Question $3$

On May $18,1980,$ Mount St$.$ Helens on the West Coast of the United States erupted catastrophically, spewing an ash plume to an altitude of $20km.$ The winds then carried these millions of tons of particles consisting mainly of silica $(70\%)$ across the U$.$S$.,$ depositing a $2cm$ layer on my campsite high $(2km)$ in the Rockies and $1000km$ away. It started raining ash just $50$ hrs after the eruption, and although I left for home soon after, I had to breath this contaminated air.

I am worried because I read on page $19$ of the June $1980$ issue of the Chemical Engineering News that silica particles smaller than $10m$ are respirable and can cause silicosis. No one told me this, I've since developed a cough, and being a normal American, I am ready to sue the government for gross negligence in not warning me of this danger. But, of course, I will only do this if the particles are in the dangerous size range.

Please estimate the size of the particles which settled on me at the start of the ash rain.

Data: Assume that the ash particles consist of pure silica for which the density is $2650k\frac{g}{m^3}$ and the sphericity $0\mathrm{.}6$

The average atmospheric conditions from $2$ to $20km$ are

$T=-30C$

$P=40$kPa

$$ ir $=1\mathrm{.}5k\frac{g}{m}*s$