《空气动力学》（双语版）Chapter 2 Aerodynamics：Some Fundamental Principles and Equations

PART I FUNDAMENTAL PRINCIPLES (基本原理) In part I, we cover some of the basic principles that apply to aerodynamics in general. These are the pillars on which all of aerodynamics is based

PART I FUNDAMENTAL PRINCIPLES （基本原理） In part I, we cover some of the basic principles that apply to aerodynamics in general. These are the pillars on which all of aerodynamics is based

Chapter 2 Aerodynamics: Some Fundamental Principles and Equations There is so great a difference between a fluid and a collection of solid particles that the laws of pressure and of equilibrium of fluids are very different from the laws of the pressure and equilibrium of solids Jean Le rond d Alembert, 1768

Chapter 2 Aerodynamics: Some Fundamental Principles and Equations There is so great a difference between a fluid and a collection of solid particles that the laws of pressure and of equilibrium of fluids are very different from the laws of the pressure and equilibrium of solids . Jean Le Rond d’Alembert, 1768

2.1 Introduction and Road Map o Preparation of tools for the analysis of aerodynamics Y Every aerodynamic tool we developed in this and subsequent chapters is important for the analysis and understanding of practical problems C Orientation offered by the road map

2.1 Introduction and Road Map Preparation of tools for the analysis of aerodynamics Every aerodynamic tool we developed in this and subsequent chapters is important for the analysis and understanding of practical problems Orientation offered by the road map

2.2 Review of vector relations 92.21 to 2.2.10 Skipped over 2.2.11 Relations between line, surface, and volume Integrals The line integral of A over C is related to the surface integral bf A(curl of A) over S by Stokes'theorem 于Ad=(×A) Where aera s is bounded by the cosed curve c

2.2 Review of Vector relations 2.2.1 to 2.2.10 Skipped over 2.2.11 Relations between line, surface, and volume integrals The line integral of A over C is related to the surface integral of A(curl of A) over S by Stokes’ theorem: A ds ( A) dS C S       Where aera S is bounded by the closed curve C:

he surface integral of A over s is related to the volume integral of A(divergence of A) over v by divergence'theorem ∫As=』(vA S Where volume v is bounded by the closed surface s If p represents a scalar field, a vector relationship analogous to divergence theorem is given by gradient theorem ∫xs=py S

The surface integral of A over S is related to the volume integral of A(divergence of A) over V by divergence’ theorem: d ( )dV S V   A S  A Where volume V is bounded by the closed surface S: If p represents a scalar field, a vector relationship analogous to divergence theorem is given by gradient theorem: pd pdV S V  S  

2. 3 Models of the fluid: control volumes and fluid particles e Importance to create physical feeling from physical observation e How to make reasonable judgments on difficult problems oIn this chapter, basic equations of aerodynamics will be derived o Philosophical procedure involved with the development of these equations

2.3 Models of the fluid: control volumes and fluid particles Importance to create physical feeling from physical observation. How to make reasonable judgments on difficult problems. In this chapter, basic equations of aerodynamics will be derived. Philosophical procedure involved with the development of these equations

1. Invoke three fundamental physical principles which are deeply entrenched in our macroscopic observations of nature, namely a. Mass is conserved, that's to say mass can be neither created nor destroyed. b, Newton's second law, force=mass Acceleration C. Energy is conserved, it can only change from one form to another 2. Determine a suitable model of the fluid 3. Apply the fundamental physical principles isted in item I to the model of the fuid determined in item2 in order to obtain mathematical equations which properly describe the physics of the flow

1. Invoke three fundamental physical principles which are deeply entrenched in our macroscopic observations of nature, namely, a. Mass is conserved, that’s to say, mass can be neither created nor destroyed. b. Newton’s second law: force=mass☓acceleration c. Energy is conserved; it can only change from one form to another 2. Determine a suitable model of the fluid. 3. Apply the fundamental physical principles listed in item 1 to the model of the fluid determined in item2 in order to obtain mathematical equations which properly describe the physics of the flow

o Emphasis of this section 1 What is a suitable model of the fluid? 2 How do we visualize this squishy substance in order to apply the three fundamental principles? 3. Three different mode/s most/y used to deal with aerodynam/cs. finite contro/ volume(有限控制体) infinitesimal/ fuid element(无原小流体微团) molecular(自由分子)

Emphasis of this section: 1. What is a suitable model of the fluid? 2. How do we visualize this squishy substance in order to apply the three fundamental principles? 3. Three different models mostly used to deal with aerodynamics. finite control volume （有限控制体） infinitesimal fluid element （无限小流体微团） molecular （自由分子）

23. 1 Finite control volume approach Definition of finite control volume a closed volume sculptured within a finite region of the fow The volume is called control volume v and the curved surface which envelops this region is defined as control surface s Fixed control volume and moving control volume o Focus of our investigation for fluid flow

2.3.1 Finite control volume approach Definition of finite control volume: a closed volume sculptured within a finite region of the flow. The volume is called control volume V, and the curved surface which envelops this region is defined as control surface S. Fixed control volume and moving control volume. Focus of our investigation for fluid flow

Control surface s S Control volume Finite control volume moving Finite control volume with the fluid such that the fixed in space with the same fluid particles are al ways nuid moving through it in the same control volume