# CBE 30355 - Lecture Notes - Oct. 4, 2022

## Announcements

## Class notes

Read through pages 158-168 of the notes and view the online narration below. Don't forget to complete the quiz in Canvas!

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. The history of the model basin may be found in an
ASME brochure given here.

## Extra Stuff for the Interested...

In the last class we talked about systems which were linearly unstable (e.g., Taylor-Couette vortices) and those which were unstable only to finite disturbances (laminar flow in a tube transitioning to turbulence). Linear stability theory is a bit beyond this class (but the graduate course covers it), however I thought those of you who are interested might want to explore the simplest problem: the instability of an autocatalytic system (e.g., an atom bomb). The writeup is given here, and a fun Monte Carlo simulation and movie is given in the file bombsim.m and in the livescript bombsimx.mlx. Have fun!

## Demonstration:

Dynamic Similarity of Vortices

David.T.Leighton.1@nd.edu