Calculating backpressure in nanoLC colmns,where's the error?

[ggerard]

Hi,

I am just entering at the world of nanoLC, and I would like to calculate which would be for a given maximum pressure, at different column ID and particle diameters, for a 15 cm column, the maximum flow rate that the system could afford.

So, the equation, found in Restek
http://www.restek.com/pdfs/F01-Sub2_and_Beyond.pdf
P = 250 L n F / dp2 dc2

So, I am interested in F, this would be
F = P dp2 dc2 / 250 L n

And now the units
F in nl/min
P = 800 bar = 80000 kPa = 80000000 Pa
dp2 = (5 um)2 = 25 um2
dc2 = (50 um)2 = 2500 um2
L = 15 cm = 150000 um
n = 1 cP (water) = 0,001 Pa s

And the conversions
1 nl = 1000000 fl = 1000000 um3
60 s = 1 min

So finally
F = P dp2 dc2 / 250 L n
= 80000000 Pa 25 um2 2500 um2 (1nl/1000000um3) / 250 150000 um 0,001 Pa s (1min/60s)
= 80000000 25 2500 (1nl/1000000) / 250 150000 0,001 (1min/60)
= 80000000 25 2500 (1nl/1000000) / 250 150000 (1/1000) (1min/60)
= 80 25 25 nl / 25 15 (1min/60)
= 80 25 25 60 nl / 25 15 min
= 8000 nl/min

This is a flow rate impossible, I will not be able to run a 50 um column with particles of 5 um, of 15 cm, at such flow rate even at 800 bar of pressure.

With 1 um of particle size, the flow rate would be of 320 nl/min, a flow rate that I also consider very high.

Thus, where is the error here?? I have been thinking all the day, and this is an information I need in order to generate these columns ...

Thanks!!

[pandrews]

Hey,
I have been searching for an equation to find a theoretical value for the pressure in an HPLC system and have had a similar problem,
A couple of equations I found were:

P = (F L n) / (dp^2 dc^2) {didn't seem to work, calculated a pressure of 0.04645 Bar for MeOH at a 1ml/min flow}

P = (F L n) / (dp^2 dc^2 Ko pi) {Ko is the specific permeability of the column, can't seem to find a value for a C18}

thought maybe this might help you until I read the date of your post, and by that time most of this was typed already

If anyone knows a good place to find permeability constants let me know!