Need some help understanding Hertz–Knudsen formula

EcoNewtonian

I'm Working on understanding the growth of snow crystals and came across this as a way to calculate the velocity of growth normal to the plane of the crystal facet.
vn. = α csat csolid r kT. 2πm σsurf. and called it the Hertz–Knudsen formula which I looked up as F = P / (2∏mkT)^1/2

Terms are from http://authors.library.caltech.edu/456/1/LIBrpp05.pdf

how are these equal to each other?

and is this:
Velocity of Growth= α((csat/csolid*kT/2πm) *(σsurf)) = α(Vkin *σsurf) the correct Excel expression. Thanks for your help everyone.