CBE 30355 - Lecture Notes - Sept. 8, 2020

Announcements

Class notes

• Derivation of the Navier-Stokes Equations

Goals:

• Derive the Navier-Stokes equations.
• Understand where each of the terms come from, and what physically each one represents.
• Know the assumptions leading to Newton's Law of Viscosity.

Reading

• The class notes.
• BS&L, chapter 3

Additional Readings:

For homework you solved for the force exerted by water on a nozzle. Probably the most classic example of this is the nozzle on a fire hose, which (ideally) can support enough pressure to loft water to the top of a tall building! A link which discusses the history of the fire hose may be found here. Interestingly, the very first product of B. F. Goodrich (long before the blimp!) was a vulcanized rubber coated fire hose. A brief history of the development of fire fighting techniques and equipment from Roman times to the present can be found here.

Demonstration:

In class today we demonstrated how hydraulics work, and how you can use a column of water and a little math to make a weighing scale. You should get to know some key numbers: 1 atm = 33.9 ft of water = 10.3 meters of water, 1psig = 2.3 ft of water, etc. These numbers are useful for doing back-of-the-envelope type calculations in designing piping networks. We'll look at such networks near the end of the term.