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8/17/2019 10_Non-Newtonian Fluids - Lecture 2
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CHE2161
Non-Newtonian Fluids
8/17/2019 10_Non-Newtonian Fluids - Lecture 2
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Textbook Reference
Fluid Flow for Chemical Enineers! second edition! F" #"
Holland and R" $ra! Edward #rnold! %ondon! 1&&'"
#(ailable online at)
htt*)++www"kno(el"com"e,*rox"lib"monash"edu"au+
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/elocit 0rofiles for 0ower %aw Fluids
The (elocit *rofile for stead! full de(elo*ed! laminar flow
in a *i*e can be determined easil b usin the euation ofa *ower law fluid instead of Newton3s law of (iscosit"
For a 0ower %aw fluid)
$ combinin these! obtain a differential euation for the
(elocit radient! which can be sol(ed 4 gives velocity
profiles for various values of .
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/elocit 0rofiles for 0ower %aw Fluids
Slope of the velocity profile at the wall is
dependent of the power law index, n
Behaviour of
real fluids
lies in the
approximate
range,0.2
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Flow of Non-Newtonian Fluids in 0i*es
e alread know) all shear stress
Now what about! 7hear rate at the wall 89"
7hear rate : ;radient of the (elocit *rofile"
Shear rate at the wall !radient of the velocity profile
at the wall"
Shape of the velocity profile is different for differenttypes of fluid.
"#uation 1
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Flow of Non-Newtonian Fluids in 0i*es
Eas for Newtonian fluids) e know the (elocit *rofile
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Rabinowitsch->oone Euation
&he solution to the pro'lem of determining the wall
shear rate for a (on)(ewtonian fluid in laminar flow in atu'e"
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Rabinowitsch->oone Euation
The wall shear rate for a non-Newtonian fluid can be
calculated from the (alue for a Newtonian fluid ha(in thesame flow rate in the same *i*e! the correction factor bein
the uantit in the suare brackets"
Clearl the flow characteristic 8or the rate of shear at thewall9 for a non-Newtonian fluid in laminar flow is not eual
to the manitude of the shear rate at the wall"
Now the flow cur(e aainst can be determined"
How@
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Rabinowitsch->oone Euation
How@
19 >easure at (arious (alues of "
29 Calculate from the *ressure dro* measurements usin
euation 1 and the corres*ondin (alues of the flow
characteristic 89 from the flow rate measurements"
.9 0lot aainst and measure the radient 8i"e" deri(ati(e9 at
(arious *oints on the cur(e"
59 Calculate the true wall shear rate from euation 829 with
the deri(ati(e determined in ste* ." An eneral! the *lot of
aainst will not be a straiht line and the radient must bee(aluated at the a**ro*riate *oints on the cur(e"
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Rabinowitsch->oone Euation
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Rabinowitsch->oone Euation
Fiure shows
t*ical *lots ofaainst
and obtained
b followin
the *rocedure
abo(e"
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Exam*le 1
• For a Newtonian fluid com*are the followin *lots)
aainst and
aainst
•
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Exam*le 1
•