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# Non newtonian pipe sizing

## Non newtonian pipe sizing

(OP)
Hi from a long time lurker and first time poster,

I am attempting to size a pipe for a shear thinning, non-newtonian fluid. I have some rheology data which I have attached to the post.

The required flow rate through the pipe is 6 m3/hr. The pipe length is approximately 60 meters.

I regularly calculate the pressure drop for newtonian fluids but am not used to the same for non-newtonian.

Having searched the web, Coulson & Richardson text books and these forums I am struggling to find any literature/case studies which could assist in performing any calculations.

Appreciate if anyone could point me in the right direction to any relevant information on this, or even better a worked example from the information provided.

Thanks

### RE: Non newtonian pipe sizing

What kind of non-Newtonian fluid model fits your data? By observation, I'd try a power law model first.

Are you sure you used "Search" under the thread title (between Forum and FAQs)? This has been discussed here and/or in the ChE forums several times. I don't think you searched too hard, because I easily found this one thread378-177111: Non-newtonian Pressure Drop.

Lastly, did you use Newtonian calcs using the "apparant viscosity" at the shear rate of the pipe (8V/D)? It's not rigorously exact, but it'll get you very close. If flow is laminar, I use the Hagen–Poiseuille equation for this.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Non newtonian pipe sizing

(OP)
Power law is something that I had come across, but I wasn't sure if this was something I'd be able to compile from the data that I have - do you know if it would be possible to do so or not?

I did happen upon that thread you posted but wasn't sure I had sufficient data to be able to work out the following:

k = proportionality coefficient
n = flow index

Correct me if I'm wrong?

The final tip you mention may be sufficient for this application, I've worked up a couple of examples using the formula you mention, if you could quickly sense check these i'd be very grateful.

Pipe I.D (D): 175 mm
Flow rate (Q): 6 m3/hr
Velocity (V): 0.0693 m/s
Shear rate (ý): 3.17
Apparant viscosity (υ): ~ 51,500 cP
Pressure drop (dP): 2.24 bar

Now say the diameter of the pipe is reduced somewhat.

Pipe I.D (D): 125 mm
Flow rate (Q): 6 m3/hr
Velocity (V): 0.136 m/s
Shear rate (ý): 8.69
Apparant viscosity (υ): ~ 24,914 cP
Pressure drop (dP): 4.16 bar

So there is a moderate increase in pressure drop. I am aiming to size the pipework smaller, as it will need to be pigged and CIP'd. Would it be reasonable to assume that decreasing the diameter to say 75mm (which using your formula would give a pipe shear rate of 40) would see a further decrease in viscosity? Is it worth asking the lab to do another test at higher shear rates to confirm this?

### RE: Non newtonian pipe sizing

I'd get the data if it's fast and inexpensive. Then see how well the data fits to the power law equation. Are you also getting shear stress values, or just apparent viscosity vs. shear rate? Because, from the referenced thread:

Definition of a power law fluid
τ = kγn

Simplify
v = kγn-1

You can start from either equation, take logarithms of both sides, do some algebra, fit the data, and get k and n (or n-1) from a least squares fit.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Non newtonian pipe sizing

(OP)
Latexman, another question I have thought of:

During a product transfer there is a pause which results in the transfer pump stopping for a period of time. The line is left primed with product that is now stationary. When the pump is re-started, will there be a considerable spike in discharge pressure at this point? Would it be possible to estimate this?

Thanks

### RE: Non newtonian pipe sizing

The pump doesn't instantaneously come up to full speed. Is there a time dependency in your fluid's rheology? That will dampen it out too. There are ways to estimate this. I've used it to estimate the time valves need to close to not exceed design pressures. I've never had a pump starting cause such problems though. Do a search on "surge pressure". Maybe you need a soft start or ramp on the pump's motor starter.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

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