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Lecture 12 - Non-Newtonian Pipe Flow

# Lecture 12 - Non-Newtonian Pipe Flow - FLUID MECHANICS...

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FLUID MECHANICS Module 3 Non-Newtonian pipe flow http://www.egr.msu.edu/~steffe/freebook/STEFFE.pdf Fluid Mechanics: Outline AIM: To be able to predict the behaviour (processing implications) of fluids in simple flows under conditions relevant to many situations encountered by process engineers PART B Fluid Flow in Pipes Lecture 8-10 Viscous Pipe Flow Lecture 11 Pumping Lecture 12 Non-Newtonian Pipe Flow Lecture 13 Compressibility

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Examples of Pipe flow of non-Newtonian Fluids http://www.youtube.com/watch?v=GX4_3cV_3Mw This one isnt pipe flow, but an interesting shear thinning phenomena called the Kaye effect: http://dsc.discovery.com/videos/time-warp-non-newtonian- fluid.html http://www.youtube.com/watch?v=dm29GAgPyn8&feature=rela ted http://www.youtube.com/watch?v=TIqMCHS7uHc&feature=related This is another quick sand video .... Slurry pumping Product filling Rheology Inelastic (De ~ 0) 𝜎 = 𝜇𝛾 viscosity = constant Viscoelastic (De > 0 ) 𝜎 = 𝑓 𝛾 𝜂 = 𝑓 𝛾 viscosity varies with shear rate 𝜎 = 𝑓 𝛾 , 𝑡 𝜂 = 𝑓 𝛾 , 𝑡 viscosity varies with shear rate and time 𝜎 = 𝑓 𝛾 , 𝑡 , 𝑇𝐻 𝜂 = 𝑓 𝛾 , 𝑡 , 𝑇𝐻 viscosity varies with shear rate, time and thermal history 𝜎 = 𝑓 … + “Yield stress” Any of these can also have yield stress
For Non-Newtonian Fluids, the relationship between stress and strain is not linear. Stress t (Pa) Shear rate (s -1 ) Newtonian fluid Shear-thinning fluid Shear-thickening fluid Yield stress fluid PWR 1.5 Rheology: Non-Newtonian Fluids …alternative names you will see…. Rheology: Non-Newtonian Fluids Stress t (Pa) Shear rate (s -1 ) Newtonian fluid Pseudoplastic Dilatant Ideal Plastic, Bingham fluid PWR 1.5

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Lecture 3 Rheology, Recap Time independent Non-Newtonian fluids i.e. shear stress is nonlinear function of shear rate, E.g.: Most non-Newtonian fluids are shear thinning and can be described according to a power law : K = consistency coefficient (Pas n ), n = power law index Many fluids also possess an apparent yield stress ( s y , a minimum stress must be applied before flow occurs, e.g. mineral slurries, mayonnaise, paint…, The Herschel-Bulkley equation is often used (reduces to Bingham if n=1): n K s 1 / ) ( ) ( n K s n y K s s ) ( s f s ) ( ) ( Stress vs. Shear rate (Linear axis) Shear rate (s -1 ) 0 100 200 300 400 500 600 Shear Stress (Pa) 0 100 200 300 400 Concentrated Orange Juice Stirred Yogurt Hellmans Mayo Honey, Newtonian Milk, Newtonian Herschel-Buckley Model Power Law Model Viscosity vs. Shear rate (Log axis) Shear rate (s -1 ) 10 100 Viscosity (Pas) 0.01 0.1 1 10 Concentrated Orange Juice Stirred Yogurt Hellmans Mayo Honey Milk Lecture 3 Rheology, Recap Rheology flow curves of some common fluid foods, obeying Newtonian, Power law or Herschel-Buckley models s ) (
Relevance of shear rate Steffe Increasing shear rate

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