CBE 30355 - Lecture Notes - Sept. 17, 2024
Announcements
Class notes
Read through pages 75-88 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:
- Derive an integral equation governing conservation of momentum.
- Apply it to determine all relevant forces in a pipe or other geometries.
Reading
- The class notes.
- BS&L, chapter 2
Additional Readings:
Our class today focused on conservation of momentum. A really interesting (if a bit extreme) example was the "DART" mission in 2022. This was the asteroid deflection mission where they cannonballed a small spacecraft into an asteroid to test asteroid deflection methods (so that we don't all go the way of the dinosaurs). There were lots of clever things associated with it: they picked an asteroid orbiting another asteroid so they could easily measure the change in velocity (only a few mm/s, but a big change in orbital period). Also, the change in momentum was about 4 times the momentum of the spacecraft hitting it: most of the momentum change was due to ejection of material from the surface (it was a pretty intense collision). The Wikipedia article is given here.
Demonstration:
A nice demonstration of both hydrostatics and Bernoulli’s equation is Torricelli’s Law (or Torricelli’s Fountain). Evangeliste Torricelli (1608-1647) was an Italian mathematician and physicist, credited with the invention of the mercury barometer and demonstration that “a sea of air” exerts pressure, resolving why it was impossible to suck water up a pipe a vertical distance greater than 10m. It was because of this work that the unit of pressure (1 torr = 1mm Hg = 133.3 Pa) is named in his honor. A colleague of Galileo, Torricelli was interested in many problems, among them the analysis of “water clocks” in which time is kept by determining how fast a water container drains out of a hole. One of Torricelli’s observations in his text Opera Geometrica (1644) was the trajectory of streams of water emerging horizontally from a filled bucket of water, where the envelope of the streams form a 45° angle. The fountain is a little messy, but fun!
David.T.Leighton.1@nd.edu