Cheg 355 - Lecture Notes - Sept. 21, 2004
Announcements
- The first hour exam will be two weeks from today!
Class notes
Scanned Notes
The main points of the lecture were
- Derivation of the Navier-Stokes Equations
Goals:
After this class you should be able to:
- Derive the Navier-Stokes equations.
- Understand where each of the terms come from, and what physically each one represents.
- Know the assumptions leading to Newton's Law of Viscosity.
Reading
- The class notes.
- BS&L, chapter 3
- Multi-Media Fluid Mechanics: Work through Dynamics:The Navier-Stokes Equations.
This section has some nice visualizations which will help you see how the
Navier-Stokes equations we are deriving in class lead to velocity profiles.
Additional Readings:
For homework you solved for the force exerted by water on a nozzle. Probably
the most classic example of this is the nozzle on a fire hose, which (ideally) can support
enough pressure to loft water to the top of a tall building! An interesting link which
discusses the history of the fire hose may be found
here.
A brief history of the development of fire fighting techniques and equipment from
Roman times to the present from the British perspective can be found
here.
Demonstration:
The sedimentation velocity of a body of revolution. As you derived for
homework, the mobility tensor of a body of revolution with fore-and-aft symmetry
(e.g., it looks the same from both ends, like a cylinder or a football) can be determined
from just two experiments. We use these to determine how rapidly a rod moves off to
the side when it falls through a viscous fluid.
Homework Exercises (Due Sept. 28, 2004)
problem set 5
solution
David.T.Leighton.1@nd.edu