Shear Stress in Pipe Flow

[aali94]

I was reading a paper on the strength of paraffin gels formed in pipelines, and I came across a part that said, "In a pipeline, a shear stress of 5 Pa would be exerted on the incipient gel deposit by an oil flow rate of approximately 16,000 barrels oil per
day in a 10-in pipeline with an oil viscosity of 10 cp (mPa s)." (Venkatesan et al., 2005)

I calculated the Reynolds Number as Re = 12544 with an oil density of 850 kg/m^3. I understand that this implies that the flow is turbulent. I'm not sure how they calculated the shear stress. I don't think I can use shear stress formulas for laminar flow to calculate the shear stress in this case. I have attached the paper; the above statement can be found on page 8.

 

[zdas04]

The velocity of the gel is in creep flow at most and it is a non-Newtonian fluid (i.e., stress is not proportional to strain). Simple shear models are assuming (either in Laminar or turbulent flow) Newtonian fluids. I didn't read the paper, but I would be really surprised if any stress-strain model really applied to this gel which has varying stress response to strain.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. —Galileo Galilei, Italian Physicist