Friday, January 29, 2010

Meniscus Fermi

As you have probably guessed from a previous post, I find that dimensional analysis is a powerful tool for back of the envelope type problems.

Therefore I present this problem on surface tension as an exercise in dimensional analysis. Of course, most dimensional analysis solutions, as with most solutions to Fermi problems, are order of magnitude. So after having some fun with the following problem, see if you can refine your model a bit.

---------- Start Fermi Problem -----------

Add water to a clean glass, and you will notice that the water likes to "climb" up the wall to a certain height. This is called a Meniscus, and is caused by a physical property called surface tension.

You can put some water in an ice tray, and freeze it, and you will be able to see the frozen meniscus as a raised lip on the top surface of the ice cube.

Estimate how high the meniscus is for water.

Here is a hint for you: 
The surface tension for water is about 0.07 N/m

------------ End Fermi Problem --------------

At the end of the day, you can do an experiment to help refine your model. Freeze some ice, and measure the height of the meniscus.

1 comment:

  1. What did you get as an answer to this then?