CBE 30355 - Lecture Notes - Oct. 7, 2025

Announcements

Class notes

• Dynamic Similarity

Goals:

• Render the equations of motion dimensionless.
• Apply the law of dynamic similarity to develop scale models.

Reading

• The class notes.
• BS&L, chapter 3

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

Dimensional analysis plays a very important role in engineering! For fluid mechanics problems such as a vortex flow where there is a free surface, the key dimensionless groups are the Reynolds number and the Froude number: keep those constant and the flow patterns should be (nearly) identical even when the size scale changes! A nice historical review of the use of dimensional analysis over the ages is provided by Macagno, which may be found here.