Back to shear wall stress basics

I'm pretty exhausted tonight, but I did dust off some basic review.

Headloss can be found using the following equation.

 where:

Combining that equation with the Darcy-Weisbach yields the following for the wall shear stress:

Thus the wall shear stress is located at the wall of the pipe, where the velocities will be smaller than what is found towards the center.

So biofouling makes the wall shear stress increase when the film gets thicker. This would effect flow rates as it will impact the velocity distribution profile. So I can now use the wall shear equation to relate it to velocity.  Right now, I get flow rates based on differential pressures in a venturi tube.

 These are based on set diameters and distances within the venturi tube. I need to review how these go back into SCADA with the Pressure Indicating Transducers (PIT). The idea is the flow rate is a true flow rate measurement and I can use the venturi meter to come up with a true velocity based on a fixed diameter. The thought is that biofilm decreases the area of the pipe. Could I get a correlation of biofilm thickness to the pipe wall with this analysis? If I used the pressure transducers I have out on the pipeline, could I come up with an aggregated thickness (like a mean thickness value)?

Non-neutonian fluids are fluids like toothpaste and cornstarch mixtures - i.e. sludges. Sludges will tend to move in the laminar flow range. (Refer to email from colleague from the Day 1 post). While algal fouled water may have a higher viscosity value, it's not moving the regime into laminar territory. I do believe viscosity is at play, so this does have merit.