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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 HerschelBuckley 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
HerschelBuckley 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 nonuniform flow field. For example: Steffe MFEE – Kinetic energy correction for Laminar flow NonNewtonian 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 timeindependent nonNewtonian 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.
 One '12
 JasonStokes

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