CBE 30355 - Lecture Notes - Sept. 20, 2022

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:

The sedimentation velocity of a body of revolution. As you are deriving for homework, the mobility tensor of a body of revolution with fore-and-aft symmetry (e.g., it looks the same from both ends, like a cylinder or a football) can be determined from just two experiments. We use these to determine how rapidly a rod moves off to the side when it falls through a viscous fluid.