CBE 30355 - Lecture Notes - Oct. 25, 2022

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. Torricelli is famous for the first measurement of atmospheric pressure (and the creation of the first permanent vacuum) using a column of mercury - that's where the unit torr comes from! The idea behind Torricelli's Law 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 bit messy, but fun. A Wikipedia article on Torricelli's Law can be found here.