Download - ChE354 Non Newt
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Non-Newtonian Fluids
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Non-Newtonian FlowGoalsDescribe key differences between a Newtonian and non-Newtonian fluidIdentify examples of Bingham plastics (BP) and power law (PL) fluidsWrite basic equations describing shear stress and velocities of non-Newtonian fluidsCalculate frictional losses in a non-Newtonian flow system
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Non-Newtonian FluidsNewtonian FluidNon-Newtonian Fluid is the apparent viscosity and is not constant for non-Newtonian fluids.
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- Apparent ViscosityThe shear rate dependence of categorizes non-Newtonian fluids into several types.Power Law Fluids:Pseudoplastic (viscosity) decreases as shear rate increases (shear rate thinning)Dilatant (viscosity) increases as shear rate increases (shear rate thickening)Bingham Plastics: depends on a critical shear stress (t0) and then becomes constant
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Non-Newtonian FluidsNewtonianBingham Plastic:Pseudoplastic:Dilatant:sludge, paint, blood, ketchuplatex, paper pulp, clay solns.quicksand
- Modeling Power Law FluidsOswald - de Waelewhere:K = flow consistency indexn = flow behavior indexNote: Most non-Newtonian fluids are pseudoplastic n
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Modeling Bingham PlasticsRigid
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Frictional Losses Non-Newtonian FluidsRecall:Applies to any type of fluid under any flow conditions
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Laminar FlowMechanical Energy Balance000
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MEB (contd)Combining:
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Momentum Balance00
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Power Law FluidBoundary Condition
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Velocity Profile of Power Law FluidCircular Conduit
Upon Integration and Applying BC
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Power Law (contd)Need bulk average velocity
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Power LawResults Hagen-Poiseuille for Power Law Fluid Recall
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Laminar Friction FactorPower Law FluidDefine a Power Law Reynolds Number
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Turbulent Flow
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ExampleA concentrated suspension flows through 75 m of 3 cm ID pipe at a bulk velocity of 5 cm/sec. From rheological data, it is determined that the fluid has a power law behavior with n=2 and an apparent viscosity of 18 poise at a shear rate of 10/sec. Find the pressure drop in the pipe.
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Bingham PlasticsBingham plastics exhibit Newtonian behavior after the shear stress exceeds to. For flow in circular conduits Bingham plastics behave in an interesting fashion.
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Bingham PlasticsUnsheared CoreSheared Annular Region
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Bingham Plastic Friction FactorHedstrom Number(Non-linear)
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Turbulent Bingham Plastic Flow