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

Size: px
Start display at page:

Transcription

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

2 Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The most relevant one is the pressure distribution as it is the pressure distribution that causes Lift force to be generated on an airplane. Air will travel from a place of high pressure to low pressure causing a lift to be generated. Most airplanes will need to have an area of low pressure on top of the plane.

3 Types of Aerodynamic Flow It is essential to understand the types of flow in order to understand the physical phenomena behind them. Types of flow include: - Continuum vs. Molecular Flow - Inviscid vs. Viscous Flow - Incompressible vs. Compressible Flow - Laminar Flow vs. Turbulent Flow

4 Continuum Flow Molecular Flow

5 Inviscid Flow vs. Viscous Flow

6 Laminar Flow Turbulent Flow

7 Compressible Flow Incompressible Flow

8 Laws of Aerodynamics Several principles or physical laws will govern aerodynamic equations. These include: Equation of state Conservation of Mass Newton s Second Law (Conservation of Momentum) Conservation of Energy

9 Equation of State Equation of State for ideal gases state how parameters such as pressure, density and temperature relate to each other. The equation of state is: ρrt = P

10 Conservation of Mass Mass can be neither created or destroyed. Hence, if we take a streamtube, the amount of fluid entering the tube and exiting it will be the same. Mass of the flow sweeping through A is: dm=ρ(avdt) Mass Flow can be derived as dm/dt

11 Continuity Equation Since mass can neither be created or destroyed, mass flow on entrance and exit will equal to each other. Thus the Continuity Equation becomes: AV A V

12 ontinuity Equation in Incompressible Flow In incompressible flow, the density is treated as constant. For most type of flows, it is possible to treat as incompressible especially for small commercial planes. Hence the continuity equation for incompressible flow is: V A V A1 1 2

13 Momentum Equation Newton's Second Law guides the flow of fluid and helps us to find the equation of momentum Force = mass x acceleration (F=ma) Force is caused by pressure, frictional shear and by gravity acting on the mass inside the element. Hence, by integrating these forces and by neglecting friction and gravity we get the Euler s equation.

14 Bernoulli Equation If we integrate the Euler equation for a frictionless and incompressible flow (density constant)

15 Wind Tunnel Speed Determination Using Bernoulli equation, it is possible to find that the velocity of the test object depends in the pressure difference in the wind tunnel.

16 Measurement of Airspeed Pitot Tube Especially for aircraft, measurement of air speed is a very important thing. For any type of flow (even for flows that are not constant), we can measure air speed by using a device called the Pitot Tube. In order to analyze Pitot Tube, we need to understand static pressure and total pressure. Static pressure is the pressure caused by the random motion of the gas particles. Type of flow doesn t change static pressure. Total pressure is the pressure caused by the flow itself and hence its pressure, density and temperature values effect total pressure. Total pressure is also defined as a pressure that would exist even if the flow was slowed down to zero velocity.

17 Pitot Tube Pitot tube uses static pressure as well as the total pressure of the flow in relation with the Bernoulli equation to measure air speed.

18 Pitot Tube Pitot tube is found frequently on the airplanes to measure air speed constantly.

19 Conservation of Energy and Flows Especially in high speed flows near or above the speed of sound, you will have to take in the energy equations into account. A high speed flow is also a high energy flow due to the definition of velocity and kinetic energy. When high speed flows are slowed down, the consequent reduction in kinetic energy appears as an increase in temperature. Hence, high speed flows, compressibility and energy changes are inter related.

20 Thermodynamics Terminology In order to understand high speed flows, we need to understand basic terms in thermodynamics. Specific Heat (c) is the heat added per unit change in temperature of the system. Specific heat (Cv) at constant volume is calculated pe constant volume Specific heat at constant pressure (Cp) is calculated at constant pressure. γ = cp/cv is termed as the ratio of specific heats

21 Laws of Thermodynamics There are four laws of thermodynamics that govern our universe: Zeroth law: Heat equilibrium First Law: Energy remains the same Second Law: Entropy always increases Third Law: As you reach absolute zero, entropy will decrease

22 Thermodynamic Equations for Perfect Gas de c v dt dh c p dt e c v T h c p T

23 Isentropic Flow One of the most important concepts of thermodynamics and compressible aerodynamics is isentropic flow. Adiabatic process is a process is one in which no heat is added or taken away Reversible flow is in which friction and dissipation does not take place Isentropic process is both adiabatic and reversible. Hence in isentropic flow entropy is constant.

24 Isentropic Flow Equations Most isentropic flows are applicable to compressible flows. Isentropic flow equations create a relationship between pressure, temperature and density T T p p

25 Energy Equation Energy equation is the third fundamental law that describes the properties of the flow. Energy equations are useful for compressible flow. Energy equation describes the fact that energy can neither be created or destroyed.

26 Energy Equation for Adiabatic Flow h 1 V h 2 V c p T V 2 1 c p T V 2 2

27 Summary of Equations For steady, incompressible and inviscid flow, you need to use the Continuity equation and the Bernoulli equation. For isentropic, compressible flow: - Continuity Equation - Isentropic relations - Equation of State - Energy Equation

28 Speed of Sound Sound waves travel through the air at definite speed. That speed is called the speed of sound Speed of sound is an important variable in analyzing compressible flow

29 Speed of Sound On a physical basis, the flow through a sound wave involves no heat addition and the effect of friction is negligible. Thus, the flow through a sound wave is isentropic. Thus speed of sound for a gas and also for a perfect gas is:

30 Why Does Speed of Sound Depend on Temperature? Speed of sound is directly dependent on temperature. This is due to the fact that propagation of a sound wave through gas takes place via molecular collisions. Hence, the energy of a soundwave is transmitted through the air by molecules that collide with each other. The mean kinetic energy associated with these collisions is linked to the temperature of the gas. (More hotter means more faster and thus more kinetic energy)

31 Mach Number Mach number denotes the magnitude of the flow as compared to the speed of sound If M < 1 the flow is subsonic If M = 1 the flow is sonic If M > 1 the flow is supersonic If M > 5 the flow is hypersonic M V a

32 Shockwaves in Compressible Flow Whenever there is a flow that is faster than a speed of sound, then shock waves can occur as the aircraft travels in a compressible region. A shockwave is an extremely thin region where the flow properties change drastically. They are usually in the order of cm. A shockwave is a explosive compression process where the pressure increases discontinuously across the wave. This huge level of compression and pressure increase can have adverse effects if the craft is not made supersonic resistant.

33 Shockwaves in Compressible Flow

34 Shockwaves

35 Characteristics of Shock Waves The biggest characteristics of a shockwave is that the pressure will increase greatly as the shockwave is passed. When a shock wave passes through matter, the total energy is preserved but the energy which can be extracted as work decreases and entropy increases. This, for example, creates additional drag force on aircraft with shocks

36 General Properties of Shockwaves

37 General Properties of Shockwaves When you pass across a shockwave: Pressure increases P2 > P1 Temperature increases T2 > T1 Density increases Entropy increases Mach number decreases M2 < M1 Flow velocity decreases

38 Viscous Flow In reality every flow in the world is a viscous flow. Viscosity is the phenomena of friction that acts on all objects and fluids. In viscous flow, friction of surfaces, heat transfer and energy transfer between molecules and mass transfer (diffusion) takes place.

39 Examples of Viscous Flow

40 Examples of Viscous Flow

41 Examples of Viscous Flow

42 Friction (Viscosity) Creates Shear Stress

43 No Slip Condition The influence of friction creates V=0 at the body surface and this is called no-slip condition.

44 Heat Transfer in Viscous Flow The moving fluid has a certain amount of energy. As it flows on the surface, the flow velocity is decreased due to friction. This decrease in velocity is translated as a decrease in kinetic energy. This loss of kinetic energy transforms into internal energy of the fluid. (Conservation of Energy) Hence, the temperature of the fluid will rise.

45 Aerodynamic Heating in Viscous Flow As a result, warmer fluid will heat the cooler surface of the body. This is called aerodynamic heating. This becomes more severe since as flow velocity increases aerodynamic heating will also increase.

46 Boundary Layer Definition Boundary Layer is the thin boundary region between the flow and the solid surface, where the flow is retarded due to friction between the solid body and the fluid flow.

47 What is the Significance of Boundary Layers? Although friction exists in all types of flow, practically it is only of consequence in the thin region separating the flow and the solid body. Hence, as far as the physical system is concerned, the boundary layer is the region where mass transfer, momentum transfer, heat transfer, friction effects and all viscosity effects are felt.

48 How Does a Boundary Layer Help Engineers! This means that instead of solving for the whole Navier Stokes equation set for the full flow, we can approximate a solution by solving for the boundary layer where the viscous effects are felt. Thus, in order to calculate skin friction and aerodynamic heating at the surface, you only have to account for friction and thermal conduction within the thin boundary layer. Hence; you wont need to analyze the large flow outside the boundary layer

49 Representation of a Boundary Layer

50 Representation of a Boundary Layer

51 Shape of a Boundary Layer Because of No-Slip condition, the velocity of the fluid is Zero at the surface and it gradually increases.

52 Reynolds Number Reynolds Number is the most important parameter in viscous aerodynamics or in fluid mechanics. It determines the type of the flow and it helps to determine the characteristics of the flow. Reynolds Number is the ratio between inertial forces to viscous forces Re V L

53 Turbulent Flow Higher Reynolds Numbers usually denote turbulent flow. Turbulent flow can be desired in certain situations

54 Laminar and Turbulent Flow

55 When is Turbulent Flow Desirable?

### Compressible Flow. Professor Ugur GUVEN Aerospace Engineer Spacecraft Propulsion Specialist

Compressible Flow Professor Ugur GUVEN Aerospace Engineer Spacecraft Propulsion Specialist What is Compressible Flow? Compressible Flow is a type of flow in which the density can not be treated as constant.

### 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

### 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

### 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

### Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

### 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

### 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

### 3. FORMS OF GOVERNING EQUATIONS IN CFD

3. FORMS OF GOVERNING EQUATIONS IN CFD 3.1. Governing and model equations in CFD Fluid flows are governed by the Navier-Stokes equations (N-S), which simpler, inviscid, form is the Euler equations. For

### 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

### 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,

### Fluid Mechanics. Spring 2009

Instructor: Dr. Yang-Cheng Shih Department of Energy and Refrigerating Air-Conditioning Engineering National Taipei University of Technology Spring 2009 Chapter 1 Introduction 1-1 General Remarks 1-2 Scope

### Objectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation

Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved

### Chapter 1: Basic Concepts

What is a fluid? A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid? Solid: can resist an applied shear by deforming. Stress is proportional to strain Fluid: deforms

### 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

### Principles of Convection

Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

### 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

### 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

### Differential relations for fluid flow

Differential relations for fluid flow In this approach, we apply basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of a flow

### 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

### Review of Fundamentals - Fluid Mechanics

Review of Fundamentals - Fluid Mechanics Introduction Properties of Compressible Fluid Flow Basics of One-Dimensional Gas Dynamics Nozzle Operating Characteristics Characteristics of Shock Wave A gas turbine

### Fundamentals of Aerodynamits

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

### 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.........................

### 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

### vector H. If O is the point about which moments are desired, the angular moment about O is given:

The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment

### 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

### UOT Mechanical Department / Aeronautical Branch

Chapter One/Introduction to Compressible Flow Chapter One/Introduction to Compressible Flow 1.1. Introduction In general flow can be subdivided into: i. Ideal and real flow. For ideal (inviscid) flow viscous

### Notes 4: Differential Form of the Conservation Equations

Low Speed Aerodynamics Notes 4: Differential Form of the Conservation Equations Deriving Conservation Equations From the Laws of Physics Physical Laws Fluids, being matter, must obey the laws of Physics.

### 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

### 4 Compressible Fluid Dynamics

4 Compressible Fluid Dynamics 4. Compressible flow definitions Compressible flow describes the behaviour of fluids that experience significant variations in density under the application of external pressures.

### 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

### Applied Gas Dynamics Flow With Friction and Heat Transfer

Applied Gas Dynamics Flow With Friction and Heat Transfer Ethirajan Rathakrishnan Applied Gas Dynamics, John Wiley & Sons (Asia) Pte Ltd c 2010 Ethirajan Rathakrishnan 1 / 121 Introduction So far, we have

Tutorial Materials for ME 131B Fluid Mechanics (Compressible Flow & Turbomachinery) Calvin Lui Department of Mechanical Engineering Stanford University Stanford, CA 94305 March 1998 Acknowledgments This

### Mechanical Engineering Science for Medical Engineers Level: 4 Credit value: 8 GLH: 62 TQT: 80

This unit has 6 learning outcomes. 1. Be able to solve engineering problems that involve variable and constant acceleration motion. 1.1. Apply dimensional analysis to an equation involving units of length,

### Performance. 5. More Aerodynamic Considerations

Performance 5. More Aerodynamic Considerations There is an alternative way of looking at aerodynamic flow problems that is useful for understanding certain phenomena. Rather than tracking a particle of

### 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,

### Isentropic Flow. Gas Dynamics

Isentropic Flow Agenda Introduction Derivation Stagnation properties IF in a converging and converging-diverging nozzle Application Introduction Consider a gas in horizontal sealed cylinder with a piston

### 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

### 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

### Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us

Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan

### 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.

CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise

### 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

### 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

### BERNOULLI EQUATION. The motion of a fluid is usually extremely complex.

BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over

### Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer

### Chapter Two. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency. Laith Batarseh

Chapter Two Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency Laith Batarseh The equation of continuity Most analyses in this book are limited to one-dimensional steady flows where the velocity

### 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,

### 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

### Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Lecture slides Challenge the future 4-0-0 Introduction to Aerospace Engineering Aerodynamics 3 & 4 Prof. H. Bijl ir. N. Timmer Delft University of Technology Challenge

### 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,

### 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

### Section 2: Lecture 1 Integral Form of the Conservation Equations for Compressible Flow

Section 2: Lecture 1 Integral Form of the Conservation Equations for Compressible Flow Anderson: Chapter 2 pp. 41-54 1 Equation of State: Section 1 Review p = R g T " > R g = R u M w - R u = 8314.4126

### Review of Fluid Mechanics

Chapter 3 Review of Fluid Mechanics 3.1 Units and Basic Definitions Newton s Second law forms the basis of all units of measurement. For a particle of mass m subjected to a resultant force F the law may

### 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,

### Notes #4a MAE 533, Fluid Mechanics

Notes #4a MAE 533, Fluid Mechanics S. H. Lam lam@princeton.edu http://www.princeton.edu/ lam October 23, 1998 1 The One-dimensional Continuity Equation The one-dimensional steady flow continuity equation

### 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

### AE 2020: Low Speed Aerodynamics. I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson

AE 2020: Low Speed Aerodynamics I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson Text Book Anderson, Fundamentals of Aerodynamics, 4th Edition, McGraw-Hill, Inc.

### Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum

### 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

### 1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature

CHAPTER 11 1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature 2.In Equation 11.7 the subscript p on the partial derivative refers to differentiation at

### 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

### 150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces

Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with

### CONVECTIVE HEAT TRANSFER

CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 3 LAMINAR BOUNDARY LAYER FLOW LAMINAR BOUNDARY LAYER FLOW Boundary

### MAE 224 Notes #4a Elements of Thermodynamics and Fluid Mechanics

MAE 224 Notes #4a Elements of Thermodynamics and Fluid Mechanics S. H. Lam February 22, 1999 1 Reading and Homework Assignments The problems are due on Wednesday, March 3rd, 1999, 5PM. Please submit your

### Entry Aerodynamics MARYLAND U N I V E R S I T Y O F. Entry Aerodynamics. ENAE Launch and Entry Vehicle Design

Atmospheric Regimes on Entry Basic fluid parameters Definition of Mean Free Path Rarified gas Newtonian flow Continuum Newtonian flow (hypersonics) 2014 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu

### Introduction. In general, gases are highly compressible and liquids have a very low compressibility. COMPRESSIBLE FLOW

COMRESSIBLE FLOW COMRESSIBLE FLOW Introduction he compressibility of a fluid is, basically, a measure of the change in density that will be produced in the fluid by a specific change in pressure and temperature.

### Chapter 5. The Differential Forms of the Fundamental Laws

Chapter 5 The Differential Forms of the Fundamental Laws 1 5.1 Introduction Two primary methods in deriving the differential forms of fundamental laws: Gauss s Theorem: Allows area integrals of the equations

### 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

### List of symbols. Latin symbols. Symbol Property Unit

Abstract Aircraft icing continues to be a threat for modern day aircraft. Icing occurs when supercooled large droplets (SLD s) impinge on the body of the aircraft. These droplets can bounce off, freeze

### 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:

### Fluid Mechanics Theory I

Fluid Mechanics Theory I Last Class: 1. Introduction 2. MicroTAS or Lab on a Chip 3. Microfluidics Length Scale 4. Fundamentals 5. Different Aspects of Microfluidcs Today s Contents: 1. Introduction to

### 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

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

Introduction to Atmospheric Flight Dr. Guven Aerospace Engineer (P.hD) What is Atmospheric Flight? There are many different ways in which Aerospace engineering is associated with atmospheric flight concepts.

### Compressible Duct Flow with Friction

Compressible Duct Flow with Friction We treat only the effect of friction, neglecting area change and heat transfer. The basic assumptions are 1. Steady one-dimensional adiabatic flow 2. Perfect gas with

### Fanno Flow. Gas Dynamics

Fanno Flow Simple frictional flow ( Fanno Flow Adiabatic frictional flow in a constant-area duct * he Flow of a compressible fluid in a duct is Always accompanied by :- ariation in the cross sectional

### 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

### n v molecules will pass per unit time through the area from left to

3 iscosity and Heat Conduction in Gas Dynamics Equations of One-Dimensional Gas Flow The dissipative processes - viscosity (internal friction) and heat conduction - are connected with existence of molecular

### 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

### 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

### 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

### Ph.D. Qualifying Exam in Fluid Mechanics

Student ID Department of Mechanical Engineering Michigan State University East Lansing, Michigan Ph.D. Qualifying Exam in Fluid Mechanics Closed book and Notes, Some basic equations are provided on an

### A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension

A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension forces. 2 Objectives 3 i i 2 1 INTRODUCTION Property:

### Lecture1: Characteristics of Hypersonic Atmosphere

Module 1: Hypersonic Atmosphere Lecture1: Characteristics of Hypersonic Atmosphere 1.1 Introduction Hypersonic flight has special traits, some of which are seen in every hypersonic flight. Presence of

UNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes

### 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

### An Essential Requirement in CV Based Industrial Appliances.

Measurement of Flow P M V Subbarao Professor Mechanical Engineering Department An Essential Requirement in CV Based Industrial Appliances. Mathematics of Flow Rate The Scalar Product of two vectors, namely

### 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

### 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

### 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

### ME3250 Fluid Dynamics I

ME3250 Fluid Dynamics I Section I, Fall 2012 Instructor: Prof. Zhuyin Ren Department of Mechanical Engineering University of Connecticut Course Information Website: http://www.engr.uconn.edu/~rzr11001/me3250_f12/

### SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow 1. Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95.

### Introduction to Turbomachinery

1. Coordinate System Introduction to Turbomachinery Since there are stationary and rotating blades in turbomachines, they tend to form a cylindrical form, represented in three directions; 1. Axial 2. Radial

### 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 /

### ( ) Notes. Fluid mechanics. Inviscid Euler model. Lagrangian viewpoint. " = " x,t,#, #

Notes Assignment 4 due today (when I check email tomorrow morning) Don t be afraid to make assumptions, approximate quantities, In particular, method for computing time step bound (look at max eigenvalue

### 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:

### IX. COMPRESSIBLE FLOW. ρ = P

IX. COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity.

### Astrophysical Fluid Dynamics (2)

Astrophysical Fluid Dynamics (2) (Draine Chap 35;;Clarke & Carswell Chaps 1-4) Last class: fluid dynamics equations apply in astrophysical situations fluid approximation holds Maxwellian velocity distribution

### ρ Du i Dt = p x i together with the continuity equation = 0, x i

1 DIMENSIONAL ANALYSIS AND SCALING Observation 1: Consider the flow past a sphere: U a y x ρ, µ Figure 1: Flow past a sphere. Far away from the sphere of radius a, the fluid has a uniform velocity, u =

### Fluid Mechanics. du dy

FLUID MECHANICS Technical English - I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's