CBE 30355 - Lecture Notes - Oct. 6, 2020

Announcements

Class notes

• The Reynolds Lubrication Equation

Goals:

• Use the Reynolds Lubrication Equation to calculate the forces in 2-D lubrication flows.

Reading

• The class notes.
• BS&L, chapter 4

Additional Readings:

One of the most interesting examples of lubrication flows is that found in ice- skating. In that winter sport, the friction between the blade and the ice melts a small quantity of water, forming a thin lubricating layer. The old story that it's the pressure of the blade which melts the ice isn't true - and the later theory that it's the frictional heating that does the trick isn't quite right either. Instead, the current theory is that there is a very thin layer of water at the surface of ice even well below freezing due to thermodynamic effects. A good discussion of the effects of a thin layer of water on ice (taken from a Physics Today article) is given here.

Demonstration:

In class today we demonstrated Torricelli's Law, which is an interesting example of hydrostatics and Bernoulli's equation. The idea is that from hydrostatics the pressure in a column of water increases with depth. If we have a hole in the side of the column, water will squirt out with a higher velocity the further below the top it starts. If we have a bunch of these sprays, their envelope will describe a 45 degree line leading from the height of the column. A Wikipedia article on Torricelli's Law can be found here.