment on Lift and Drag Coefficients The X-15 and Its Wedge Tail Viscous Flow: Shock-Wave/ Boundary-Layer Interaction Historical Note: Ernst Mach-A Biographical Sketch 659

6 Contents xv 9.12 Summary Problems 663 Chapter 10 Compressible Flow through Nozzles, Diffusers, and Wind Tunnels Introduction Governing Equations for Quasi-One-Dimensional Flow Nozzle Flows More on Mass Flow Diffusers Supersonic Wind Tunnels Viscous Flow: Shock-Wave/ Boundary-Layer Interaction inside nozzles Summary Problems 707 Chapter 11 Subsonic Compressible Flow over Airfoils: Linear Theory Introduction The Velocity Potential Equation The Linearized Velocity Potential Equation Prandtl-Glauert Compressibility Correction Improved Compressibility Corrections Critical Mach Number A Comment on the Location of Minimum Pressure (Maximum Velocity) Drag-Divergence Mach Number: The Sound Barrier The Area Rule The Supercritical Airfoil CFD Applications: Transonic Airfoils and Wings Applied Aerodynamics: The Blended Wing Body Historical Note: High-Speed Airfoils-Early Research and Development Historical Note: The Origin of The Swept-Wing Concept Historical Note: Richard T. Whitcomb-Architect of the Area Rule and the Supercritical Wing Summary Problems 776 Chapter 12 Linearized Supersonic Flow Introduction Derivation of the Linearized Supersonic Pressure Coefficient Formula Application to Supersonic Airfoils Viscous Flow: Supersonic Airfoil Drag Summary Problems 794 Chapter 1 a Introduction to Numerical Techniques for Nonlinear Supersonic Flow Introduction: Philosophy of Computational Fluid Dynamics Elements of the Method of Characteristics Internal Points Wall Points Supersonic Nozzle Design Elements of Finite-Difference Methods Predictor Step Corrector Step 817

7 xvi Contents 13.5 The Time-Dependent Technique: Application to Supersonic Blunt Bodies Predictor Step Corrector Step Flow over Cones Physical Aspects of Conical Flow Quantitative Formulation Numerical Procedure Physical Aspects of Supersonic Flow Over Cones Summary Problem 838 Chapter 14 Elements of Hypersonic Flow Introduction Qualitative Aspects of Hypersonic Flow Newtonian Theory The Lift and Drag of Wings at Hypersonic Speeds: Newtonian Results for a Fiat Plate at Angle of Attack Accuracy Considerations Hypersonic Shock-Wave Relations and Another Look at Newtonian Theory Mach Number Independence Hypersonics and Computational Fluid Dynamics Hypersonic Viscous Flow: Aerodynamic Heating Aerodynamic Heating and Hypersonic Flow the Connection Blunt versus Slender Bodies in Hypersonic Flow Aerodynamic Heating to a Blunt Body Applied Hypersonic Aerodynamics: Hypersonic Waveriders ,9.1 Viscous -Optimized Waveriders Summary Problems 890 PART 4 Viscous Flow 891 Chapter 15 Introduction to the Fundamental Principles and Equations of Viscous Flow Introduction Qualitative Aspects of Viscous Flow Viscosity and Thermal Conduction The Navier-Stokes Equations The Viscous Flow Energy Equation Similarity Parameters Solutions of Viscous Flows: A Preliminary Discussion Summary Problems 925 Chapter 16 A Special Case: Couette Flow Introduction Couette Flow: General Discussion Incompressible (Constant Property) Couette Flow Negligible Viscous Dissipation Equal Wall Temperatures Adiabatic Wall Conditions (Adiabatic Wall Temperature) Recovery Factor 944

8 Contents xvii Reynolds Analogy Interim Summary Compressible Couette Flow Shooting Method Time-Dependent Finite-Difference Method Results for Compressible Couette Flow Some Analytical Considerations Summary 963 Chapter 17 Introduction to Boundary Layers Introduction Boundary-Layer Properties The Boundary-Layer Equations How Do We Solve the Boundary-Layer Equations? Summary 979 Chapter 18 Laminar Boundary Layers Introduction Incompressible Flow over a Flat Plate: The Blasius Solution Compressible Flow over a Flat Plate A Comment on Drag Variation with Velocity The Reference Temperature Method Recent Advances: The Meador-Smart Reference Temperature Method Stagnation Point Aerodynamic Heating Boundary Layers over Arbitrary Bodies: Finite-Difference Solution Finite-Difference Method Summary Problems 1018 Chapter 19 Turbulent Boundary Layers Introduction Results for Turbulent Boundary Layers on a Flat Plate Reference Temperature Method for Turbulent Flow The Meador-Smart Reference Temperature Method for Turbulent Flow Prediction of Airfoil Drag Turbulence Modeling The Baldwin -Lomax Model Final Comments Summary Problems 1030 Chapter 20 Navier-Stokes Solutions: Some Examples Introduction The Approach Examples of Some Solutions Flow over a Rearward-Facing Step Flow over an Airfoil Flow over a Complete Airplane Shock-Wave/Boundary-Layer Interaction Flow over an Airfoil with a Protuberance The Issue of Accuracy for the Prediction of Skin Friction Drag Summary 1045 Appendix A Isentropic Flow Properties 1047 Appendix B Normal Shock Properties 1053

9 xviii Contents Appendix C Prandtl-Meyer Function and Mach Angle 1057 Appendix D Standard Atmosphere 1061 Bibliography 1071 Index 1077

### Fundamentals of Aerodynamics

Fundamentals of Aerodynamics Fourth Edition John D. Anderson, Jr. Curator of Aerodynamics National Air and Space Museum Smithsonian Institution and Professor Emeritus University of Maryland Me Graw Hill

### FUNDAMENTALS OF AERODYNAMICS

*A \ FUNDAMENTALS OF AERODYNAMICS Second Edition John D. Anderson, Jr. Professor of Aerospace Engineering University of Maryland H ' McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas

### Introduction to Flight

l_ Introduction to Flight Fifth Edition John D. Anderson, Jr. Curator for Aerodynamics, National Air and Space Museum Smithsonian Institution Professor Emeritus University of Maryland Me Graw Higher Education

### Syllabus for AE3610, Aerodynamics I

Syllabus for AE3610, Aerodynamics I Current Catalog Data: AE 3610 Aerodynamics I Credit: 4 hours A study of incompressible aerodynamics of flight vehicles with emphasis on combined application of theory

### Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

### Inviscid & Incompressible flow

< 3.1. Introduction and Road Map > Basic aspects of inviscid, incompressible flow Bernoulli s Equation Laplaces s Equation Some Elementary flows Some simple applications 1.Venturi 2. Low-speed wind tunnel

### Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION

FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS SECOND EDITION Mc Grauu Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur

### Boundary-Layer Theory

Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22

### Detailed Outline, M E 521: Foundations of Fluid Mechanics I

Detailed Outline, M E 521: Foundations of Fluid Mechanics I I. Introduction and Review A. Notation 1. Vectors 2. Second-order tensors 3. Volume vs. velocity 4. Del operator B. Chapter 1: Review of Basic

### 1. Introduction, tensors, kinematics

1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and

### Fundamentals of Fluid Mechanics

Sixth Edition Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department

### 1. Fluid Dynamics Around Airfoils

1. Fluid Dynamics Around Airfoils Two-dimensional flow around a streamlined shape Foces on an airfoil Distribution of pressue coefficient over an airfoil The variation of the lift coefficient with the

### INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 AERONAUTICAL ENGINEERING TUTORIAL QUESTION BANK Course Name : LOW SPEED AERODYNAMICS Course Code : AAE004 Regulation : IARE

### High Speed Aerodynamics. Copyright 2009 Narayanan Komerath

Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil

### Continuity Equation for Compressible Flow

Continuity Equation for Compressible Flow Velocity potential irrotational steady compressible Momentum (Euler) Equation for Compressible Flow Euler's equation isentropic velocity potential equation for

### Given a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.

Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular

### Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow

### AOE 3114 Compressible Aerodynamics

AOE 114 Compressible Aerodynamics Primary Learning Objectives The student will be able to: 1. Identify common situations in which compressibility becomes important in internal and external aerodynamics

### Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

### An Introduction to the Finite Element Method

An Introduction to the Finite Element Method Third Edition J. N. REDDY Department 01 Mechanical Engineering Texas A&M University College Station, Texas, USA 77843 11 Boston Burr Ridge, IL Dubuque, IA Madison,

### Given the water behaves as shown above, which direction will the cylinder rotate?

water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0

### Contents. I Introduction 1. Preface. xiii

Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

### Compressible Potential Flow: The Full Potential Equation. Copyright 2009 Narayanan Komerath

Compressible Potential Flow: The Full Potential Equation 1 Introduction Recall that for incompressible flow conditions, velocity is not large enough to cause density changes, so density is known. Thus

### Introduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald

Introduction to Fluid Mechanics Chapter 13 Compressible Flow Main Topics Basic Equations for One-Dimensional Compressible Flow Isentropic Flow of an Ideal Gas Area Variation Flow in a Constant Area Duct

### Steady waves in compressible flow

Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

### GAS DYNAMICS. M. Halük Aksel. O. Cahit Eralp. and. Middle East Technical University Ankara, Turkey

GAS DYNAMICS M. Halük Aksel and O. Cahit Eralp Middle East Technical University Ankara, Turkey PRENTICE HALL f r \ New York London Toronto Sydney Tokyo Singapore; \ Contents Preface xi Nomenclature xiii

### 6.1 According to Handbook of Chemistry and Physics the composition of air is

6. Compressible flow 6.1 According to Handbook of Chemistry and Physics the composition of air is From this, compute the gas constant R for air. 6. The figure shows a, Pitot-static tube used for velocity

### PEMP ACD2505. M.S. Ramaiah School of Advanced Studies, Bengaluru

Governing Equations of Fluid Flow Session delivered by: M. Sivapragasam 1 Session Objectives -- At the end of this session the delegate would have understood The principle of conservation laws Different

### SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the

### AEROSPACE ENGINEERING

AEROSPACE ENGINEERING Subject Code: AE Course Structure Sections/Units Topics Section A Engineering Mathematics Topics (Core) 1 Linear Algebra 2 Calculus 3 Differential Equations 1 Fourier Series Topics

### Aerodynamics. Lecture 1: Introduction - Equations of Motion G. Dimitriadis

Aerodynamics Lecture 1: Introduction - Equations of Motion G. Dimitriadis Definition Aerodynamics is the science that analyses the flow of air around solid bodies The basis of aerodynamics is fluid dynamics

### AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS

AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS Hierarchy of Mathematical Models 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 2 / 29

### 1. Introduction Some Basic Concepts

1. Introduction Some Basic Concepts 1.What is a fluid? A substance that will go on deforming in the presence of a deforming force, however small 2. What Properties Do Fluids Have? Density ( ) Pressure

### CHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION

CHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION 7.1 THE NAVIER-STOKES EQUATIONS Under the assumption of a Newtonian stress-rate-of-strain constitutive equation and a linear, thermally conductive medium,

### Hypersonic flow and flight

University of Stuttgart, Aerospace Engineering and Geodesy Dept. - Lecture - Hypersonic flow and flight Master Level, Specialization 4 lecture hours per week in WS, 3-6 LPs/ECTS Lecturer: Dr. Markus J.

### Egon Krause. Fluid Mechanics

Egon Krause Fluid Mechanics Egon Krause Fluid Mechanics With Problems and Solutions, and an Aerodynamic Laboratory With 607 Figures Prof. Dr. Egon Krause RWTH Aachen Aerodynamisches Institut Wüllnerstr.5-7

### Configuration Aerodynamics

Configuration Aerodynamics William H. Mason Virginia Tech Blacksburg, VA The front cover of the brochure describing the French Exhibit at the Montreal Expo, 1967. January 2018 W.H. Mason CONTENTS i CONTENTS

### AERODYNAMICS STUDY NOTES UNIT I REVIEW OF BASIC FLUID MECHANICS. Continuity, Momentum and Energy Equations. Applications of Bernouli s theorem

AERODYNAMICS STUDY NOTES UNIT I REVIEW OF BASIC FLUID MECHANICS. Continuity, Momentum and Energy Equations. Applications of Bernouli s theorem UNIT II TWO DIMENSIONAL FLOWS Complex Potential, Point Source

### INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, yderabad - 500 043 AERONAUTICAL ENGINEERING COURE DECRIPTION FORM Course Title Course Code Regulation Course tructure Course Coordinator Team

### Continuum Mechanics Lecture 5 Ideal fluids

Continuum Mechanics Lecture 5 Ideal fluids Prof. http://www.itp.uzh.ch/~teyssier Outline - Helmholtz decomposition - Divergence and curl theorem - Kelvin s circulation theorem - The vorticity equation

### Copyright 2007 N. Komerath. Other rights may be specified with individual items. All rights reserved.

Low Speed Aerodynamics Notes 5: Potential ti Flow Method Objective: Get a method to describe flow velocity fields and relate them to surface shapes consistently. Strategy: Describe the flow field as the

### ACD2503 Aircraft Aerodynamics

ACD2503 Aircraft Aerodynamics Session delivered by: Prof. M. D. Deshpande 1 Aims and Summary PEMP It is intended dto prepare students for participation i i in the design process of an aircraft and its

### Introduction and Basic Concepts

Topic 1 Introduction and Basic Concepts 1 Flow Past a Circular Cylinder Re = 10,000 and Mach approximately zero Mach = 0.45 Mach = 0.64 Pictures are from An Album of Fluid Motion by Van Dyke Flow Past

### Thin airfoil theory. Chapter Compressible potential flow The full potential equation

hapter 4 Thin airfoil theory 4. ompressible potential flow 4.. The full potential equation In compressible flow, both the lift and drag of a thin airfoil can be determined to a reasonable level of accuracy

### FUNDAMENTALS OF GAS DYNAMICS

FUNDAMENTALS OF GAS DYNAMICS Second Edition ROBERT D. ZUCKER OSCAR BIBLARZ Department of Aeronautics and Astronautics Naval Postgraduate School Monterey, California JOHN WILEY & SONS, INC. Contents PREFACE

### PEMP ACD2505. M.S. Ramaiah School of Advanced Studies, Bengaluru

Two-Dimensional Potential Flow Session delivered by: Prof. M. D. Deshpande 1 Session Objectives -- At the end of this session the delegate would have understood PEMP The potential theory and its application

### Differential Equations

Differential Equations Theory, Technique, and Practice George F. Simmons and Steven G. Krantz Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota

### William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory

### Aerodynamics for Engineering Students

Aerodynamics for Engineering Students Aerodynamics for Engineering Students Sixth Edition E.L. Houghton P.W. Carpenter Steven H. Collicott Daniel T. Valentine AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK

### Chapter 6: Incompressible Inviscid Flow

Chapter 6: Incompressible Inviscid Flow 6-1 Introduction 6-2 Nondimensionalization of the NSE 6-3 Creeping Flow 6-4 Inviscid Regions of Flow 6-5 Irrotational Flow Approximation 6-6 Elementary Planar Irrotational

### Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

### Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017

Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering

### APPLIED FLUID DYNAMICS HANDBOOK

APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.-nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /

### BLUFF-BODY AERODYNAMICS

International Advanced School on WIND-EXCITED AND AEROELASTIC VIBRATIONS OF STRUCTURES Genoa, Italy, June 12-16, 2000 BLUFF-BODY AERODYNAMICS Lecture Notes by Guido Buresti Department of Aerospace Engineering

### ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific

### Summer AS5150# MTech Project (summer) **

AE1 - M.Tech Aerospace Engineering Sem. Course No Course Name Lecture Tutorial Extended Tutorial Afternoon Lab Session Time to be spent outside of class 1 AS5010 Aerodynamics and Aircraft 3 0 0 0 6 9 performance

### Flight Vehicle Terminology

Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes

### 1. (20 pts total 2pts each) - Circle the most correct answer for the following questions.

ME 50 Gas Dynamics Spring 009 Final Exam NME:. (0 pts total pts each) - Circle the most correct answer for the following questions. i. normal shock propagated into still air travels with a speed (a) equal

### CALIFORNIA POLYTECHNIC STATE UNIVERSITY Mechanical Engineering Department ME 347, Fluid Mechanics II, Winter 2018

CALIFORNIA POLYTECHNIC STATE UNIVERSITY Mechanical Engineering Department ME 347, Fluid Mechanics II, Winter 2018 Date Day Subject Read HW Sept. 21 F Introduction 1, 2 24 M Finite control volume analysis

### OUTLINE FOR Chapter 3

013/4/ OUTLINE FOR Chapter 3 AERODYNAMICS (W-1-1 BERNOULLI S EQUATION & integration BERNOULLI S EQUATION AERODYNAMICS (W-1-1 013/4/ BERNOULLI S EQUATION FOR AN IRROTATION FLOW AERODYNAMICS (W-1-.1 VENTURI

### Supersonic Aerodynamics. Methods and Applications

Supersonic Aerodynamics Methods and Applications Outline Introduction to Supersonic Flow Governing Equations Numerical Methods Aerodynamic Design Applications Introduction to Supersonic Flow What does

### Introduction to Aerospace Engineering

4. Basic Fluid (Aero) Dynamics Introduction to Aerospace Engineering Here, we will try and look at a few basic ideas from the complicated field of fluid dynamics. The general area includes studies of incompressible,

### [.B.S.E., M.I.E.T., F.H.E.A. Environment, Heriot-Watt University

Sixth edition JOHN F. DOUGLAS ".Sc, Ph.D., A.C.G.I., D.I.C., C.Eng., M.I.C.E., M.l.Mech.E. Fomieily of London South Bank University JANUSZ M. GASIOREK B.Sc, Ph.D., C.Eng., M.l.Mech.E., M.C.I.B.S.E. Formerly

### Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility

### GAME PHYSICS SECOND EDITION. дяййтаййг 1 *

GAME PHYSICS SECOND EDITION DAVID H. EBERLY дяййтаййг 1 * К AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO MORGAN ELSEVIER Morgan Kaufmann Publishers

### Chapter 3 Bernoulli Equation

1 Bernoulli Equation 3.1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline, is a line that is everywhere tangent to the velocity vector at a given instant. Examples of streamlines around

### DEPARTMENT OF AEROSPACE ENGINEERING, IIT MADRAS B. Tech. Curriculum Semester wise credit distribution

DEPARTMENT OF AEROSPACE ENGINEERING, IIT MADRAS B. Tech. Curriculum Semester wise credit distribution I II III IV V VI VII VIII Total 28 22 25 24 25 28 18 14 184 SEMESTER I AS1010 Introduction to Aerospace

### CLASS SCHEDULE 2013 FALL

CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties

### Boundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON

APPLIED PARTIAL DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fifth Edition Richard Haberman Southern Methodist University PEARSON Boston Columbus Indianapolis New York San Francisco

### Turbomachinery Flow Physics and Dynamic Performance

Turbomachinery Flow Physics and Dynamic Performance Bearbeitet von Meinhard T Schobeiri 1. Auflage 2004. Buch. XXI, 522 S. Hardcover ISBN 978 3 540 22368 9 Format (B x L): 15,5 x 23,5 cm Gewicht: 2070

### 58:160 Intermediate Fluid Mechanics Bluff Body Professor Fred Stern Fall 2014

Professor Fred Stern Fall 04 Chapter 7 Bluff Body Fluid flows are broadly categorized:. Internal flows such as ducts/pipes, turbomachinery, open channel/river, which are bounded by walls or fluid interfaces:

### V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)

IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common

### Mechanics of Flight. Warren F. Phillips. John Wiley & Sons, Inc. Professor Mechanical and Aerospace Engineering Utah State University WILEY

Mechanics of Flight Warren F. Phillips Professor Mechanical and Aerospace Engineering Utah State University WILEY John Wiley & Sons, Inc. CONTENTS Preface Acknowledgments xi xiii 1. Overview of Aerodynamics

### Part A: 1 pts each, 10 pts total, no partial credit.

Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,

### Several forms of the equations of motion

Chapter 6 Several forms of the equations of motion 6.1 The Navier-Stokes equations Under the assumption of a Newtonian stress-rate-of-strain constitutive equation and a linear, thermally conductive medium,

### Engineering Fluid Mechanics

Engineering Fluid Mechanics Eighth Edition Clayton T. Crowe WASHINGTON STATE UNIVERSITY, PULLMAN Donald F. Elger UNIVERSITY OF IDAHO, MOSCOW John A. Roberson WASHINGTON STATE UNIVERSITY, PULLMAN WILEY

### AE301 Aerodynamics I UNIT B: Theory of Aerodynamics

AE301 Aerodynamics I UNIT B: Theory of Aerodynamics ROAD MAP... B-1: Mathematics for Aerodynamics B-: Flow Field Representations B-3: Potential Flow Analysis B-4: Applications of Potential Flow Analysis

### To study the motion of a perfect gas, the conservation equations of continuity

Chapter 1 Ideal Gas Flow The Navier-Stokes equations To study the motion of a perfect gas, the conservation equations of continuity ρ + (ρ v = 0, (1.1 momentum ρ D v Dt = p+ τ +ρ f m, (1.2 and energy ρ

### Fluid Mechanics for Engineers

Fluid Mechanics for Engineers Meinhard T. Schobeiri Fluid Mechanics for Engineers A Graduate Textbook ABC Prof.Dr.-Ing. Meinhard T. Schobeiri Department of Mechanical Engineering Texas A&M University College

### Iran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics

1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration

### Chapter 9 Flow over Immersed Bodies

57:00 Mechanics of Fluids and Transport Processes Chapter 9 Professor Fred Stern Fall 009 1 Chapter 9 Flow over Immersed Bodies Fluid flows are broadly categorized: 1. Internal flows such as ducts/pipes,

### for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?

1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first

### In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.

bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,

### FLUID MECHANICS AND HEAT TRANSFER

AN INTRODUCTION TO FLUID MECHANICS AND HEAT TRANSFER AN INTRODUCTION TO FLUID MECHANICS AND HEAT TRANSFER WITH APPLICATIONS IN CHEMICAL & MECHANICAL PROCESS ENGINEERING BY J. M. KAY AND R. M. NEDDERMAN

### DEPARTMENT OF AEROSPACE ENGINEERING, IIT MADRAS M.Tech. Curriculum

DEPARTMENT OF AEROSPACE ENGINEERING, IIT MADRAS M.Tech. Curriculum SEMESTER I AS5010 Engg. Aerodyn. & Flt. Mech. 3 0 0 3 AS5020 Elements of Gas Dyn. & Propln. 3 0 0 3 AS5030 Aircraft and Aerospace Structures

### AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics

AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:

### Concept: AERODYNAMICS

1 Concept: AERODYNAMICS 2 Narayanan Komerath 3 4 Keywords: Flow Potential Flow Lift, Drag, Dynamic Pressure, Irrotational, Mach Number, Reynolds Number, Incompressible 5 6 7 1. Definition When objects

### Department of Mechanical Engineering

Department of Mechanical Engineering AMEE401 / AUTO400 Aerodynamics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy HOMEWORK ASSIGNMENT #2 QUESTION 1 Clearly there are two mechanisms responsible

### Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics

Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI (after: D.J. ACHESON s Elementary Fluid Dynamics ) bluebox.ippt.pan.pl/

### AA210A Fundamentals of Compressible Flow. Chapter 5 -The conservation equations

AA210A Fundamentals of Compressible Flow Chapter 5 -The conservation equations 1 5.1 Leibniz rule for differentiation of integrals Differentiation under the integral sign. According to the fundamental

### Contents. 1 Introduction to Gas-Turbine Engines Overview of Turbomachinery Nomenclature...9

Preface page xv 1 Introduction to Gas-Turbine Engines...1 Definition 1 Advantages of Gas-Turbine Engines 1 Applications of Gas-Turbine Engines 3 The Gas Generator 3 Air Intake and Inlet Flow Passage 3

### AA210A Fundamentals of Compressible Flow. Chapter 1 - Introduction to fluid flow

AA210A Fundamentals of Compressible Flow Chapter 1 - Introduction to fluid flow 1 1.2 Conservation of mass Mass flux in the x-direction [ ρu ] = M L 3 L T = M L 2 T Momentum per unit volume Mass per unit

### MDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag. G. Leng, MDTS, NUS

MDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag 2.1. The design of supersonic airfoils For efficient lift generation at subsonic speeds, airfoils look like : So why can t a similar

Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...

### Dynamic Systems. Modeling and Analysis. Hung V. Vu. Ramin S. Esfandiari. THE McGRAW-HILL COMPANIES, INC. California State University, Long Beach

Dynamic Systems Modeling and Analysis Hung V. Vu California State University, Long Beach Ramin S. Esfandiari California State University, Long Beach THE McGRAW-HILL COMPANIES, INC. New York St. Louis San

### Drag (2) Induced Drag Friction Drag Form Drag Wave Drag

Drag () Induced Drag Friction Drag Form Drag Wave Drag Outline Nomenclature and Concepts Farfield Drag Analysis Induced Drag Multiple Lifting Surfaces Zero Lift Drag :Friction and Form Drag Supersonic

### The E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012

The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel