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## Column pressure estimation equation

Discussions about HPLC, CE, TLC, SFC, and other "liquid phase" separation techniques.

### Column pressure estimation equation

Can you estimate/guesstimate expected pressure on the column for simple solvent mixtures?

I've found two resources however I'm not able to replicate the data in the HPLCtips table on my calculator.

https://hplctips.blogspot.si/2011/08/pr ... olumn.html

https://imgur.com/a/u9Mkf

Any idea why the values for the same column dimensions differ in those two links?

### Re: Column pressure estimation equation

the data in the table seems to be ok.
They're in accordance to the following equation (as in U.Neue: HPLC columns)

p=(4000 n L F) / (pi dp2 dc2)

everything in SI units
p = pressure drop [Pa]
n = viscosity [Pa s]
L = column length [m]
F = Flowrate [m3/s)
dp = particle size [m]
dc= column diameter [m]

The ones from the Agilent presentations are also not so wrong but it's hard to follow them because it's not clear what units to use, what viscosity was used and the 'structural constant' seems to point to some approximation.

Be aware that the calculated pressure drop is just for the column. There will be another pressure drop from the tubings, so the observed overall pressure will be higher.

### Re: Column pressure estimation equation

"Can you estimate/guesstimate expected pressure on the column for simple solvent mixtures?"

Yes, you can. An estimate is exactly what you will get because there are many variables which must be considered (including details about the exact column support used, tubing etc). The table provided on the HPLC Hints and Tips provides you with exactly that, a good estimate for 100% water, as stated. In fact, the values are relative, so good for comparisons which show trends. If you are trying to work out what the exact pressure should be for your own specific HPLC system and Column, then you are better off forgetting the tables for now and measuring it.
For an isocratic solution or homogeneous mixture (e.g. MeOH/Water) you can work out the total viscosity using a Solvent Properties Table [http://www.hplctools.com/lcsolvent.htm] plus a separate forumula (multi-step process used, e.g. Refutas equation) to work out the viscosity of the mixture (because it is NOT linear!). Single pure solvents are easy using the published viscosity values, but that does not work with mixtures. With a final viscosity # obtained for the MIXTURE, you could estimate the backpressure through a packed column and that value would be good for comparison to other solution mixture on the SAME column.

BTW: For typical HPLC solvent mixtures (MeOH/Water; ACN/Water...) It is far easier to mix up the various solutions and measure their viscosity than it is to calculate it. Use a zero dead volume union in place of the column to obtain the system backpressure for each specific mixture (or solution), then add the column back in and measure again (subtract to obtain the column only value). Most CDS will even plot system pressure over time which is great for measuring the pressure change over a gradient method.

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