Cheg 355 - Lecture Notes - Oct. 6, 2005
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
- Multi-Media Fluid Mechanics: Work through Dynamics:Reynolds Number: Dependence of Forces on Reynolds Number and Geometry.
The behavior of liquid jets at different Re is quite dramatic, and shows how inertia
strongly influences flow behavior.
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. A picture of the truly collossal towing tank facility is
given
here, and the gallery
section located
here has some fun pictures of ships and
models. I found the sub-chasing hydrofoil to be
particularly interesting.
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.
Demonstration:
Dynamic Similarity of Vortices
David.T.Leighton.1@nd.edu