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The Darcy-Weissbach friction factor for laminar flow would be $\frac{64}{Re}$

Now, having a shear thinning (non-newtonian) fluid where the viscosity is not constant how do I arrive at $Re$?
To know an apparaent viscosity, I'd need to know the shear rate, but that is not constant over the diameter of the pipes. Obviously I need to make allowances anyway (like assuming that my fluid obeys a power law over the relevant shear rates), so the method doesn't neet to be uber-exact. Bu I will want to know where I'm off.

Googling this, I only ound numerical/CFD solutions to far more complex problems an I couldn'T draw my answer from there.

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