Non - Newtonian(Shear Thinning) Flow through a circular hose.

[InternGM]

Let me start off by saying this is my first post so please let me know if I am doing anything wrong!

I am dealing with psuedoplastic non - newtonian fluids that are flowing through a circular pipe. I am looking to calculate the flow rate at one end of the pipe and the information that I currently have includes:
Pipe length and diameter
Temperature
Pressure drop

From prior research I think some important things I am missing are apparent viscosity, the flow consistency index (usually denoted as k) and the flow behavior index (usually denoted as n).

Does anyone have a clear formula that relates the variables I have? (I am having trouble finding a solid answer through a seaarch of the Internet).
Can anyone also help me figure out how to find out or test for the values of apparent viscosity, k and n?

Thank you!

 

[Latexman]

Psuedoplastic (shear thinning) fluids are usually represented very well as a power-law fluid.

k and n can be obtained a number of ways. There are expensive rheometers that will measure the fluids rheology and report the constants to a large number of correlations, the power-law or Ostwald-de Waele correlation being one of them. Or, you can select a spindle with known shear rate vs. RPM on a Brookfield viscometer and vary the RPM vs. the measured "apparent viscosity". Then, you graph or model the power law vs. your data to obtain the power-law constants. You can download Brookfield's "More Solutions to Sticky Problems". It will help. Another good reference is A. H. P. Skelland's book, Non-Newtonian Flow and Heat Transfer. Another help is the fluid flow section in Perry's Chemical Engineers' Handbook. Most college fluid flow textbooks barely scratch the surface on non-Newtonian flow. Some fluid flow textbooks that are slanted towards Chemical Engineers do better, like McCabe and Smith's, Unit Operations of Chemical Engineering.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[InternGM]

Thanks for your help! One more thing, do you by any chance have the equation, Latexman? I read some of your earlier comments on a thread similar to this where the guy asking the question wanted to calculate pressure drop. I had some trouble deciphering that equation. Could you help me with that?

Thank you.

 

[Latexman]

Did you see this thread: thread378-177111

I went step-by-step. I don't think I can explain it any better.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[InternGM]

Yes, that was the first post that I looked at. But I am not sure what short hand is being used when writing the pressure drop equation:

dP = ((3.n+1)/n)^n * (Q/pi/r^3)^n * (2.L.K/r) i.e. what do the periods represent?

And is the flow rate(Q) just a generalized flow rate along the course of the pipe or is it referring to a specific place along the pipe?

 

[Latexman]

. means multiply.

same as dP = ((3n+1)/n)^n * (Q/pi/r^3)^n * (2LK/r).

Steady state is assumed, so Q is the same at every point. Velocity will change with flow area though. Reference the continuity equation. But in this equation it is for a pipe that does not change diameter.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[InternGM]

Thank you very much.

My overall goal is to be able to calculate the maximum length of hose I can have while still have a flow rate that is high enough to refill a 166cm^3 tank in 15 seconds.

Appreciate all your help!