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.

 

[Valerie Park]

The Hertz–Knudsen formula is a derived version of the Maxwell-Boltzmann equation, which states that the pressure (F) exerted by a gas on a surface is proportional to the square root of the temperature (T) and the inverse of the mean free path (m) between collisions. The Hertz–Knudsen formula is an adaptation of this equation to calculate the velocity of growth normal to the plane of the crystal facet, and it can be written as:vn. = α csat csolid r kT. 2πm σsurf. where α is a constant, csat is the saturation concentration of the species in solution, csolid is the concentration of the species on the crystal surface, r is the rate coefficient for the process, k is Boltzmann's constant, T is the absolute temperature, m is the mass of the particle, and σsurf is the surface energy of the crystal face.The Excel expression for this equation is: Velocity of Growth= α((csat/csolid*kT/2πm) *(σsurf)) = α(Vkin *σsurf).