CBE 30355 - Lecture Notes - Oct. 9, 2008
Announcements
Class notes
Scanned Notes
The main points of the lecture were
Goals:
After this class you should be able to:
- Render the equations of motion dimensionless.
- Apply the law of dynamic similarity to develop scale models.
Reading
- The class notes.
- BS&L, chapter 3
Additional Readings:
A classic example of the use of dynamic similarity and the laws governing scale-up is the
design of ships. In the U.S. the main ship model design and testing center is the former
David Taylor Model Basin (now the Carderock Division of the Naval Surface Warfare
Center). While you can't really keep the Reynolds number constant between model and the
full scale ship, you can keep the Froude number constant. This allows you to see how hull
design, etc., affects bow waves, wakes, and drag. Provided the Reynolds number is "high" for
both model and full scale (so that viscous effects can be neglected), the drag on the model can
be related to that on the full scale ship.
Alas, their old website died, and most of the interesting stuff went with it
(a cautionary tale as to why you need to reference journal articles rather than
websites in your lab reports and papers!), however a few bits and pieces are
left in their multimedia gallery given here.
In particular, the movie of a tank test of a hull shape in rough seas given
here is
interesting, as it shows how preserving Fr allows you to -see- what a wave
would do to a full size ship.
It is also perhaps not surprising that the Carderock Division is also in charge of all the Navy's
ship models - wherever they are on display across the country! If you are interested in ship
models, the Curator's website is something
you won't want to miss. This site, at least, is still there!
Demonstration:
Dynamic Similarity of Vortices
David.T.Leighton.1@nd.edu