CHAPTER 8
ENTROPY GENERATION AND TRANSPORT
8.1 CONVECTIVE FORM OF THE GIBBS EQUATION
In this chapter we will address two questions.
1) How is Gibbs equation related to the energy conservation equation?
2) How is the entropy of a uid affected by its 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, the equations of motion for compressible ow becom

CHAPTER 14
THIN AIRFOIL THEORY
14.1 COMPRESSIBLE POTENTIAL FLOW
14.1.1
THE FULL POTENTIAL EQUATION
In compressible ow, both the lift and drag of a thin airfoil can be determined to
a reasonable level of accuracy from an inviscid, irrotational model of the

CHAPTER 4
CONTROL VOLUMES, VECTOR CALCULUS
4.1 CONTROL VOLUME DEFINITION
The idea of the control volume is an extremely general concept used widely in
uid mechanics. In Chapter 1 we derived the equations for conservation of mass
and momentum on a small cu

AA200A Homework 7 2014 -2015
Due Thursday May 28
Read: Chapters 12 and 13
Problem 1 Take the 2-D wing you studied in Homework 6 and use it as the cross-section of an elliptical
planform 3-D wing with aspect ratio 10. Determine the lift, skin friction drag

AA200A Homework 6 2014 -2015
Due Tuesday May 19, 2015
Read: Chapter 11
Recommended Reading: Chapter 3 in Wing Theory by R. T. Jones
Problem 1 Reproduce the results in section 11.2 for the flow around a Joukowsky
airfoil. Using that airfoil or, if wish a J

AA200A Homework 5 2014 -2015
Due Tuesday May 12
Read: Chapter 10
Problem The 2-D stream function for potential flow over an elliptically shaped body at
zero angle of attack is produced by the superposition of a uniform flow plus a source and
a sink of equ

AA200A Homework 4 2014 - 2015
Due Tuesday April 30
Read Chapter 9
Problem 1 - Consider a zero pressure gradient laminar boundary layer on a flat plate with mass transfer at
the wall. Let the vertical component of velocity at the wall be a power law of the

AA200A Homework 3 2014 -2015
Due Thursday April 23
Review: Chapters 3 and 4
Read: Chapter 5
Chapter 5 - Problems 7 and 8 and
Problem - The image below by Werle shows a visualization of the flow around a circular cylinder attached
to a wall in a water chan

AA200A Homework 2 2014 -2015
Due Thursday April 16
Read: Chapter 2
Chapter 2 - Problems 1, 4, 6 and 12
Use some basic physics to help your analysis. Check the solution using the web if you wish but try to work
the problem using dimensional analysis first.

AA200 HOMEWORK 4 SOLUTION
Man Long Wong
May 4, 2015
Problem 1
Assumptions:
Boundary layer assumptions:
L,
x
y ,
and V
U
Two dimensional ow
Steady ow
t
=0
Laminar ow xx = yy = 0
Incompressible ow
D
Dt
No pressure gradient
=0
P
x
=0
Start with the

AA200 HOMEWORK 6 SOLUTION
2014-2015 Spring
May 22, 2015
Problem 1
The procedure to compute the pressure is given in section 11.2 of chapter 11. The pressure coecient is
given by Eqn (11.65):
2
2
Cp = 1 (Ux + Uy )
Note that the velocity is already normaliz

AA200 HOMEWORK 3 SOLUTION
Man Long Wong
April 20, 2015
Problem 5.7
The given velocity eld is:
2
= y + 3y 2 + 3x2 y y 3
3
= 3xy 2
U
V
To nd the critical points:
V (x, y) = 0 when x = 0 or y = 0
For y = 0,
U (x, 0) = 0 for any x
x-axis is a critical line
F

CHAPTER 3
THERMODYNAMICS OF DILUTE GASES
3.1 INTRODUCTION
The motion of a compressible uid is directly affected by its thermodynamic state
which is itself a consequence of the motion. For this reason, the powerful principles of thermodynamics embodied in

CHAPTER 2
DIMENSIONAL ANALYSIS
Any physical relationship must be expressible in dimensionless form. The implication of this statement is that all of the fundamental equations of physics, all
approximations to these equations and, for that matter, all func

WWW M ij= , 7JSC'1
at]; A~ M A f
T) P? )ttwta
now alimnmfa dimnf/on; +0 35+
1 I
I T 1913. 7T ~= ng IT -; (ta) . T = U 4 From Mknhm
' IOUCP) Q 'pq7/'? #03) cfw_L4 7,169 (PITheorerjw/
(9'56 COaM have Walkway ofem CLGMCJPNSJXE)
MSW km or volqne of amp/MM Mat

CHAPTER 12
WINGS OF FINITE SPAN
_
12.1 FLOW OVER A THREE-DIMENSIONAL WING
The images below from Van Dykes Album of Fluid Motion depict low speed flow over a
lifting wing of finite span. The images include a view from the side, a plan view from
above and a

Stanford University Department of Aeronautics and Astronautics
AA200A
Applied Aerodynamics
Chapter 1 - Introduction to fluid flow
Stanford University Department of Aeronautics and Astronautics
1.1
Introduction
Compressible flows play a crucial role in a v

CHAPTER 10
ELEMENTS OF POTENTIAL FLOW
_
10.1 INCOMPRESSIBLE FLOW
Most of the problems we are interested in involve low speed flow about wings and
bodies. The equations governing incompressible flow are
Continuity
!iU = 0
(10.1)
Momentum
$
!U
P '
+ "i& UU

CHAPTER 11
TWO-DIMENSIONAL AIRFOIL THEORY
_
11.1 THE CREATION OF CIRCULATION OVER AN AIRFOIL
In Chapter 10 we worked out the force that acts on a solid body moving in an inviscid
fluid. In two dimensions the force is
F
d
=
# "ndl $ U% (t ) & ' (t ) k
! (

CHAPTER 13
COMPRESSIBLE
THIN AIRFOIL THEORY
13.1 COMPRESSIBLE POTENTIAL FLOW
13.1.1
THE FULL POTENTIAL EQUATION
In compressible ow, both the lift and drag of a thin airfoil can be determined to
a reasonable level of accuracy from an inviscid, irrotational

CHAPTER 9
VISCOUS FLOW ALONG A WALL
9.1 THE NO-SLIP CONDITION
All liquids and gases are viscous and, as a consequence, a uid near a solid boundary sticks to the boundary. The tendency for a liquid or gas to stick to a wall arises
from momentum exchanged d

CHAPTER 6
THE CONSERVATION EQUATIONS
6.1
6.1.1
LEIBNIZ RULE FOR DIFFERENTIATION OF INTEGRALS
DIFFERENTIATION UNDER THE INTEGRAL SIGN
According to the fundamental theorem of calculus if f is a smooth function and
the integral of f is
x
I (x) =
f ( x' ) dx'

CHAPTER 5
KINEMATICS OF FLUID MOTION
5.1 ELEMENTARY FLOW PATTERNS
Recall the discussion of ow patterns in Chapter 1. The equations for particle
paths in a three-dimensional, steady uid ow are
dx
- = U ( x ) ;
dt
dy
- = V ( x ) ;
dt
dz
- = W ( x ) .
dt
(5.

CHAPTER 1
INTRODUCTION TO FLUID FLOW
1.1 INTRODUCTION
Fluid ows play a crucial role in a vast variety of natural phenomena and manmade systems. The life-cycles of stars, the creation of atmospheres, the sounds
we hear, the vehicles we ride, the systems we

AA200 HOMEWORK 1 SOLUTION
Man Long Wong
April 19, 2015
Problem 1.2
Assumptions: steady, incompressible, 2D ow
Under the assumptions, we can relate velocity to the streamline height from continuity. Using continuity,
m = U A U h = constant
By measuring the