Alex DeCaria's Derivations Page

This is a page where I've put some derivations that I think are interesting, but are not included in the notes for my courses.  They are by no means groundbreaking, and not all are original.  They are just some that I have wondered about over the years, figured out, and thought perhaps others may find them interesting also.  The files are in PDF format.

Approximation for Virtual Temperature
Shows the rational behind a common approximation for virtual temperature using degrees Celsius and dimensional mixing ratio (g/kg).
Coriolis and Centrifugal Torque:  Explores the torques from apparent forces on an object viewed in a rotating reference frame.
Running in the Rain - Will You Get Wetter?:  Discusses whether you will stay drier, or get wetter, by running versus walking to shelter when it is raining.
Mean Distance Between Cloud DropsA derivation from probability theory to show the mean distance between cloud drops, rain droplets, or other aerosols.
Monty Hall (Game Show) Problem:  A derivation from probability using Bayes' Theorem to show an unintuitive result.
Vorticity Equation and the Conservation of Angular Momentum:  Shows how the barotropic vorticity equation can be derived directly from the conseration of absolute angular momentum.