Chapter 2 Kinematics
Kinematics is a study of the geometry of motion independently of applied forces. It consists of descriptive tools and various constraints that limit in important ways how the uid can respond to the application of forces. We will learn

Chapter 5 Inviscid Flows and Irrotational Flows
This chapter is divided between two topics that are related but must be distinguished carefully: inviscid flows and irrotational flows. Even though there is considerable overlap between the two topics, invis

Chapter 3 Dynamics
Newtons second law of mechanics is a monumental achievement. It validates the concept of point particles and shows the relevance of forces; maybe more importantly, it brings mathematics (calculus) to the center of our understanding of m

Chapter 1 Motivation
This chapter, adapted from Trittons book, presents the need for more advanced tools. For internal ows, the canonical case is the ow in a circular pipe. The student should be familiar with the laminar (Poiseuille) parabolic velocity pr

Chapter 11 Linearization
This chapter combines wave motion and linear stability theory. Within the time-frame of the course, only a few simple cases can be treated, with the purpose of illustrating mathematical techniques and important physics. Because of

Chapter 8 Narrow Flows
A distinct type of approximation is associated with dierent scaling in dierent directions: narrow ows encompass boundary layers, but also jets, mixing layers, shear layers, wakes and similar congurations where the streamwise length

Chapter 9 Flow Separation and Secondary Flow
Secondary ows imply a primary ow. There are many variants of this idea. In this chapter, we leave aside secondary ows that can be attributed to instabilities of the primary ow, which rely on linearization (see

Chapter 4 Dimensionless expressions
Dimensionless numbers occur in several contexts. Without the need for dynamical equations, one can draw a list (real or tentative) of physically relevant parameters, and use the Vaschy-Buckingham theorem to construct a

Chapter 6 Stokes Flows
One of the earlier approximations to the Navier-Stokes equations goes back to Stokes himself, who studied the limit of very small Reynolds number. This has applications to very viscous ows, suspensions and bubbles, and the recently

Control Volume Analysis Used for flow through systems HEAT
CONTROL VOLUME
WORK
Use closed system analysis (fixed system mass M) to derive expressions for conservation of mass and energy
Time t MS(t) = MCV(t) + mi
Time t+ t MS(t+ t) = MCV(t+ t) + me
Note:

Lecture Notes in Incompressible Fluid Dynamics: Phenomenology, Concepts and Analytical Tools.
Jacques Lewalle Syracuse University
2 c Jacques Lewalle 2006
Contents
0.1 0.2 What is dierent about these notes? . . . . Overview . . . . . . . . . . . . . . . .

Chapter 10 Rotating Flows
Flows in rotating frames of reference include atmospheric ows and ows in turbomachinery. Fictitious inertia forces are added to the Navier-Stokes equations: the centrifugal force is easily included the conventional framework, but

Chapter 12 Additional Reading
The following texts are, more or less directly, relevant to this course. Most of them will be on library reserve for the semester. There is no attempt to list titles for the many topics beyond the scope of the course, I would

Finite Control Volume Analysis
Application of Reynolds Transport Theorem
CVEN 311
Moving from a System to a Finite Control Volume
Mass Linear
Momentum Moment of Momentum Energy Putting it all together!
Conservation of Mass
B = Total amount of _ in the sys

Using AD to solve BVPs in Matlab
L.F. SHAMPINE Southern Methodist University and ROBERT KETZSCHER and SHAUN A. FORTH Craneld University (Shrivenham Campus)
The Matlab program bvp4c solves twopoint boundary value problems (BVPs) of considerable generality.