Re: if the equation to find the height of a mushroom cloud from a nuclear bomb?

There are numerous resources on the internet, just two of those being the 
following:

Trinity Atomic Web Site http://www.cddc.vt.edu/host/atomic/nukeffct/airburst.html

Effects of nuclear explosions http://en.wikipedia.org/wiki/Effects_of_nuclear_explosions

A better technical reference, if you can still find a copy, is:

Effects of Nuclear Weapons, Glasstone and Dolan, US GPO, Washington, DC, 
1977

Double check your terminology.  It is more common to compute the height 
of burst as a function of yield, and is simply algebra to determine the 
yield, given the height of burst.  The cloud height is not the same as 
the height of burst.

Good luck with your paper.

sid