Impendance - why N^2?

[KonstantinSychev]

Can you please explain why the definition of impendance E = t0*P/(n*N^2) includes N^2? As far as I understand E means that we are trying in minimal t0 and wasting minimal pressure resource P/n to reach... what? Maximal N^2? Why square??? Why not square root? It would look much more logical... E = t0*P/(n*N^1/2) for example

[HPLCaddict]

AFAIK the origin of the square is that you relate both t0 (as a measure of speed) and the pressure drop to the efficiency N, normalized to the viscosity.
Look at the formula like this: E = (t0/N) * (P/N) * (1/n)

The impedance basically tells you the "effort" in terms of pressure and time you need to reach a certain efficiency. At least that's the practical interpretation I'm aware of. There might be more from the theoretical/academical point of view.

[mattmullaney]

Hey HPLCaddict and Konstantin,

The world is a small place...I've "met" Konstantin a bit before!

In another thread, for HPLCaddict's benefit, I suggested the following text and link:

HPLC Columns: Theory, Technology, and Practice, Uwe D. Neue, ISBN: 978-0-471-19037-0, 416 pages, July 1997, Wiley-VCH.

"I'd try Chapter 2, around about page 33 or so. This link here seems to lead to that text:"

http://altair.od.ua/analit/HPLC%20columns.%20Neue.pdf

And Konstantin properly noted in the other thread...Neue's explanation of N^2 may leave a bit to be desired. Guess I'm still a Neue fan, though, anyway.

And thanks, Konstantin, again. Interesting topic, regardless of location!

Regards, Gentlemen.