Non-newtonian Pressure Drop 1

[777gne]

Now that I have my pressure drop spreadsheet all polished up I get thrown a curve ball; I got handed some rheology data for a several shear thinning fluids. I'm a little rusty with non-newtonian fluids. Here's what I think I know, I'm hoping someone can give me a nudge...

The data that I have is:
Shear Rate in Sec^-1
Apparent Viscosity in centipoise
% Soilds
Specific Gravity
Specific Heat
Thermal Conductivity

...and a legend that reads n = 30,210*y^-.6310

This is a good start - at least I can determine the apparent viscosity at a given shear rate. I don't know if I have enough information to calculate pressure drops in piping though(?)

I believe that I need the constant of proportionality, usually shown as K, or the shear stress so I can calculate K. Can anyone verify this? Is this something that the lab who did the rheology would be expected to have access to?

The pressure drop equation that I have is:

delta P = (3 * n + 1 / n)^n * (Q / pi * r^3)^n * (2 * L * K / r)


- Is there a way to determine K from the info that I do have?
- Is there another means of determining pressure drop using the info that I do have?

 

[Latexman]

Look at the equation for apparant viscosity above:

[ν] = k[γ]^n-1 or k = [ν]/([γ]^n-1)

The units of [ν] are cP.

The units of [γ] are 1/sec

The units of 1/[γ] are sec

Therefore the units of k are cP.sec^(n-1)

Good luck,
Latexman

 

[Latexman]

I collected enough references to derive what I was looking for in the other thread, but before I could do the derivation I thought of a different approach and just filed the information "for a rainy day".

Good luck,
Latexman

 

[777gne]

Whoa, you snuck a few posts in up there that I just saw.

I'm working in English units. The only reference material I have on this subject is in SI units.

v = Pa.s
K = Pa.sⁿ