Lecture 12 - Non-Newtonian Pipe Flow

E q and p from pipe flow using various l ds measured

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Unformatted text preview: o recall: f ' sw shear stress in pipe 2 2 v 2 kinetic energy per unit volume f ’ = Fanning friction factor (Steffe uses this but uses the symbol f) f = Moody friction factor (which we use) f 8s w 4 f ' 8 v 2 Laminar Pipe Flow of NonNewtonian Fluids Yield stress fluids: A minimum stress is required before flow occurs. Laminar Flow in a Pipe of NNF: Yield Stress Fluids Can you think of examples of Yield stress fluids ? These are fluids that behave as a solid (i.e. don’t flow) until a stress is applied to a sample that is greater than a critical value. Constitutive models used to describe such fluids: Bingham model s s y B Herschel-Buckley model s s y K n Laminar Flow in a Pipe of NNF: Yield Stress Fluids Pipe flow of Yield Stress Fluids : • the fluid may NOT flow. This will be the case if: sw < sy (wall shear stress is below the yield stress) hf 4 Ls y gD hf in terms of wall shear stress: 2 Ls w 2 Ls w P P h f hf R gR g 4 Ls w hf gD Example Crude oil is being pumped along a 1000m horizontal pipeline of inside diameter 0.5m. It has partially crystallised (i.e waxy crude oil) and has a yield stress of 500 Pa. Assuming negligible frictional and other losses, what is the minimum pressure drop required for flow to occur Add a wick and we have a giant candle 2 Ls y PR sw P sw s y R 2L P 2 Ls y R P 2(1000)500 40000 Pa 0.25 Laminar Flow in a Pipe of NNF: Yield Stress Fluids s s y B Bingham model s s y K n Herschel-Buckley model s R0 Pr 2L sw PR 2L Flowing region s>sy s y 2L P Solid plug ssy Ls w s y 2 vz , Bingham plug P B MFEE – Friction factor, turbulent flow Just like turbulence of Newtonian fluids, equations are available for time independent inelastic fluids, i.e obtain f from equations or charts if you know Re; for example: Newtonian s Power Law s K n Bingham fluid s s y B 1 4 Log Re f ' 0.4 f' Re v D 1 0.4 4 (1 n ) 0.75 Log Re PL f ' 2 1.2 n f' n v 2n D n 4 n n Re PL n 1 8 K 3n 1 1 4.53Log (1 c) 4.53Log (Re B f ' ) 2.3 f' sy v D c Re B sw B f 4f' Steffe MFEE – Friction factor, turbulent flow f 4f' Steffe Steffe, p 132 f’ f 4f' Re PL v 2n D n 8 n 1 K 34nn1 n Steffe, p 130 N He s y D 2 B 2 f’ f 4f' Re B v D B MFEE – Kinetic energy correction for Laminar flow Just like Newtonian fluids, corrections for kinetic energy term in MFEE is required due to the non-uniform flow field. For example: Steffe MFEE – Kinetic energy correction for Laminar flow Non-Newtonian Pipe Flow, summary P sw PR 2L Fluid model: e.g. n s K Q or vav Measurable Measurable Provided with the tools to predict the velocity profile of fluids Can now account for Viscous Pipe Losses and minor Losses, as well as time-independent non-Newtonian fluids in pipe flows in the MFEE / extended Bernoulli 2 2 2 P P2 v2 v1 v2 L v 1 1 z1 2 z2 f K L hq 2g 2g D 2 g all minor 2 g losses End of Lecture Supplementary slides Frictional losses during flow in pipes Evaluate losses for sections of pipes. Average V with distance is constant for constant diameter (Continuity holds) but pressure decreases due to friction / viscous losses 1...
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This note was uploaded on 04/17/2013 for the course CHEE 2003 taught by Professor Jasonstokes during the One '12 term at Queensland.

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