# CBE 30355 - Lecture Notes - Oct. 31, 2023

## Announcements

## Class notes

Read up to p233 of the notes and view the online narrations below. The narration is divided into three pieces. The first is the solution to flow past a sphere via index notation (the pages with no page numbers between 217 and 218), the second is the same problem but done using streamfunctions and some hand-waving (pages 218-226), and the third is showing how you can use the velocity an pressure distributions to calculate the drag on a sphere, as well as finishing off creeping flows with some useful integral theorems (pages 227-233). Don't forget to complete the quiz in Canvas!

The main points of the lecture were
- The Streamfunction: Flow Past a Sphere

## Goals:

After this class you should be able to:
- Solve axisymmetric problems using the axisymmetric streamfunction.
- And do it the more sophisticated way using index notation...

## Reading

- The class notes.
- BS&L, chapter 4

## Additional Readings:

Fluid mechanics is important in a wide range of biological systems. At the cellular
level the Reynolds number is usually quite low, and viscous forces are dominant. At
the organism level the Reynolds number is usually high and inertial forces are
important. Occasionally flows are so fast that cavitation
effects are important! A really cute example of such a flow is the phenomenon of the
snapping shrimp, described
here. A Science
article describing the details of the phenomenon is given
here.

## Demonstration:

Stokes Flow Reversibility

David.T.Leighton.1@nd.edu