Prediction of batch heat transfer coefficients for pseudoplastic fluids ...

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PREDICTION OF BATCH HEAT TRANSFER
COEFFICIENTS FOR PSEUDOPLASTIC FLUIDS
IN AGITATED VESSELS
BY
DONALD WILLIAM HAGEDORN
A THESIS
PRESENTED IN PARTIAL FULFILLMENT OF
THE REQ,UIREMENTS FOR THE DEGREE
OF
DOCTOR OF ENGll1EERING SCIENCE IN CHEMICAL ENGINEERING
AT
NE~IARK
COLLEGE OF ENGH.jEERING
Tlilis thesis is to be US~Q 019.ly vii th Que regaJ?d
to the rights o~ the author. Bibliographieal
referemee may be m0ted, but passages must not be
80pled without permission of the College amd
without erealt bein~ givem in subsequent written
or published work.
Newark, New Jersey
1965

605·36
Llbrary
Newark Colle e of Enp:lneerfn
ABSTRA.CT
Experimental batch heat-trans~er
data were obtained
for both Newtonian ~nd
pseudoplastic liquids in a baffled
agi tated vessel.
The fluids tested had flo1f behavior indexes
between 0.36 and 1.0; and the apparent viscosity
ranged from 1 to 1200 centipoise. Four types of impellers
(anchor, paddle, propeller, and disk and vane turbine)
were studied using eleven separate impellers.
The probable
error in the measured heat trall.sfer coefficient was ± 20
percent.
The effects of the generalized Reynolds number, generalized
Prandtl number, and viscosity ratio were studied.
In
addition the effect of impeller diameter was studied for
paddles, propellers, and turbines; and the effect of impeller
width was studied ~or the paddles and turbines. The
vertical height of the impeller above the bottom of the
vessel was shown to be a significant variable.
The data for the Newtonian liquids, in general, substantiated
presently accepted correlations. For the pOi..Jer
laH pseudoplas tic fluids bJO correlations 1.Jere developed ..
One correlation l'1faS based on the dimensional analysis of
the equations describing a flOi..] model of the system.
The
second correlation is based on Metzner's evaluation of the
rate of shear in an agitated vessel.
The former correlation
has five to seven constants which vary with impeller type

while the latter has five to seven constants, two of k'lhich
vary "ri th the impeller type..
1fmen the flow behavior index
is 1.0 both correlations reduce to the generally accepted
correlations for :HeHtonian liquids.. The correlations fit
the experimental data 'I'li th an average error of ± 10 to 11].
percent ..
1/

APPROVAL OF THESIS
FOR
DEPARTMENT OF CHENICAL ENGINEERING
NEWARK COLLEGE OF ENGINEERING
BY
FACULTY COJI-1MITTEE
APPROVED:
NEhlARK, NEW JERSEY
JUNE, 1965

ACKNOWLEDGEMENTS
The auther ex~resses
kis smeerl!$ a:ppreeiatien to his
thesis auvisor, Dr. Jl!$rome J. Sal~one,
fer all his t~e,
i~eas
in dire~ting
and interest. Dr. SalaMone's aid has been inval~able
this research to a sueeessful eonelusion.
The author also wishes to aeknowledge the interest
shown and the useful suggestions rendered by the otner
members of the deetoral eommittee. Dr. L. Bryee Amderson
espeeially was-instrumental tm the development of ~e
theoretieal eorrelatiene
Mamy ~ersons
gave assistanee in the pl~ing and eORstruetion
of the experimental ap~aratus, namely, Mr. Tony
La Sala, Mr. John S~~~03 ana Dr. Edwin O. Eisen.
A ~reat
deal of appreeiation is due tke NeE Computer
Center fer the "large ~ount of eomputer t~e used and espeeially
the eomp'I.llter eenter staff wao 'Vlere always willa&:
to give their assist~ee. The Ell tho:r is grateful for tke
fin~eial help received through the National Defense
Edueation Aet.
The autho~
is espeeially grateful to his Wife, Martina,
who always gave eneonragem~t amd aided in the presentation
0f the tkesis.
I/f

IV
VITA
D@llalcil. W. Hagedorn received. his 'B. S. im Cltlemieal
En~iBeerimg ~rem Newark College of ER,imeerimg im 1961
aRd v.IaS awarded a three year Natioma1 Edueatiol'l. Defense
Act Fe11ewshi~
for sttldy towards tke doet@rate at the
s~e institutien. He reeeived the M. S. degree in 1963
summa eum laude.
He worked 0Jle SUlm'!:l.er at Pieatinny Arsenal a:md three
summers for the Amerieam Cyanamid C@mpaay at the Warners
Plant, Beumd Brook Plant, &Rd Lederle Labarat0ries. He
is presently emp1c)'yed in tile Tee:hni~ull.
Gl?OU19 @f' the Dye15
Department of' the American CYJuut "l1id .. Com.pany a. t Bo"tUld
Bro@k, New Jersey.

Chapter 1:
Chapter 2:
Introducticm
TABLE OF CONTENTS
Review of Background t-1ateriaJ.
Pseudoplastic Fluids
Rheological Investigation of Power
Law Fluids
Mixing of Non-Newtonian Fluids
Methods of Study of Batch Heat
Transfer Used by Previous Authors
Summary of Literature Results for
Batch Heat Transfer to Newtonian
Fluids
page
1
6
6
13
20
3h
Chapter 3:-
Chapter 4:
Chapter 5:
Chapter 6::
Conclusions
Recommendations
Studies of Batch Heat Transfer to
Non-Newtonian Fluids Reported in
Literature
Development of Correlations
Theoretical Correlation
Semi-Empirical Correlation
Experimental Phase of this Thesis
Equipment
Operating Procedure
Calculations
Results
Heating and Cooling Water
Correlations
Discussion of Results
52
57
C,7
./ .
73
7h
74
89
95
102
105
ill
131
147
149

page
Table of Nomenclature
150
Appendix A:
Appendix B::
Appendix C:
References
Fluid Properties
Viscosity
Thermal Conductivity
Heat Capacity
Density
Computer Programs for Evaluating
Rheological Data
Data and Calculations
Heat Transfer Data
Computer Programs for Calculating
Heat Transfer Results
Heat Transfer Results
Correlation of Data
Computer Programs for Multiple
Regression Analysis
157
157
119
180
182
187
195
196
224
233
266
270
285

LIST OF FIGURES
page
2-1 FlGW Behavior of Pseudoplastic5
3-1 Flow Patterns in Propeller Agitated Baffled Vessel
4-1 Heat Transfer Vessel
4-2 Location of Wall Thermocouples and Scale
4-3 Piping Diagram
4-4 Anchor Agitator
4-5 Recorder Chart
5-1 Effect of Impeller Height for Heating of Water;
5.2 inch Propeller
5-2 Effect of Impeller Height for Heating of Water;
Anchor
5-3 Effect of Impeller Height for Heating of Water;
6 inch Disk and Vane Turbine
5-4 Batch He~t Transfer Using Propellers
5-5 Batch Heat Transfer Using Propellers
6-1 Comparison of Newtonian Fluid Data with
Literature Correlations: Anchor
6-2 Comparison of Newtonian Fluid Data with
Literature Correlations: Paddle
6-3 Comparison of Newtonian Fluid Data with
Literature Correlations: Propeller
6-4 Comparison of Newtonian Fluid Data with
Literature Correlations: Turbines
A-I
A-2
Viscosity of 93.7% Glycerine Vs. 1/'1'
Correction Factor, f, in Equation for
Viscosity of 93.1% Glycerine
A-3 Constant Temperature Apparatus for
Viscometer
A-4 Rheology of 0.15 Percent Carpopol
A-S Rheology of 0.20 Percent Carbopol
A-6 Rheology of 0.24 Percent Carbopol
1
58
75
71
80
8S
92
109
109
110
122
125
134
136
137
139
160
162
161
176
171
178

VIII
LIST OF TABLES
2-1 Mtn~ Reymold3 Nnmber Needed to Ae~eve
MGvement at a Vessel Wall flDr Pseude­
~la.stie Fluids
4-1 Heat Tran.sf'er Vessel
4-2 A~itati(!)n
4-3 Impeller Dim.ensiens
5-1 Impelle~ Pesitions Used in ~e Majer Pertion
of' th~s Tb.~sis 103
5-2 Summary: of' Addi tianal Data Points Measured in
the Prelintinary Study of' Heat Transf'er to
Water 104
5-3 Summary of Data Points Used in Correlatiens 113
5-4 Correlation A 114
5-5 Correlation B 117
5-6 Correlation C 118
5-7 Varianees f'o~ Cerre1ations A$ B, and C 119
5-8 Correlation D 121
5-9 Correlation E 124
5-10 Correlation F 126
5-11 Correlation G 128
5-12 Varianees f'er Correlations D, E, F a.J:ad G 129
32
81
82
86
A-I
A-2
A-3
A-4
A-S
A-6
A-7
A-8
A-9
A-IO
Viscosity of' 93.7 Pereent G1yeerime
Correetion Fieters for Glycerine Viscosity
1$9
Equati~
C~araeteristies of Brookfield Cyl~drical
161
Spindle
Slo];!>e of Leg Shear Stress Versus Leg
165
Rotationa.1 Speed 168
RReo1egiea1 Data f'or Carbopol Solutions 170
Constants f'or Equations 7-10 amd 7-11
Flow Behavior Index and Fluid Consistency
173
Index of' Carbepol Solutions 169
Flow Behavior Index and Fluid Consistency
Indexf'or Oarbop01 Selutions 175
~erimental Values f'or the Thermal Conductivity
of' Carbep01 SlDlutiol1s 181
Densi ty of' Carbopel Se1utions 184
Table or Nemenelature r0~ Appen&ix A 185

CHAPTER I
INTRODUCTION
BATCH HEAT TRANSFER
Heat transfer from one fluid through a wall to another
fluid is usually described using an overall heat transfer
coefficient, U.
dq := UdA6To (1-1
where q is the amount of heat transferred through heat
transfer area dA.
The driving force,.6 To, is the overall
or total difference in temperature bettr-J8en the hot and
cold fluids. The reciprocal of the overall heat transfer
coefficient is the sun of all the resistances to heat
floWe
Equation 1-2 defines the overall heat transfer
I :=l+l+L 1
1 U 11m hf kw + h (1-2
coefficient for a jacketed vessel where h m is the coefficient
of heat transfer of' the fluid heat transfer medium.
Its
reciprocal is thus the resistance of this fluid to the flow
of heat. ~f
is the resistance due to the fouling of the
heat transfer surfaces. L is the thickness of the wall
and kvJ is its therm.al conductivity. The
resistance to heat flow due to the l-Jall.
ratio, {r is the
-1.v
~ is the resistance
on the batch side of the heat transfer surface and h is
called the batch heat transfer coefficient.
In many cases the batch heat transfer coefficient
is small and tkus is a controlling factor determining the

2
value of the overall heat transfer coefficient. The
agitation of the fluid, the system geometry, and the fluid
properties determine the value of the batch heat transfer
coefficient.
NON-NE1'ITONIAN FLUIDS
Hany factors may influence the behavior of fluids under
shear..
'remperature and pressure influence the viscosity
of fluids; the temperature effect is large and the pressure
effect small.
Newton postulated that for fluids at constant
temperature and pressure the rate of shear is directly proportional
to the shear stress. Subsequently, many fluids
Here found and studied 1.Jhich did not conform to Newton T s
theory.
The duration of shear, the shear rate, or the previous
history of the fluid influenced the shear stress required
for a particular shear rate..
All of' these fluids ltJere given
the npJl1e non-Nelliftonian.
Non-Newtonian behavior is fou-nd in two basic types of
fluid systems (118):
1. Solutions or melts of high-molecular Height
pol}Dneric materials.
2.. Suspensions of liquids or solids in a liquid
medium.
In general the degree of non-NeHtonian behavior increases
Hith the concentration of the polymer or disperse phase.
A large fraetima of non-NeHtonian fluids are classed

3
as pseudoplasticso
Pseudoplastic fluids exhibit shearthirLYling
flm.; behavior.
As the shear rate is increased
the shear stress required to provide the shear rate does
not increase proportionately.
Thus, as the shear rate
is increased the apparent viscosity (the ratio of the
shear stress to shear rate) decreases.
PURPOSE .. OF_T~~JS
A large f"PI!I..~ttml
of .fluids nOH handled indus trially
are nOn-N81f\rtonian and a large percentage of these are
pSeUdOl)lastics.
The design correlations developed for
Nei:ltonian fluids carLnot be used for pseudoplastics because
of the variable viscosity of the latter. In recent years
many authors have contributed to the development of design
equations for pseudoplastic fluids.
These equations have
been in three main areas:
1. Fluid flO1tJ, including friction factors for
isothermal and non-isothermal flOl-1!1 entrance
effects, kinetic energy, and onset of
turbulence.
2. Heat transfer in pipes.
3. POHer requirements in agitated vessels.
Much of this material is reviewed in the literature. (118,
120, 121, 190, 213).
To date, only tvJO papers have been published on the
prediction of batch heat transfer coefficients to pseudo-

4
plastic fluids. These papers are quite Ibnited in scope.
The purpose of this thesis is to develop a design correlation
(based on the analysis of a flow model and experimmtal
data) for the prediction of batch heat transfer coefficients
for pseudoplastic fluids.
SCOPE OF THESIS
& -·e -
T'HO types of correlation were developed..
One is an
equation based on a dimensional analysis of the equations
describin-.g a simplified flo1-l modeL.
The second is a
modification of the l'JeHtonian correlation using an apparent
viscosity developed by A. B. Metzner, et ale (122, 125).
The experimental variables studied cover a fairly
l-lide range..
Four types of impellers Here used:
Type
Flat bladed paddle
Disk and vane turbines
Marine propeller
Anchor
Number of impellers studied
6
2
2
1
All data 'frJere taken Hi th fo'Ll!' baffles attached to the
wall.
The heat transfer surface Has the vessel wall (Some
papers on Ne1tJtonian fluids have studied coils). Both
Ne1tTtonian and pseudoplastic fluids were studied.
':Phe flow
behavior index range for these fluids extended from 1.0
to 0.36.

5
~n addition to studying the effect of Reynolds Number,
Prandtl Nmnber, and viscosity ratio, the ratio of tank
diameter to impeller dia.."11eter i

CHAPTER 2
R,EVIE\rJ OF B,ACKGROD1m l1ATERIAL
PSEUDO PLASTIC FLUIDS
-< -.' "- - - •
wnile Newtonian behavior is only one of many rheological
types, the large majority of fluids h~~dled
industrially
are Newtonian.
Pseudoplastic fluids are second
in i1nportance to the NeHtonians (118)..
The Bingham plas tics
are probably third in importance but many of these have been
treated as pseudoplastics (126).
There are very few industrial
dilatants, and the time dependent and viscoelastic
fluid groups are small 8nd are often treated as pseudoplastics
(7, 118, 120, 121, 126, 128, 179, 186). Pseudoplastic fluids
l.Jere studied in this Hork because of their relative importance.
~1elts a..Yld sol'll'tions of substances Hi th high mole cular
weight are usually pseudoplastic (118, 196) ..
Suspensions
of asymmetrie solids are often in this category. (120, 213).
Typical examples of pseudoplastics are polystyrene, copolymers
of styrene, low and high pressure polyethylene, rubber
modified styrene polymers, and slurries of cement rock in
water (96, 212).
The flm ..! behavior of pseudop1astic fluids is shov.ffi
graphically in Figure 2-1.
At very lov.T a..Yld very high shear
rates the apparent viscosity is a constant, as shown in
curve A.
Thus in these ranges the fluid acts as a Newtonian
fluid. BetvJeen these two extremes., hOl

7
A
B
SLOPE = /'n- .( 10
~y
FIG 2-1
FLOW BEI-IAVIOR OF PS£.UDOPLAST/CS

8
curve (Curve B) is straigkt at the tw0 extremes ei' sl!lJ.ear
main~er. Tke sl~pes o~ the str&ight p&rtions are tae Newten.iaE.
ViS60sities f'0r that regiea, ancil. tile slope of' !it
bet1'J'een any Fl0int or the curved ~@rtion
lime
and zer® gives the
apparent viscosity at that shear rate. Tke Newtonian viscosity
at l0i-J shear rate is orten called the tl zero shear-rate vis-
. t It 1/
cos:t. y '/~o.
Likewise, the Newtonian viscosity at very hi~
shear rates is of'te:m named the "i:V1i'inite shear-rate viscositytl,
/Leo. The l®gari t~ic rlOl-J curve (Curve C) e01l.ltai1l.ls three
straight lines. The two extreme lines R&Ve a slope or unity
and rSFlresent the Newtonian p0rtions @f the shear rate spectrum.
The middle line h.a.s a slope "'\AThich is beti.reen zer@ aRd uni ty.
The closer to zero it is, the more non-Newtonian tae f'luid.
T.hl.e
shear-rate range or the Ilzero shear-rate viacosi tylf
is of'ten very narr0W.
The Iti:afinite shear-rate viscositylt
occurs at very high Shear rates and is very seldom encountered
in industrial proeesses sueh as f'low through a conduit, heat
transfer, or mLxing 1~th
or turbine ..
a paddle, anchor, marine propeller,
'A f'eirJ special impellers and precesses (such as
bl7US1'1l.ing of' a paint) produce hi~ :hear rates, so that the
infini te shear-rate visc0sL ty may be approached.
Many authors 'have tried to derive theoretical expressions
i'or the fl®w eurv~s ef pseua@~lasties ana mamy ethers have
tried t@ aevelep empirical equati@ms (79, 109, 135, 152, 154

15.5, 183, 185).. Most of their efforts 'i-Jere in vain because
the equations vJere not very accurate or '>Jere too complex
to 1.Jork I'Jith (120).
Huch of the early teclmological lvork
vJas done using an empirical equation to express the flow
curves (22, 214, 215).
(2-1
This relationship, the Williamson equation, is fairly complicated,
and is valid for only a small nu.mber of fluids"
In an effort to simplify the equation, the first term lims
often dropped, placing too much emphasis on the infinite
shear-rate viscosity, "lv-hich in practice is rarely approached
(22, 118).
Another equation for describing pseudoplastic flow
behavior which has gained some acceptance is the Pm'

0
beeemes negligible fu~d
agaim Newt~nianbehaviGr is ~redieted.
~e equation als~ preaiets a saear-th~ing phenomenon at
intermea.iate shear rates (120). Thus this equatien is very
gGod if a very wide shear-rate range must be aeeurately
pertrayed er if existing data must be extra~olated.
There are a few disadvantages to using the Pewell­
Eyring equation.
1. 'Three eORstants must be evaluated.
2. The equation eannet be selved explicitly fer
shear rate.
3.. The eorrelations whieh have been aeveloped
using this equatien ean only be solved using
published graphs.
These are based en two or
three parameters in addition to ~e dimensionless
groups represented by the eeordinates (42,
43) •
The Ostwald-deWaele model, mere eommonly ealled the
"p0wer lawlf is ancempirieal equa.tion whieh aceurately €l.eseribes
the ~lew eurve of most pseudeplastie fluids ~
the shear rate range most commonly eneountered in industrial
processes.
(2-4
K is named the It~lu.id e0r:lsisteney i:ID.dex" and. is somewhat
a.:m.alogous to the Newt@l!'lian viseesi ty in that it

va:ry withl. the slaear I'Rte.. 11.1. is ealled the n.rlw belilaTi(:!)J!'
index" amd is a measure o.f the deTiatioE. from NewtoRiam
belaavier. n is equal to the slo~e of the logaritkmie flow
/I
eurYe (Figure 2-l-e).. For Newtonian fluias E. equals 'UJ.'i\l.i ty
aad the .fluid cONsistency index equals the Newt0ni~ Tis­
€esity. FOF pseuaeplastie .fluids n is bet"Y-lee1a zero and
u-'l1li ty.. TJae ])0Wer law als® deseribes the .flow eurves of
shear-taickening .fluids (dilat~t fluids), iN which case
11.1. is greater th~ unit~. Because of the aceuraey ~d
simplicity of the power law, it is the most widely used
rheological equation for pseudoplastie tluids.
The eelasisteney index (]l0Wer law, K) is very slmilar
to Newtonian viscosity in that there is ru~ appreCiable decrease
for am increase in temperature amd an appreciable
imerease for an increase iR concentration. For suspensions,
the ratio o.f K to the viscosity o.f the suspending medium is
often nearly c@E.stant. The decrease with inereasing temperature
is ofte~ at the same rate as tke s@lvent or suspending
medi~ (118).
Tae flow wehavior index, n, is relatively constant with
temperature, although there are slight changes. For water
dispersible p@lymers, n :i.Jt'l.ereases slightly with tem.perature
and approaches ~ity at high temperatures. As the concentration
of solids or polymer imcreases, R decreases (118, 128).
An~ther temperattlPe effect is that of initial ske~r stress

12
sheaF stress at whieh nem-NewtoRian behavi@r eo~e~ees.
Fer PQl~etkyle~e the iRitia.l ~ear stress is 2000 dynes/e~2
at 120~C ana 500 ~ynes/em2 at 230 e O (145).
Tke 'P!!>wer law was ehesen a.s the equatiol'l u.sed to
represe~t
the rhe@legieal data beeause:
1. It has bee~ ShOWB to accurately represemt the
raeol®gieal ~ata 0~ the majority af pseuGo­
]?lastie fluids il:! the shear rate raRge elll.-
cOUBtered im industrial processes.
2. It is general in that it reduces to NewtoRts
rheologieal law fer n = 1.0.
3 .. It CaR be used to apIDr0xirt1ately represent
otaer types of flow behavior, sueh as ~ixotropy
amd viscoelasticity.
4 .. It is a very easy relationship to work 'tdth
matliter'ltatieally.

13
RHEOLOGIC_~
INVESTIGATION OFPO~~R LAW
FLUIDS
There are many e~ereial visGGmeters available ~or
the aatermimatiGn o~ Newtonian viscosity but very ~ew are
available for the quantitative determination o~ shear stress
and shear rate (97). There are two basie types o~ viscometers
l...rhich GaE. be used to determine these quantities; a
eapillary tube viseometer and a r0tating cylinder viscometer.
The ca~illary tube viscometer has a ~ew serious disadvantages.
The pressure drop corrections are very time cons~~ng
and a great deal of tiMe is spent in Gleaning and
assembl~g the apparatus (121).
The Rotational Viscometer
Since the rotational viscometer vTaS used in this study
its use is described in More detail. The exact procedure
followed and the experimental results are iRcluded 1m
Appemdix A ..
The rotational viscometer is very easy to clean and
assemble. The data are easily taken and only one correction,
a constant eorreefion, must be made. Moreover, a model with
a 200 fold shea~-rate range (Bro0~ield S~e~o-Lectrie) is
commercially available, and was used in this study. Tae
rotational viscometer is basically a eylin~ical fluid container
called the eup ana a cyliRarieal b~b whieh is immersed eoneentrieally
~ the cup @f fluid. ~ s®me models the cup

11-
rotat~s at va~ious spe~ds and the resultant to~que om the
bob is measUl1'ed.. In othel'" models val'!'ious tOl'"ques lU'Pe applied
to th~ bob and the resultant speed of the bob ~easured. The
viscomet~r ~sed
in this work was oOMposed of a bob drivem by
a sync~onous motor at a eomst~t val~e of RPM~ (Eigh~
diffel'"ent speeds weF'e possible) .. The tOl"'que required to
attain the desired speed was measured ..
wall of the bob is
(2-5
wher~ Ts is the torque required to rotate the bob ..
Rb is the radius of ~e bob.
hb is the height of the bob ..
The shear 1 rate in ~e annular space between the bob ~d
cup depends upon the ratio of the radius of th~
cup to tine
bob, s, the angular speed of the bob, and the fluid parameters ..
FOF Bingh&m plastics the relati0nanips are given by Fitch (64),
Wilkinson (213), Green (79), and V~ Wazer (196).
For power
law fluids, Y,.:pieger and MaPon (100) developed an equation fop
the she~ ratewhieh is valid to a m~~ cup to bob radius
ratio of 1 .. 2 ..
D .. K, (~,,-/) +Ji Z
(~,,-/)2J
[ 1+ ~ /hV 1 (oJ)
(2-6
(2-7

IS
In(s) (2-8
(2-9
where Re is the radius Gf t:B.e ell]) ..
nil is the slC!1pe of a logarit1::l:m.ie 1"'10t of t

16
can be s~p1i~ied to (100~ 125, 213).
'2fw = 47r N/:t!l.u (2-12
Fer any cup rond bob a~-amgement t~ eup radius~ the bob
radius, and the equivalent height of the bob &re eonst~t.
The sneaP stress and she&r rate are thus evaluated by
taking readings o~ torque versus angular veloCity or the
bob. These values are plotted on log-log graph paper to
evaluate slo~e,' ntT. The shear stress and shear rate are
then ealeulated using equation 2-5 and 2-11. ~e power
law eonstaats, R and K, e~ be evaluated from a logarithmic
plot or shear stress versus shear rate. (~e slope n shonld
be equa.l to 11. 11 ).
E,nd e~fe_et.~.
Equation 2-5 is an expression ror the
shear stress on the curved surface of the bob •. However,
when the lengtli of the bob is not very large im comparison
with the bob diameter tae torees on the ends of the cylinder
m~ ~ot be neglected. These are usually taken into account
by eonsiderimgthe m ds as extensions at.' the cylindrical
height ~d ealling the total the effective height. Ir
more bobs of equal diameter but different lemgths are
available th~ value of the et.'feetive height f0~ that bob
di~eter oaE be evaluated by plotting the to~que ~t CORstant
speed versus bob height ~d extrapolating to zero
torque. The absolute value or height at zero torque
(this height will be a negative value) should b$ added to
the aetual height to get the effective height (54, 107).

'7
ft~
easier method of calibrating the bob with a Newtonian
flllid has been sh01.Jn to be accurate.
!1 NeHtonian fluid of
knovm viscosity is placed in the viscometer and the torque,
angular velocity, and appropriate dimension data taken.
The shear rate is calculated using equation 2-11 laJi th n tl
equal to Ul~ity.
The shear stress is then calculated using
the shear stI'ess-ra te relationship for Nev.rtonian fluids
/ =/1 r (2-13
The effective height is then calculated using equation 2-5.
Metzner and otto (125) have sho~~
that viscometer bobs calibrated
in this manner give accurate values for shear stress
even Hhen using highly pseudoplastic fluids.
Turbulence.
for laminar flmeJ.
Equations 2-5 through 2-12 are only valid
Above a critical Reynolds Number the
flov! becomes turbulent and the shear stress increases at a
mOI'e than proportionate rate, resulting in an increasing
apparent viscosity. Van Wazer (196) reports that the
critical Reynolds nu~ber
is a function of the linear velocity
of bob surface, Vb' the clearance bet",reen bob and cup, and
the viscosity of the fluid.
NReCCRIT.) = "i (Re -R 6 )f
~ = 41.3/Rc/th?c-H2)
/It = 2100
(2-14
{2-l5
It was found in this work that the less viscous fluids

18
suddenly seemed to become more viscous when a large diameter
bob 'i;'JaS used at high speeds. The problem was easily eliminated
by using a smaller diameter bob, thus greatly reducing
the linear velocity of the bob at the expense of a small
increase in clearance.
T.emJ2erature effects..
In very viscous fluids the heat
generated by fluid friction is enough to cause a temperature
rise. The un1tJary investigator may then mistakenly report
pseudoplasticity or thixotropy due to the decrease in
apparent viscosity which in actuality is caused by the increase
in temperature.
McKelvey (114) reports that the heat
generation per unit volume is the product of the shear stress,
shear rate,
Heat generation = "~i J (2-16
and convers ion factor to heat units. WeI tmann (206) has
derived a complex equation giving the temperature variation
with radius caused by viscous heating. Heat generation is
not a problem for lOH viSCOSity materials and good temperature
control.
Time dependency.
Thixotropic fluids may best be measured
in a rotational viscometer.
The shearing stress is determined
for various times of shear at a constant shear rate. The
apparent viscosity is plotted versus the natural logarithm
of the time of shear and the slope is called the I1 coefficient

19
of' thixotropic breakdown l'Ji th time!l ( 79). If' the slope
is zero the f'luid is not time dependent.

20
l'UXIlfG OF NON -NE1rJTONIAN FLUIDS
The mixing of non-Newtonian fluids in an agitated
vessel is a 'lIDi t operation somel'1fhat similar to batch heat
transfer. It is presented because some of the results of
the Hork on mixing can be utilized in developing a correlation
for predicting batch heat transfer coefficients.
Batch heat transfer could be classified as a problem involving
the quality of mixing but it is usually considered
as a separate study.
A review of the small amount of Hork
on batch heat transfer to non-Nel'ITtonian fluids will be
considered later in this chapter.
This section reviel'JS
the study of pov-rer requirements and the quality of mixing.
Much of the work on fluid flow and heat transfer to pseudoplastics
in pipes (revie'tved in \1Iilkinson.1 213; Metzner, 118;
and Thomas, 190) was theoretical in nature. The geometry
and flO1..J patterns in an agitated vessel, hmvever, are rather
complex for this approach.
The velocity profile in a pipe
could be quantitized since it was only a function of wall
shear stress, average velocity, and rheological parameters.
In addition the flow Has in only one direction.
In a mixing
vessel the floH is three dimensional, the "\-lall shear stress
is QnY~OHn,
and the average velocity is not only difficult
to define, but is dependent upon the rheological properties,
the speed of the agitator, the shape, dimensions, and position
of the agitator, and the vessel geometry..
Because of great
number of 'lIDknown relationships, which are made even more

21
complicated by a variable viscosity, all of the 1~ork
to
date has been experimental rather than theoretical.
Power Requirements
POl.'lTer requirements for Newtonian fluids have been
studied by many investigators and are summarized in many
good reviel.Js (12, 9~., 142, 158,162,163 ) • The approach used
vJas to def'ine the variables and use dimensional analysis to
combine these variables into dimensionless groups..
An all
inclusive analysis is given by (12,158)
where P
N
is the power requ~red.
is the rotational speed of' agitator.
D' a.
is the diameter of' the agitator.
D t
is the diameter of' the vessel.
IlL
Hc
is the liquid height.
is the clearance between impeller bottom and
vessel bottom.
is the width of' the agitator.
is the baf'fle 1.Jid th ..
is the number of baffles.
is a reference n~unber
of baffles.
is the number of blades on the impeller.
is a reference number of blades on the impeller ..

22
C il _,
aI' b l
, cl' dl, el, fl' gl, hI' and jl are all
constants to be evaluated.
The group to the left of the equal sign is called the
POv-Ter number.
The first group to the right is the mixing
Reynolds nmnber, and the second group to the l"ight is the
Froude number. The Froude n~unber is required to account
for the vortex formation in a s\-lirling system.
Thus if
baffles or off-center impeller location is used the Froude
number is not needed.
Host authors have also neglected the
remaining groups and have specified a different value of
C4 for each change in geometry. The effects of impeller
style, blade Hidth, number of blades, impeller pitch,
impeller clearance, Dt/Da, and spacing of multiple impellers
have been studied by Bates et al. (12)..
Richards (158) has
studied the effect of impeller spacing, nurnber and 1.ddth
of baffles, number and vddth of impeller blades, and the
effects of coils.
Host of the Horl~
on non-iJel.Jtonian systems has been
similar but not as extensive.. BrOv.ffi and Petsiavas (31)
have investigated the mixing of Bingham plastics. They
found the P01-Jer number \hTaS
a function of the Reynolds,
Froude, and Hedstrom numbers.

2J
Schultz-GrQnow (174) used a dimensional analysis but
in a slightly different form for pseudoplastics 't~hich
could
be represented by the Pr~ndtl
equation
(2-18
where ApR and CpR are empirical constants. His results are
plotte d as the log (l>1/Da 3 APR) versus.-lttiCPR l-vhere 1'-1 is the
required torque and AI'" is the angular velocity. This result
is not very general, h01.Jever, because the impellers studied
are not connnonly used and most pseudoplastic fluids are
best represented by the p011er laH or POHell-Eyring equation ..
1110 s t of the more general 1-lork has be en concerne d '-1i th
finding a Viscosity term which can be used for all pseudoplastics
as well as NeHtonian fluids. Magnusson (D2) found
an apparent viscosity for pseudoplastics hy first developing
a P01.Jer number-Reynolds number curve us ing the equipment
geometry v.rhich was to be used for the pseudoplastic fluid.
He then repeated the experiments with pseudoplastic fluids,
calculating the POHer number for each value of agitator
speed.
By comparing the pseudoplastic data vJith the
NevJtonian Pot.-rer number-Reynolds number curve an apparent
Reynolds number could be calculated for the pseudoplastic
fluid..
Th.e agitator difu"TIeter and speed "lATere lmOvffi as Vlell
as the fluid density; thus the only unknown, the apparent
viscosity, could be calculated. While this is a good method

24
~or
determining the apparent viscosity, it is rather time
consuming and expensive, since it requires much experimental
work.
Metzner and Otto (~ used a similar approach, but
generalized it so that prediction o~
the apparent viscosity
can be made directly from the rheological data ~or
any time
independent fluid. They noted that an agitator in a vessel
is some1tJhat analogous to the rotating bob of a viscometer.
For a viscometer bob rotating in an i~inite
fluid the
shear rate is proportional to the bob's rotational speed.
(2-19
They reasoned that the shear rate at the agitator of a mixing
vessel might also be represented by this equation.
If
this CAJere true and Ks 'i-Jere evaluated the apparent viscosity
could be determined from the rheological data plotted as
apparent viscosity versus shear rate.
Metzner and Otto tested this idea by first determing
the NevJtonian Pm-Ier mnnber-Reynolds number curve for many
different system geometries.
They then evaluated the
rheological properties of five non-Nev-Ttonian fluids and
plotted the apparent viscosity versus the shear rate. These
~luids Here then mixed and the pO'L..rer data taken. The apparent
viscosities \Alere calculated by the method o~
I'lagnussen (1J2)
and the shear rates determined from the rheological curves.

2S
The results shm-red that equation 2-19 1"a3 valid and Kg
equalled 13.0. Godleski and Smith (75), Metzner, et al. (122),
and Calderbank and Moo-Young ( 34) as 1mll as the data of
Foresti and Liu (65) support fietzner and otto's conclusion
that the shear rate can be expressed by equation 2-19,
1..rith I~s
betifTeen 10 .. 0 and 13.0. l.Jfetzner et al (J2?) made the
most extensive study and, based on their 1-rork and the others
given abov~ report that in an agitated vessel the shear
rate at the impeller can be expressed as
(2-20
for these conditions:
1. Baffled and unbaffled vessels.
2. For pseudoplastics "Ti th flow behavior index bet'Heen
0.16 and 1.0 ..
3. Tank dia..."'1leters. 0.5 to 1.83 ft.
4.. Impeller diameters.. 0 .. 167 to 0.67 ft.
5. 'rank diameter/Impeller diameter. 1 .. 3 - 5.5 (laminar
region) 2.0 - 5.5 (transition region)
6. Impeller speeds 0.5 to 29 rev./sec.
7. Flat bladed turbines, fan turbines, ~nd marine
propellers.
8. For dilatant fluids up to n :: 1.5 if the nu/Da is
greater than 3.0.
For dilatant fluids "Ii th Dt/Da less than 3 .. 0 the shear

26
rate is proportional to the square of the impeller speed
and the proportionality const~nt
is dependent upon the Dt/Da
ratio (122).
Calderbank and I'-'Ioo-Young (34) report that dilatants
may be correlated by
Da./ )0.5
t = 12.3 ( /Dt N (2-21
Obviously, more 1-Jork must still be done for dilatant fluids
but the shear rate for pseudoplastics, Bingh~m
plastics and
Newtonians may be calculated by equation 2-20.
For the special case of pseudoplastic p01"Ter 1m-IT fluids
the generalized Reynolds nQmber may be calculated.
(2-22
The apparent viscosity is defined by
(2-23
The pOHer Im-J can be expressed by
Therefore
I:::KtVJ'l
(2-4
(2-24
or
/. ) ./J'l-{
/La. =: /{~//.5N (2-25

Su.bstituti011 of equati 2-22 gives
I IJ~ 2 1112 -~
NRe == ItS ~-f I{ f- (2-26
27
Metzner and otto found that by using equation 2-19
'lid th the aI:'pr0priate censtant the RG>n-NewtoniaE. power dlata
fell en the NewtG>niaR Power number-Reynolds nQ~ber curve
in the laminar and turbulent regi0ns.. I:vl the transitiQl]'l
region (NR~ fr~ 10 to 70) the power required by the pseu.doplastic
f1ui

22>
fluids studied (apparent viscosities behv-een 3000 and 11,000
centipoise) there was little effect of baffles on power
cons~mption, even at Dt/Da as low as 1.67. Dual impellers
required tvdce the pOl-leI' of' a single impeller and this remained
true for various spacings between the impellers.
Quality of Mixing
The quality of mixing is a very important criterllnto
be considered Hhen designing an agitation system, since the
quality or composition of a product is dependent upon the
degree to Hhich reactant or temperature fluctuations are
minimized throughout the vessel. This is especially true
Hi th many processes involving nOn-Nev.Itonian f1uids:l such as
the heating of food products or the polymerization of a
monomer.
l1etzner and Taylor (127) studied the f'lovJ patterns in
an agitated vessel in an attempt to learn more about the
mechanism of' mixing in such a system. They suspended 0.02
"
inch spheres of Plexiglas": in both Ne,itonian and pseudoplastics
fluids and photographed them as the fluid was
being mixed by a disk and vane turbine. The loqal
velocities
were calculated by measuring the streak lengths and dividing
by the exposure time.
A plot of the local velocity versus
radius was differentiated to obtain the local shear rates.
';"Trademark of Rohm and Haas Co.

29
In both Newtonian and non-Newtoni~D
fluids the shear
rates flere found to be directly proportional to the agitator
speed.
There seemed to be an impeller diameter effect 'tv-hich
was greater for Newtonian than for non-Newtonian fluids.
The shear rate at a given distance from the impeller is
slightly greater as the impeller diameter is increased.
For dilatant fluids the effect might be even greater.
In the laminar region (NR~ - 7.0) the al110Ullt of fluid
movement is much greater for Ne1-vtonian fluids than for the
pseudoplastics at the same rotational speed, a.nd flO1~
extends
almost to the periphery of the tank for the NevJtonians
vJhile flow is circular and is confined to the region of
the impeller for the non-Newtonian fluids.
In the first half of the transition region (NR~
about
10.3) fluid turnover begins for the Ne,-vtonian fluids and
mixing is carried out by the transport and blending.
The
radial veloci ty increases 14i th rotational speed quite
rapidly. However, for the pseudoplastics the movement is
still confined to the center and does not extend to the
edges of the baffles until the Reynolds number reaches 28.
At a Reynolds number of 78 the floH is 1>Jell into the
transition region and the radial velocity component of the
pseudoplastic fluids is high and there l.s an infloVling
vertical component..
Tll.e flo"V>J patterns for the NevJtonian
fluids are similar but the vertical inflm-.r is s lightly less

30
than ror the non-Newtonians.
As the middle of the transition region is approached
(NR~
= 100) turbulence begins near or betvJeen the impeller
blades. For the pseudoplastics, this turbulence is rapidly
damped.
In the turbulent region there is much turbulence near
the impeller but it is damped out quickly at any distance
from the Lmpeller.
There is not as much turbulence ror the
Newtonian fluids but it extends further into the bulk of
the fluid.
In the horizontal plane of the impeller the local velocities
increase slightly more than linearly with rotational
speed for the NeHtonian r ..... 1uids. For the pseudoplastics the
increase in velocity is almost exponential.
Thus at high
shear x'ates the pseudoplastics may flow more than the NeHtoni8~l.s
1>Ihile at 10H rotational speeds the reverse is true.
Metzner et al. (122) used the onset of fluid movement
near the vessel Hall as a criterion for good mixing.
At low
Dt/Da ratios there is no advantage to using tHO turbines.
For values of Dt/Da above 2 .. 0 less power is consumed for
equal mixing if two tUl"bines are used, since at high values
of this ratio tHO turbines circulate hlice as much fluid
as one ..
The data indicate that propellers are only desirable

31
for viscous pseudoplas tics at 101'1 values of' Dt/Da • A fan
turbine seems to be better than both one or hw disk and
vane turbines except at high values of Dt/D a . The a..'dal
flmAj" component must aid in mixing normally stagnant regions.
At high Reynolds n~mbers the fan turbine loses its advantage.
Table 2-1 lists the minimum Reynolds nlli'l1ber required
for movement near the wall for pseudoplastic fluids.
Mixing is best accomplished in the turbulent regions.
For pseudoplastic fluids this region is usually confined to
the center of the vessel. Thus to improve mixing efficiency
low values of the tffiL~ diameter to impeller diameter ratio
should be used and/or multiple impellers. Dilatant fluids
are not sensitive to lowering Dt/Da or usli~g multiple impellers
(122).
Lee, Finch and Wooledge (104) injected dye one inch
above the impeller ru~d noted the time needed for complete
mixing. Godleski and Smith (75) added a saturated solution
of phenolphthalein to the fluid and then acid Has added. A
short time later base was added and the time required for
the indicator to change color was measured. Both groups
report that the mixing time in baffled vessels vJaS longer
than in unbaffled vessels. Godleski and Smith report that
the mixing time (in seconds) is related to the voy'tex depth,
H v ' and the impeller dia.me-ter by

32.
TABLE 2-1
f i
MDlllroM REYNOLDS NUMBER NEEDED
TO ACHIEVE MOVEMElfi~NEARA VESSEL WALL FOR
PSEUDOPLASTIC FLUfD~:
Dt/Da SINGLE TWO FAN PROPELLER
TURBINE TURBINES TURBIJ:m
4.8 640
3 • .5 300 90
3.0 270 120
2.4 7.5
2.3 320
2.1 160 70
2 .. 0 110 50
1.75 50-55
1 .. 50 90 200
1.40 40-45
1.33 50 30
1.17 40-45
1 .. 05 35
1.02 35
.
~}
Data from Metzner et al. (122)

33
(2-29
when both the distances are measured in inches.

!4ETHODS OF STuDY OF B..4.TCH HEAT TRANSFER
USED BY PREVIOUS AUTHORS
Experimental Work
The ex.perimental portion of the work in developing a
correlation is the measurement of data needed to calculate
the batch heat transfer coefficients for a variety of conditions.
The basic equipment used is a jacketed vessel
equipped with a variable speed motor or drive and provisions
for measuring the jacket and batch temperatures (and possibly
the wall temperature) ..
The tank is sometimes equipped
-v.ri th baffles, usually four "\,,)"i th a width equal to 1/10 to
1/12 the vessel diameter. The vessel is often constrllcted
of stainless steel to enable corrosive materials to be
tested and also to help prevent fouling.
The diameter of
the vessels used to date has varied from one to five feet"
The most frequently tested impellers are paddles, disk and
vane (straight blade turbines) and retreating blade turbines,
marine propellers (dOl,ffi thrusting), and anchors.
There is
usually a relatively close clearance (an inch or less) beh.reen
the vessel floor and v.ralls and the anchor type impeller
although sometimes there is more clearance.
The
standard position for the other impellers is about one third
the liquid height.
The temperature of the batch is usually measured in
about three different locations to ensure complete mix.ing.

JS
Thermometers or thermocouples are used in the batch and
thermocouples are also used for the jacket space temperature.
If the wall temperatl~e is desired the junction of
a thermocouple is soldered or peened into a small groove
in the vessel I'Jall (or coil). The surface is sanded smooth
and the wires lead out of the vessel through the liquid and
out the top_
If a jacketed vessel is equipped with a coil, steady
state experiments can be made 'tvi th the heating (or cooling)
rate of the jacket balanced by the cooling (or heating)
rate of the coil ( 37~39).
The temperature of the jacket,
coil, and batch thus remain constant. Most authors, however,
have used an unsteady state method where readings of
the batch and jacket (or wall) temperatures were taken
versus time as the batch 14as heated, or cooled.
The latter
method has the disadvantage of changing fluid properties
Hhile the former has the disadvantage of not being able to
detel~ine
the heat transfer coefficients of a jacketed
vessel in which the flow patterns are not disturbed by the
presence of a coil. Balancing the heat transfer rates betHeen
the coil and jacket is also a time .... consuming task.
Calculation of Heat Jransfer Rate
The amount of heat Hhich is transferred per unit time
in the steady state system can be calculated from the product
of the enthalpy change of the medium in the jacket and the
flow rate of this fluid, the enthalpy change-flow rate product

36
of the fluid flO'i>Jing tln">ough the co iI, or a.."l average of
these t\:.;ro values..
It must be remembered, however, to
correct for heat exchange between the jacket fluid ~nd
the
surroundilJ.gs ..
For the unsteady-state experiment the heat transferred
Can be calculated from the product of the flow rate of the
heat transfer medium and its enthalpy change..
This value
must be corrected for heat losses to the surroundings and
the gain in heat content of the vessel..
If steam is the
heating medium in the jacket the condensate flow-rate must
be measured as Hell as its temperature.
It is this authorfs
experience that this f1O't-J rate is not constant during a
heating run ~nd
thus the condensate collected during one
time interval, had actually condensed during an unknO't-JU
previous time interval. Hence~its
measurement is subject
to large errors. If the heating or cooling medium is \-Jater
the 1'101-1 rate is usually very high in an effort to keep the
heat transfer surface at a constant temperature over its
entire surface at anyone time..
Therefore the actual
change in temperature of the floVoring fluid is kept small ..
This also leads to large errors because a fraction of a
degree error in the inlet and outlet temperature readings
is often a large fractional error of the actual temperature
change..
In addition to these errors there are the problems
of calculating the heat losses to the surroundings and the

.37
2: a in in heat cQ@tent of the vessel.
A second method of calculating the qtta....'1ti ty of heat
transferI'ed is to calculate the change in enthalpy of the
batch.
There are three corrections 1lrhich must be taken
into account ..
1. The heat losses from the sUT'face of the
fluid.
2. The mechanical energy input from the ar;itator.
3. The gain in heat content of the impeller and
shaft.
There is usually at least 20 percent vapor space during a
heat transfer experiment and the vessel is covered Hith an
insulated lid. If the temperature of the batch does not
approach the boilinl; point the heat losses from the surface
are negligible. The mechanical energy input to the system can
be calculated if DOHer measurements are made (they llsually
are). ROHever, the mechanical energy input is significant
only if very viscous fluids are being aGitated.
The gain
in heat content of the impeller 8illd shaft is also neglicible
because of their small ilJeic;ht and heat capacity in
comparison v'Ii th that of the batch fluid.
The temperature
change of the batch can be chosen large enough so that
errors in measurinrz it are small.
It is this author's
opinion that this second method is the most accurate means
of determining the heat transfer rate.

38
Calculation of Batch Heat Transfer Coefficients
If the jacket temperature was measured, the batch heat
transfer coefficients may be calculated by first calculating
the overall heat transfer coefficient using equation 1-1
and then determining the batch heat transfer coefficient
using equation 1-2 (32,49~182).
. ,
In order to use this equatlon
the fouling factor, I/hf' the medium heat transfer coefficient,
L
:b ., and the resistance of the \.Jall, 'f:!. ,
•-m.
must be determined •
KlrJ
The resistance of the wall may be calculated using the values
of wall thickness and thermal conductivity.
The fouling
factor may be estimated from a knowledge of the condition
of the heat transfer surface. The fouling factor is usually
neglected on the basis of visual observation of the inside
of the jacket. If condensing steam is the heating medium
the film coefficient of the medium is often estimated to
be about 2000, based on measurements for pipeso
The batch
heat transfer coefficient, h, is then the only unkn01tITl in
equation 1-2 and can thus be calculated. If water is the
heat transfer medium the estimation of hm becomes more difficuI
t..
Heat trans fer coefficients for liquids are much Im-Jer
than for condensing gases and depend largely upon velOCity.
Very little work has been done in the field of correlations
for the prediction of heat transfer coefficients for the
jacket side of jacketed vessels.
Many investigators use the vHlson method to determine
the s~m
of resistances to heat transfer on the heating or

J9
cooling mediu..:m side, the heat transfer wall, and that
caused by fouling (30, 150, 19L~).
If the flofJ rates of
the heat transfer mediurQ are approxliaate1y the S8~e
for
all the heating (or cooling) runs and there is no evidence
of fouling or corrosion of the heating surface the swn of
these three resistances, ERR' may be asswned to be the same
for all heating (or cooling) runs.
Thus equation 1-2 may
be 1,Jri tten as
(2-30
for the heating runs and
(2-31
for the cooling rlms, Hhere ERR and:ERc are the S1-1111S
of the
constant resistances for heating and cooling respectively_
Thus the only factor that changes the overall heat transfer
coefficient, U, is a change in the batch heat transfer coefficient,
h.
Previous authors have reported that h is a function
of the Reynolds number raised to the 2/3 p01-{er.
(2-32
Thus equation 2-30 (or 2-31) may be written
(2-33

40
The s~m
of the resistances,£RR' can thus be found by
plotting the values of l/U for the heating ru.ns versus 1/NR~/3
and extrapolating the curve to zel;'o .. I:RH is the value of the
ordinate vJhen 1/NR~/3
is zero .. i::Rc can be evaluated in a
slifiilar manner by plotting the data for the cooling runs.
Once the resist~nces
are evaluated the batch heat transfer
coefficients may be calculated from equations 2-30 and 2-31.
There are several serious disadvantages using the above
methods for calculating the batch heat transfer coefficients.
1. The temperature of the jacket fluid must be knOl~
accurately. It was found in this work that the
temperature of the steam entering the jacket was
o
often about 108 C and the temperature of the
cdndensate was about 90 0 to 95 0 0.. In this case,
l'11hich temperature should be used?
2 •. In the above case part of the jacket had a condensing
steam film while part had a water fina.
Is one justified in assuming a condensing steam
film for the entire area?
3. The heat transfer coefficient is a function of
the Prandtl number, viscosity ratio, and geometrical
factors.
These could produce much scatter on a
Wilson plot if not held constant.
4. The 2/3 power is not necessarily the proper exponent
for the Reynolds number.
Pursell (150) re-

41
ports a value of 3/4-..
He then replotted Dblt s
a~data on a Wilson pl0t using I/NR~/4 as the
abscissa and fOILnd the};Rc I·JaS .020..
used I/NR;/3 and foundZR c to be .010.
Uhl (11P had
Thus the
Wilson plot method is very dependent upon the
form of the abscissa (and personal choice of the
investigator). Small errors in the estimation
of the ste8111 coefficient often are not ma..rdfest
in the result for the batch heat transfer coefficient
since the former is very small compared
to the latter. H01vever, if water is the heat transfer
medium the surface coefficient of heat transfer
on the jacket side is much smaller and thus errors
in the estimation of the jacket resistance result
in errors of like magnitude in the calculated batch
heat transfer coefficient.
A second method of calculating the batch heat transfer
coefficient is to measure the i,

42
disadvantage is the installation of the thermocouples so
that the junction measures the heat transfer surface and
does not disturb the heat flow through the wall.
By proper
installation techniques, hov-rever, this can be closely
approximated.
In some cases the thermocouple junction has
been embedded in the 't\fall rather than at the surface..
However,
if the exact position of the junction and the thermal
conductivity of the wall is knovrn the results can be
corrected to give the surface temperature.
The Correlation of Results
- ,
The correlation of the data is difficult because of
the large number of variables.. A fe'ltJ authors used a
method of plotting the Nusselt n~mber versus a dimensionless
group on logarithmic coordinates, keeping all the variables
constant (39, 58, 137,1;D)"
Once the effect of
Ylgroup 1" has been determined the Nusselt number, divided
by the IIgroup ll! effect, is plotted versus "group 2".
The effect of "group 3 11
is found by plotting the Nusselt
number, divided by 'che product of the "group 111
and flgroup
211 effect, versus ltgroup 3". There are disadvantages to
this method since it is very difficult, experimentally, to
change the value of only one dimensionless group at a time.
Some authors seem to have assltmed that the Chilton (39
equation and exponents are accurate and thus use his exponents
for some of the dimensionless groups and by plotting

43
find the effects of one or two other groups (30,32).
These methods leave much to be desired because there
is much scatter in most of the experli.~ental
data and fitting
a straight line "by eyell is an almost hopeless task.
Due
to the scatter of the data the slope of the line drat-ill to
represent the data :t;s subject to hwaan error and choice.
This is evidenced by the large number of Itrecalculations[!
reported in the literature.
A more scientific approach to the task of correlating
the experimental data is to use a rtleast squares ll method
of mathematically fitting a straight line through a set of
data points (49,]82).
For the many variables such as obtained
in a heat transfer study a multiple variable regression
analysis is described by Levenspiel et ale (K5) and Volk
(198). This method eliminates the proble:m of strict experimental
control because it provides an objective and
reliable estimate of the true values of the exponents.

44
smwiARY OF LITERI\TURE RESuLTS FOR
BATCH HEAT TRANSFER TO l~iTONIAN
FLUIDS
The study or heat transfer coefficients to fluids in
agitated vessels is a complex problem.
The many variables
involved make it very difficult for rigorous mathematical
analysis and thus the methods of dimensional analysis nBVe
been used. The dimensional analysis yields ~8~
(2-35
"llfhere
Dc is the vessel diB-meter ..
Dtt is the agitator diameter ..
k is the thermal conductivity of the batch fluid ..
ji is the viscosity of the batch fluid.
f
is the density of the batch fluid.
C p is the heat capacity of the batch fluid ..
N
is the rotational speed of the impeller.
f'w is the viscosity of the batch fluid evaluated
Wa
at the 1

45
The group to the left of the equal sign is called the
Nusselt number.
The first group to the right is the mixing
Reynolds number, the second is the Pr~ndtl
number, and the
third is a viscosity correction factor similar to the one
used by Sieder and Tate (181) in pipes..
Very fe1.o[ investigators
have studied the effects of the remaining groups.
The results of most of the vwrk done in the field of
correlation of heat transfer rates in jacketed agitated
vessels to Newtonian fluids can be sw~marized
2-36
by equation
NNU (2-36
A survey of the experimental conditions and correlation
results of the papers published to date for the jacket and
coil types of heat transfer surfaces Sh01'ITS
that the exponent
of the Reynolds nlwber is usually reported as 0.67 althol~h
it varies from 0.5 to 0.75.
Likewise, the exponent of the
Prandtl num.ber is usually reported as 0 .. 33 but varies from
0.25 to 0.50. The viscosity ratio exponent varies behJeen
o.lL~ and 0.90 with the majority reports about 0.14. The constant,
C, varies over a 1rlide r~nge-,
from .035 to 39 .. 0 and is
probably a function of the impeller type and system geometry.
One author (160) reports C to be a function of Reynolds
nlwber.
This function is different for each type of impeller.
Another author (137) reports that the exponent of the viscosity

48
correction factor is a function of the batch viscosity. In
summary, the equation is usually reported
AI 0.67 O.3Y;U/ )'0.14
~tt:::: C'VRe Il~ ,/#w, (2-36a
Viscosity Ratio Exponent
A reviel

47
the highest heat tra...nsfer coefficients "Jere obtained 1-clhen
the impeller was positioned at 50 pereent of the liquid
height. Ske11and (182 studied the effect of impeller
height using upthrusting propellers. He reports that
where HeB is the center height of the impeller from the
floor of the vessel.
Thus, he obtained greater coefficients
1,-rhen the im.pe11er 1,'1aS closer to the floor of the vessel.
Uh1 and Vosnick (lqD')'sumrnarized the effects of clearance
betv.leen an anchor agitator and the vJa11s and floor of a
vessel, as determined by Uh1, Bro~m
et 0.1. (32),and Huggins
(92). The results are reported as the ratio of h at the
specified clearance ratio to h for a clearance ratio of
0.02. The clearance ratio, HclDt, is the ratio of the
clearance distance to vessel diameter.
At zero clearance
ratio (scrappers are used) the relative heat transfer coefficient
is 1.lL~
for thin fluids and up to 1.50 for more
viscous fluids. For pseudoplastics the relative h is as
high as 4 .. 0 or 5.0. BetHeen zero clearance and 0.02
clearance ratio the relative h varies between 1 .. 37 and 1.03.
At a clearance ratio of 0.02 the relative h is by definition
1 .. 0. As the clearance ratio increases the relative h increase
up to about 1.25 a-t a clearance ratio of 0.080.
Uh1
and Vosnick explain the increase in relative h at high

18
clearance ratios as being caused by turbulence. At 0.02
clear~nce ratio there is little or no turbulence. At very
small clearance the high shearing force at the wall increases
the relative heat transfer coefficient.
Baffles
Brooks and Su (30) studied the effects of baffles. Below
a Reynolds n~unber
of 400 the baffles had no effect but
above 400 there was a 37 percent increase in the heat transfer
coefficient. Thi s increas e ,·ras independent of the nu.mber
(one, two or four) of baffles used.
Ackley (1) reports that
using four baffles his data support Brooks and Su.
Ubl
(194) reports that baffles had no effect in the Reynolds
number range of 25 - L~OOO • Chilton (39) reports that removal
of his coil did not seem to effect the heat transfer rate of
the jacket..
Oldshue and Gretton (137) report that Hhen the
baffles were placed 1 inch off the l~all
01'" betHeen the coil
~nd
the impellel'" the heat transfer coefficients al"'e 5 percent
lower th~n
Hhen the baffles are at the Nal1.
Impeller Geometry
Using a coil as the heat transfer surface, CURmings
and vlest (49) found that using t1-JQ
l"'etreating blade turbines
did not increase the heat transfer coefficient but suggested
that this is probably because the fluid height Has equal to
only one vessel diameter.
For a greater fluid height the
second impeller 1 ..vould be expected to increase the coefficient.

49
A pitched blade turbine gave coefficients about ten percent
lower than the retreating blade turbine and reversing the
flow direction of the pitched blade turbine did not increase
the heat transfer rate..
Oldshue and Gretton (J.l7)using a
coil, report that a rotating impeller causes two phenomena:
a. Turbulence in the region of the impeller and
its wake.
b. Bulk fluid flm..r ..
Both these phenomena are needed for good heat transfer, but
bulk fluid flow is probably more important.
An increase in
the impeller diameter to vessel diameter ratio at constant
Reynolds number, should increase the bulk flow component at
the expense of the turbulence component.
Thus the heat transfer
coefficient should increase Hith increasing diameter
ratio. They report
lJhich is in accordance ljd th their theory.
Pursell (150) and
Ruckenstein (160) using jackets, and thus the vessel wall as
the heat transfer surface,. report that the heat transfer coefficient
decreases \-lith increasing eliameter ratio..
data indicate
Their
{2-39
h 06 CD /Do )-0 02 5
a, t
(2-40

.so
respectively..
These contradicting results may be results
of complex interactions between the geometrical dimensionless
groups.
As the v.Tidth of the impeller blade increases one
would expect the heat transfer coefficient to increase.
Pratt (149) reports
(2-41
where 1th.
is 1.Jidth of the impeller blade and
PH is the diameter of the coil helix.
Pursell (150) reports
(2-42
~vhere
Da is the impeller diameter.
Coil Geometry
Oldshue and Gretton (137)r>eport that lrlhen a coil is
used as the heat transfer surface the coil geometry is
important.
A i

SI
done on the correlation of heat transfer coefficients in
agitated vessels, but that many differences or even contradictions
exist among the present correlations.
Some of
the difficulty may be due -to the problems of obtaining
accurate data..
Chilton et al. (39) report that duplicate
results for heating and cooling water have an average
deviation of 17.5 percent. Brooks and Su (~)
report reproducibili
ty of ± 20 percent for ltTater and corn syrup and
±5 percent for motor oil.. Cummings and '\tlest (49) claLm that
their correlation in 90 percent of the cases it is used will
predict the batch heat transfer coefficient l«1i thin 20 percent
of its true value.

Si
TO NON-NE1:;JTONIAN FLUIDS REPORTED.-..!~~
LITEIZATURE
To date only two papers have been written on the correlation
of batch heat transfer coefficients in agitated
vessels.
Hork of Thomas Blanchard and J1..1. Chin Ch12. (22)
-~---... ~-=""'-'~--"-- "-¥". - *"
Thomas Blanchard and J1..1.
Chin Ch1..1.st1..1.died heat transfer
to pseudoplastic fluids in an agitated tank (156).
They
performed heat transfer experiments on aqueous solutions
of 2.0 percent hydrolyzed polyacrylonitrile, 3 .. 5 percent
polyvinyl alcohol, ffiLd 2.0 percent polyacrylam~de
in a three
gallon stainless steel vessel equipped Hith both jacket and
coil. The vessel diameter was 10 5/16 inches and a )~- .. 5 x 1.0
inch paddle vv-as the impeller. They used the steady state
method and determined the heat transfer coefficients by
measuring the wall temperatures.
The exponents of the
Reynolds and Prandtl numbers 1

5J
evaluated at the wall temperature divided by the viscosity
at zero shear evaluated at the bulk temperature..
Blanchard
thus assumes that the shear rate at the 1".Tall is very high and
the shear rate in the remainder of the vessel is low.
He
points to the 't

54
The es tima ted accuracy is ± 17% fu"'1d ± 2076 for the jacket
and coil respectively.
There are five criticisms or limitations to this
1-1ork.
1. The Hall velocity term t.!aS chosen on an unsound
basis.
2. The viscosity term in the Reynolds and Prandtl
numbers does not take into account changes of apparent
viscosity with changes in agitation rate.
3. Only one impeller was used.
~-. The viscosity range covered is limited.
5. The viscosity ratio term does not revert to the
one generally accepted for Newtonian fluids as
fLoo approaches fLo
ltJork of Salamone et al (165)
The second Hork on this subject, dealing with jacketed
vessels only, was done by J. J. Salamone, A. Cristaldi, and
A. Korn.
Salamone et ale studied the heat transfer characteristics
of power-law pseudoplastics, Hith flow behavior indexes varying
from 0.33 to 0.77, in a 12 inch diffi~eter
stainless steel
vessel, using a four inch flat bladed turbine with six blades.
The heat transfer runs Here of the unsteady state variety
and the Hilson plot method was used to calculate the batch
heat transfer coefficient. The results were cross plotted

ss
to
(2-46
where ill is the consistency index factor used for flow in
pipes (118) ..
(2-L~ 7
The generalized Reynolds number range covered was 83 to
1286 and the fluid consistency index, evaluated at the
average bulk temperature, ranged from o.ol~_6 to 0.609
Ibfsec~/ft2.
Equating the generalized Reynolds number to
the NeHtonian Reynolds number Sh01-JS that the apparent viscosity
used in the above correlation is
1:Jhich is very similar to the apparent viscosi ty in pipes
if N is substituted by V/D.
As reported earlier in this
chapter, Netzner and his co-workers have experimentally
determined that the apparent viscosity in agitated vessels
could best be represented by
fL (
c' 1\T) n-l
a.= K II.:.; l~ (2-25
and that the Reynolds num.ber be expressed as
{2-26
The Sal~10ne
(165) correlation is an improvement over

SI3
Blanchard's equation since it does have a viscosity term
which changes "lith agitation rate but the exact form is
not the best suggested by the Ii terat'Llre.
This study was
also limited by the use of only one impeller and a small
Reynolds nu..mber range.
Nei ther of these tlrJO studies 1..ras
based on a ne1,,;r dimensional analysis but only modified the
results of the Ne1

CHAPTER .2
DEVELOPMENT OF CORRELATIONS
Tl3.eoretieal Co;:;relatien
In a baffled vessel agitated by a propeller tme rlGw
or rluid is essentially axial. That is" the p:r'opeller
eauses a do-v.TnvTard i'10-v.T of rluiel. Near the bottom.

58
HEA T TRANSFeR
FIG 3-/
FLOW PATTERNS IN PROP£LLER AGITATED BAFFLEO VESSEL
Near the wall the temperature gradient is negligible
in the @ and z directions compared to that in the r direction.
The velocity gradient in the @ direction is negligible
Itihile the velocity gradient in the r direction is the most
important.
The velocity gradient in the z direction is
negligible except at the top and bottom hThere the radial
flow takes place.
Since only the major portion of the
wall is being considered, the velocity gradients in the z
direction will be neglected.
(The experimental portion of
this paper developed heat transfer data taken in a vessel
I,"i th both the cylindrical wall and the bottom j acke ted.
However, the theoretical analysis only considers the cylindrical
wall portion of the heat transfer surface.
A more
complete analysis would lead to the same final equation for
correlating experimental data.)
In general, the equations for the conservation of

momentum" mass" and energy may be ~'Iritten.
the z direction the equation of motion is (21)
( (J Y ~ + 'VA. J V
z + V g J Vz -+ V z ) V
z L _ d?
)1; )A. A, Je Jz )- cJz
(
~ J (.-2 1A.z) -+.-! J l"sz + J Izz. L.,L ~ q z
-..-i. .J A.. --i. d- e j z j -J
For flow in
(3-1
For the model being considered in the region near the wall:
1. The flmv is as slLrned to be cons tan t 1-li th
time, therefore j ;z ~ tJ
2. The velocity gradients in the 8 and z
directions are assumed to be zero.
3. The velocity in the 8 direction is assumed
to be zero.
?t.
For a power 1m·] fluid r::: K;; .
Therefore,
1.4z = _Kr.:!!k -f- ~ 7 ~ - K [d h. J~ (3-2
L)/t.. dz..l "d4
2. Tzz ~ - ;:(}:) ~ 0 U-3
3· I;z"-;;'lj1 +1 jf1: 0 (H
The equation of motion for this model is thus
The continuity equation is (21)
/
-r - h-
-f
I
(3-5
For the model vJi th negligible velocity gradients in the z

6D
and e directions and constant density, the equation becomes
I
A
J(eA i£)_ 0
eJft - (3-7
In the system being considered the mechanical energy input
is negligible compared to the heat transferred through the
1..Jal1s. The energy equation for this case is (21)
d T 0tdT J/p
(-'c;; ( d-c -;- J~ ";-;t
) 7 -f liz dT ) =
J& oiL!
J [;
(3-8
The temperature gradients in the e direction are zero,
and the temperature gradients in the z direction are also
assumed zero..
Therefore equation 3-8 reduces to
Equations 3-5, 3-7 and 3-9 thus describe the model
(3-9
discussed above.
These equations cannot be solved since
the velocity and temperature gradients cannot be expressed
analytically. However, the system can be characterized by
solving the equations dimensionally.
The follo-vring dimensionless variables are defined by
Bird, et al. (21) as
r-lH~ = ( riDs. ) (3-10
Z~:- = z/Ds. 0-11

61
Vr;> Jt.- ,,"Ii'\...
..", ::: (Vr/V) (3-12
Vz .. ~~
= Vz/V (3-13
p
-li-
p-p
= Ie f/ Z
0
(3-14
t~=-
-- tV/Da (3-15
T~~ T
=
- Too (3-16
Ts - %0
where V is a characteristic velocity which can be quantitatively
evaluated.
For an agitated vessel, NDa is such a velocity.
Da is the diameter of the impeller and N is its rate of
revolution ..
Solving equations 3-10, 3-11, 3-12, 3-13 and 3-14 for
the variables in equation 3-5
r = r~~~:"D a (3-17
z ...
J~
z"Da (3-18
Vr :: V ~~-!~V
r (3-19
V z = Vz·:"'V (3-20
p :: p~:. (e V2 ) + po (3-21
Equation 3-5 also has differential terms. Equation 3-22
is valid since it is an identity ..
(3-22

62
l'lultiplying the right side of this equation by Vz~}/Vz~1-
and
riH}j riH~
does not change the value of the rignt side since
each of these ratios is equal to unity.
J.tIz )'Yz d,k{* d A.,.,;Jfi/f
).h.
-
-
.,

63
Substitution of these dimensionless values into equation
3-5 yields
Dividing both sides of equation 3-30 by
V 2 /Da and com-
(3-31
The only variables i.Ji th dimensions remain in tvw groups,
each of ~rrLich
is dimensionless.
The first group, K/(V2-n Dan, is the reciprocal of
the mixing Reynolds number.
This is more easily seen if
NDa is sUbstituted for V.
//
F4 N
2 2-n.
(3-32
=
K.
(The double primes, NR;" are used to denote tlgeneralizedll
Reynolds number based on this analysis. Single primes,
NR~' refer to }1etzner's generalized Reynolds num.ber, eq ..
2-26). The mixing Reynolds nmuber for Newtonian fluids is
(12)

64
z
e Dei! IV
/I
The second group is the reciprocal of' the Froude number
(3-33
t3-34
For baffled vessels there is no v0rtex, hence gravitational
forces and the Froude nQmber are unimportant (21).
3-31 thus reduces to
Jtiz. .ik-
I
Equation
(3-35
The solution of the equation of motion is thus dependent
upon the value of the Reynolds number. Schlichting (171)
recommends eliminating the Reynolds number from the equation
of' motion in order to make the solution more general.
The
solution will then be valid f'or any Reynolds nQmber f'or a
given geometrical system.
The Reynolds number may be eliminated f'rom the equation
of' motion by defining the dimensionles s variable s r-lE-
and V r~tas
(3-36
(3-37
Acrivos et. ale (3) extended Schlichting's method to power
la1rJ" fluids by using 1/ (n + 1) as the exponent of the Reynolds
number.
Thus, Acrivos, by analogy to Newtonian f'low, used

l/(R + 1) and was able t@ elim.iE.ate the Rejl"rlo1ds number f'r

66
(3-42
(3-43
In order to dimensionally solve equations 3-5, 3-7 and
3-9 the differentials must also be ~xpressed using dimensionless
variables. This is done using the method described by
equations 3-22 to 3-27-
jp/Jz has already been redefined
in equation 3-28. The remaining differentials are redefined
(3-45

67
All of the variables and differentials are now redefined
in terms of dimensionless variables. Substituting these
variables into equation 3-5 gives
e( LI /1/1. f: A/;e (Y;./~).J!. NRe
(J{ ~4 d liz ),:-r 11. 1;0 ~
Del j./& -;Y if 012 .y
-f NRc> (7~,j -< JllRe(j{~n) t/Jn.-4':L /j Vz )?V (tf plz if') 111 /7. (3-52
D2 /l. ~ L\Dd ) { j/l, 'r lj~¥ + J/l;-K / JJ(Jz
or
or
or
(3-55
The Froude number may be neglected for the same reason it
1Nas elLl11inated from equation 3-31..
The equation of motion
(3-56
Thus Vr is only a function of n.
Substituting the variables into equation 3-7 gives
(3-57

68
(3-58
or
(3-59
(3-60
"'Thich reduces to
l.Jhere the group
as (21)
The local heat transfer coefficient, hL is defined
h[ ~ t?L/,14 (T5- Tae,)/( (3-63
l.Jhere Q L
is the local heat transfer rate ..
Ts is the temperature of the heat transfer surface.
~ is the temperature of the bulk of the fluid.
Using Fourier'S law for heat conduction
(3-64

69
The average heat transfer coefficient h, is defined
by equation 3-63 if the total heat transfer rate, Q, is
substituted for QL and the total heat transfer area for dA.
The total heat transfer rate is calculated by summing
up these local heat transfer rates over the whole area of
heat transfer.
(3-65
(3-66
(3-67
(3-68
substituting equation 3-68 for Q in equa~lon 3-63
(

70
(3-71
The ratio Dt/HL is a constant for all the heat transfer data
t~{en fu~d thus has no meaning for the enclosed data. The
ELIDa term could be used as such, however the fluid height
",ras not varied and thus HL is a constant..
Other authors
(137, 150, 160) have correlated data using Dt/Da and the
use of this group is useful for s~{e of comparison. Since
Dt is a constant it may be substituted for HLo
Equation
3-71 may thus be lrJritten.
I~ (3-72
The original set of equations vJaS set up assuming a
constant fluid consistency index, K..
HOvJever, in practice
the consistency at the wall is usually quite different from
the consistency of the batch because of the large temperature
gradient. A fourth dimensionless group, K/K w , is thus intraduced
to correct empirically for the consistency index
dependence upon temperature.
The use of K/K"'J has been
successfully used Ln similar problems in both Newtonian and
non-Newtonian systems.
Although the exact form of the function in equation
3-72 is not known, it is assumed that equation 3-73 l

N"v = C Iv''' (;';~-"')&'i'~ (%t-n,) ) ~! K )+(lJt f ~3-73
fie ('N Fe ) ()( w {D d.) V1V
The same f(H~ !las beeR found su(!;cessf'ul for the resu.lts 01'
7 1
The Peelet number cam be \~itte~ as t!le pro~uet of the
Reynolds number and the Prandtl llfl..:m:J.ber, provided the apparent
visc0sity u.se~
e Npe:: IJJ. V
;ta"
waleh CaE. be written
is the same in beth.
C p I'd //
A
(3-74
Jf/pe =eL>a Z N
,/ / 1/
/Va
if NDe. is substituted
for V.
(3-75
The Reynolds num.ber vIas previ0usly defined as
II j) 2 C -../1'V I
~e := f Q IV / /.(
(3-32
An apparent viscosity may be 0btained by equatiag
equatioR 3-32 with equati0~ 3-33 and solving for the viseosity..
Simee this term is n0t a true viscosity, it is
called an aJYparent viscosi ty,fta. It ..
r
/1
q = f(AI t/YV-/
(3-76
With equation 3-76 as the definiti~n of the apparent viscosity,
the Reyn0lds number is defined by equation 3-32
and tlae Prana tl number by

72
(3-77
Substituting these terms in equations 3-75 ru~d
3-73 ~nd
placing the Prandtl number in the nu..merator, as for Ne1oJtonian
(3-78
or
C YRe" -;;;;;; -; A?~ (~- ( ~ nv
K"J1I Dei
( / -2~ I- cZ ) / K) J? /[J ) C d
(3-79
Equation 3-79 then characterizes heat transfer to pmver law
fluids being agitated by geometrically similar marine
propellers. This characterization is based on a model which
is believed to represent the flo1.J patterns fairly accurately.
If the impeller geometry changes; that is, if the vertical
"VJill increase
and thus a higher Nusselt number will result. Equation
3-79 may be expanded to correct for geometrically unsimilar
impellers by adding a sixth di!l1ensionless term, WalDa' where
\-1 a is the impeller 1rddth ..
AI. - c NJ~:;: f~/" iI.(f)i~V CjNjci e
AI U - Re /Vp-1. K'w (Ii (;;- -1V (3-80
at
Other geometry effects could be taken into account by adding
more dimensionless groups such as found in the dimensional
analysis for Newtonian fluids as presented in equation 2-35.
4i

73
Semi-Empirical Correlation
i .., .. ' in
Metzner has show~
that the shear rate in an agitated
vessel is related to the agitation rate of the bnpeller
v a =
(11 .. 5 N) (2-20
as discussed in Chapter 2 and thus the apparent viscosity
could be defined.
(2-25
It was felt that using this apparent viscosity in place of
the Nelvtonian viscosity in the Reynolds and Prandtl ntunbers
of the l'lfeHtonian fluid correlation would yield a correlation
suitable fol'" power-law fluids..
The Reynolds and Prandtl
nurabers evaluated using this apparent viscosity are designated
as NR~ and Np~ respectively_ The correlation Has
expressed as
(3-81

GHAPTER It
74
EXPERIMENTAL. ,PHASE OF THIS ~SIS
A iar,e p0rtl~B o~ ~e e~fort to aeve10p ~ experimemtal
ea>3:relat10R is devteci t@ ec9l1eetiRg data.. TRe
equi~meBt needed ~0r the experime~tal portion must be
de siple

75
7I1C1?/lfOCOUPLc
.JuNe T/ON IMBEfX)eO
4 TINS/Of' 5URFIJ(;e
OF rcSSCl. .41 3
LOCATIONS /'20' APART
17 "
19"
It; I-/OL£5 ON !3/' R
-:if 7 DRILL ~ -20U,vC-t?A
/'STt£L NippLe
2" LONG
r
'I
I STeEl. NIPPLE:
Z" LONG
~~===p==~~~J--~
(4)Z~2"x}4
ANGLES AT 90°
cO
7;&. S7Ect.
~~ .3/~ ",,5.
/" 3/G SSNIPPLc
3" LONG
FIG 4-/
/-lEA T TRANSFER VESSEL

76
Three vertiehl grooves 1/16 x 1/16 inches It,Jere machined
in the inside 'ltIall of the vessel, extending dov-m from the
top 8, 14,and 18 inches.
Iron-constantan thermocouple
wires encased in a 0.04 inch diaY'leter 316 stainless steel
sheath Here placed in the three grooves.
(One sheath per
groove. )
The tip of the sheath v!as bent slightly tm..rard
the inside of the vessel ELYld
the sheaths Here then cemented
in place 1,-]"i th the tip of the sheath flush l,,)'i th the inner
surface of the vessel wall.
The sheath extended up the
groove to the top and from there to a junction block in a
protected spot behind the vessel. The entire groove l'!aS
filled with a heat transfer cement having the same thennal
conductivi ty as 316 stainless steel (mermon T-85/~
Arter
the cement had hardened the excess vms sanded off to give
the inside wall a smooth surface.
In this manner the surface
temperature is measured Nithout interfering with the heat
f'loH in the 'lATall and 1ili thout having the thermocouple leads
dangling in the solution. The heat transfer cement was
used because
a. Its thermal conductivity vJaS the same as
that of the wall.
b. Regular solder may have caused corrosion
problems.
c. The use of silver soldermtp.t have damaged
the thermocouple junction.
Figure 4-2 shows the placement of the sll.rface or wall
->: Trademark of Thermon HaYlufac turing Co., Hous ton, Texas.

77
_I"---- /
SCALE
I
~~,
.5 j
t
/Z.5
.'
I I I
I
I
I
I
12-
/1
10
'I
g
7
6-
"
S"
Ie 4
3
2
11:,
~.5
~ ~
/
:~
#3 1 t-
f
t'
t
7 "
/lG 4-c
LOCATIOiv' OF WALL 7h'E/?OCOUPLES AND SCALE

78
to me insicl$ wall :fer the meas~emel!lt
of f'luid height".
The batek te:m.J>erature is lD.easured by three therm0-
eoup1es..
One Ilileasures the tentperature o;t' tke batek abeut
two inches above me ves sel bott~m aRd about i~ inehes f'r®m
the eemter liRe..
This ther-,noecn::tple sheats enters the pipe
:fittings un&er the tamk by passing through a bush~ ~d
then enters the vessel through the drain nipple" The
other two ]lr0jeet dO"tffi into the f'luid f'rom above" O]1le 7
imehes and the other 15 inehes f'r0m tJae top.
These therm0-
eoup1es were supported by the lid. All three bateh therm0-
.,
eoup1es as well as those in the piping system were ironeonstaatan
thermoeenples protected by a 1/100 inch thiek
316 stainless steel sheath. The error due to the time lag
was estimated to be about one pereent.
T.ne vessel jacket had three :fittings :for introduction
and exit Cl:f :fluids, two positioned 2 inehes :from the t0P
on opposite sides o:f the tank and ome on the underside ..
The f'itting on:the underside was hooked up so that steam
could enter and condensate could leave at the same time.
During the heating cycle steam enterea ome o:f the top
f'ittimgsand the bettom f'ittilAl.g.
The eondensate draim.ed
tfurough the bottom :fittiag; its temperature was measured by
I
a thermometer (0-200@0 0.2°0 divisioms) am~ it le:ft tn~

also cop~ected
to the pipes leading to the bottom fitting.
A thermometer (0-200 0 0, 0.2°0 divisions) and a thermocouple
measured the inlet steam temperature at the top fitting.
~Jhen
in the cooling cycle the cold water passed t~~ough
a rotameter (Fisher-Porter Fl01~ator Meter (Series 10A27000)
9.4 gallon per minute), and entered the t~nk t~~ough the
same ports used by the steam.
The cooling 1.vater was removed
from the jacket throus-h the second nipple at the top \Alhere
both a thermocouple and a (O-lOOOC, O.loC division) thermometer
measured its temperature.
Figure 4-3 Sh01-JS the piping
layout and the placement of the batch thermocouples.
Table
1-1_-1 is a sU11nnary of the vessel and associated equipment ..
Agit,ation
Four 1 inch baffle s Here welded to a circular frame
v,rhich could be removed from the vessel if desired.
The
length of these baffles was 20 inches. Although the baffles
touched the vessel \>

80
K£Y
TH - TJ.lCRMOME TEl<
TC - TI-/£RfrlO
- - - THERMO (!OUPL E WIRE
R070MCicR
WATeR SUPPLy
rll
I
I
I
1
I rc
DRAIAI
--
TI-I
STEAM TRAP
FIG 4-3
PIPING DIAGRAM

81
Ve8sel
:J all th:l c]me 8 8
.) '] 6 .', ' :;/. L'l.cn
I~ei~'l~t
of cylindrical no::d.tion
20 ~;nche3
Shane :-)f floor
I1az:irrlllJll depth of floor
Dim1etcr
lI;. lnc}l.o 3
linch
ITonin;J.l plpe :Ji~~c
of v0:1801 fittinC3
Fl l 1.id dopth WJl'Jllly 11.:>e,l
(fT'on lOHost
point)
Carr;; spc)n(lin,,= 3 C[tJ_8 1-")0 n.rlln,S:
Aron of clich
')
1 .. 15 ft.L.
.J06
/
ft .. -/inch
6.20 ft.2
VOJ_c'210 of cyllIY!1--;Icr'1 TlOrt:Lon (0;-1 tIl.
b".fl(; 8 ins t2~.lo(·)
.0Cf] ft. 3 jinch
Toto.l voluno u;JH'1.11y ~),:Jecl

TABLE ~.-2
AGITATION
}\1otor
POHor rating
Electrical pOHor requirement
3/4 HP
220 Volts
15 amps
Speed range
Shaft diameter
75-2500 RPl"I
0 .. 5 inches
Baffles
Number
Width
Length
4
1 inch
20 inches

83
potentiometer for varing the motor voltage, and hence
speed.. The speed range vJas from 75 to 2500 RPl"I. The
motor \.Jas mounted on a se t
of bearings 1;.rhich allo'Hed it to
rotate freely. ~\Then the shaft turned the motor rotated in
the opposite direction and Hith it a 61 inch diameter pully.
A string was 'Hound around this pully and attached to a
0-25 pound scale. The torque of the rotating shaft was
counterbalanced by the pully-scale system ~nd
thus measured.
TORQUE = (Radius of pully) (Force recorded on
scale)
(in Ibs.) = (inches) x (lbs.) (4-1
Before any heat transfer data l'ITaS
taken this dynamometer
10TaS
tested 811.d it was determined that '",hen the motor l.Jas
operated under no-load conditions the dynamometer scale
read zero.
Thus there vJas negligible friction in the
bearings supporting the motor.
The motor, bearings, and scale assembly 1:mre mounted over
the 15-gallon vessel on a f1Unistrut!l~~
frame which al101.Jed
three dimensional adjustment "t..Ji th very little eff'ort.
The
motor "ras placed so that the shaft lr-ras coincident Hi th the
center line of the vessel.
The major portion of the work
was perforr!1ed lrJi th eleven diff'erent impellers of four types;
paddle, six bladed disk and v~ne
turbine, three bladed marine
propeller, and an anchor.
Hany other impellers in addition
to these eleven Here used for the ""'Tater runs.
The dimensions
~~
Trademark of Unistrut Products Co., Chicago, Illinois

S4
IlllB/J/DV.51I tw:)lve point strlp chn.rt reccrder~
rl'b.is
Point lTUJilber
ItOnl ilP['snred
Po::ltion
1 Water or steaR inlet
2 DB. tch (00 ttom)
3
1 inch Eeed to ton
oE jDcl:et
2 inches Erom bottom
6 inches Erom top
7 inches Erom top
:1.'3.11
(Eidena)
12.5 inc~as frrnn top
6 Batch (IIiddle)
7 Coolinr'; 'IB. ter nutlet
e
Batch (Bott:::>m)
9 1.{all (Bot tom)
10 Batch (Top)
'l5 i nc'le '"
...L _ 1. -... ..L. .C0 1 "' '--',,_ ·"1'1 top
1 inch drain at top
of jacket
Same as 1/2
lC inches from top
,cu.'l 8 "'''''e 0.. "d,.:) it~- .1J:1 1

85
MATERIAL 7:0 STAIIJLESS STEEL
/
/ "
TWO SeT ScREWS
FIG 4- 4
ANCI-IOR AGITATOR

86
TABLE 4.-3
IHPELIJER DI1'lENSIONS
__ '* 1
Diameter
~inches)
\vidth or hei&h.t
(inches)
Anchor
Disk ~Dd
(6 bladed)
Vane Ttu~bine
9.0
L~ .. 0
5.0
6 .. 0
7.0
Open straight blade turbine 4.0
Open reversing blade turbine 4.0
Open retreating blade turbine 4.0
Paddles 4.0
l~. 0
5.0
5.0
5.0
6.0
6.0
7.0
7,,0
7.0
8.0
8 .. 0
8.0
6
0.75
1.0
1.25
1 .. 375
0.75
0.50
0.50
1.0
2 .. 0
1 .. 0
1 .. 5
2.0
1.0
2 .. 0
1.0
2.0
3 .. 0
1.0
2.0
4-.0
Reverse pitch paddle 9.0 0.7
Propellers
4.1 }
5.2"'

11
Wa.ll (Mi€1dl~)
Same as #5
81
12
Bateh. (Middle)
Same as #0
The ahove €o~diti0~S a~~ly t@ all tke water rtlns. Whe~
usimg m0re viSCGUS flui€is seme vaFiati0nl im '!;,Jall temperat1ltre
was Boted and tke tkermocouple panel was modified so that
the taree wall therm.oeouples were eenneeted. Thus fer all
runs after run number 185 the ten~erature points 3, 5, 9
ane! 11 record the average of' the three wall temperatures
lIDO. :not the mdividual posi tioRs as give~ abcnre ..
Before the therr~oeouples were metalled they were
connected to 'the recorder and calibrated. They were placed
in iee water; a 25°c co~stant tem~erature bath, and boilimg
water. At all three temperatures the system reeorded the
exaet temperature, pr0vided the recorder was 1tJarrl1ed up for
f'ifteen m±nutes prior to measuring the temperature. I~
all the heat transf'er runs the reeoraer was therefore wa~led
up f'ar thirty minutes before data was takem. The chart
speed used was 0.5 mcnes per winute although 1, 2, 4 and 5
inches per minute were also available at the flick of a
switch.
The three wall-temperature ther.mocouples gave sligatly
tiiifferent temperatures at the Glifferent l@catiems. It was
found that the vertical loeation of the impeller was a large
faetor in the matnitude of the deviati6ns. T.me impeller
p0sitiens listed in Table 5-1 were exper~entally
determ~e~

88
to give the minimu..rn deviations in Ivall te:m..perature readings
vJhen water "lims the fluid being heated or cooled in the
vessel ..
For the ItJater ru:

89
shea.r ra.tes, tl?1ey a.re unaffeateel by agin/il::, are Bot attaakea
by baeteria, aR~
I
kave a wide raBge of flew beha.vior inelexes.
The manufacturer states in the descriptive balletin,
nCarbopol: Water-Soluble Resims n , that these resims are
completely selable. It is the 0p~iom of the authGr and
Hetznel? (12,5) th.at these "solutions" are col10-idal suspensie:N.s
rather than true solutions. The most import~t faet is
they are ~se~doplastie fluids whieh ean be eharacterized
by the power law and are easily studied.
OPERATING PROC~DURE
Prepara.ti,en ,rfJ,f. Batela
When water or glyceri:N.e was used as tae test flui

(1)
the batch was then laeated to abou.t 85 C ana agitated for
another thirty minutes.
90
€I
The bateh was then ceoled to about 25 C and neutralized.
The neutralization is necessary sinee the resin is sup~liea.
1m the free acid ferm and the solutions will mot develop
their hi~ €eRsisteney unless they are neutra.lized to a
PH of' about 7. OveFneutraliza.tieR to PH of' 8 OP 9, nowever,
is not harmfUl. Seaium hydroxide as a. 10 ~ereent
solution was added gradually TIRtil a PH of 7 to 7.2 was
reaehed. The solution beeame very viscous as 60mplete
neutralizati0n vras reaehed.
Water 1-JaS then adided to the vessel to bring its
volume up to the 1.623 eubie foot volume (10 3/4 inches
OR steel seale) and agitated for about forty-five minutes.
A 600 ml. s~~le
~roperties.
was removed to measure its rheelogiesl
The fluid level in the vessel was then l0wered
to the 9~ ~eh mark (1.512 eu. ft.) and heated to 90°C
and e00led..
A BeH 600 mI. sample was ta.keR and the ola sa:Ml\'le
added to the vessel to keep its,level. The heating and
eooling cyele was repeated a second t~e to make sure that
the fluid properties were constant.
The Motor! s pOlver supply and the recorder were first
warmed u~ for about 30 mi~utes. Tke batch level w~s eReeke~,

and if' lO"V'l$'
a sm.all amount of' wate~ was added -Go make up
fol' I!,..,.apora tiol"i los ses (0 A series of Fower m~!HilSU3Jl'(!I)ments were
then made. At each speed the dymrunometer s~aleg the rotational
speed, and the flm.id height we:pe noted.
There vIas not mueh
variati1!lB. in ~ight because the baffles elimina:ced vOJ?tex
f'ormatiol'l..
However, there were slight increases and these
't-lere taken int ten di.f'f'erm t speeds were investigated
~nd
f'our were selected f'or heat transfer runs.
The heat transfer run was started by tu:Mll.il1lg en the
recorder and steam (low pressure, 8-12 paig.). The water
drain valve was closed when steaM started to bellow out of
it. The rotational speed was measured with a Smiths Haad
Tachometer (11[04el ATH7,,:f: 0.5% aecW?acy).. Between :minute
:
number four and six the condensate was colleeted ~d weighted.
The 8te~ and eondensate temperatures were eaehread ~ee
different times. When the batch temperature reached 80-90 0 C
the s team was shut off and the Hater drain opeBed.
CGolfmg water was then turned OB and set at about 95 ~epeent
The
of' the rotometer flow rate. Tke speed 1-J'as also mea..::rured
twiee more aRd water floH rate H'as checked periodically ..
When the batch temperature was e@oled to 25-30 0 C the cooling
91
water was turned o~~
and the jaeket drained.
The s trip chart f'rom. a typical run is shovm il'!!. Figu.:ve
4-5.. During hl~ heating cycle the wall temperature is higher

tkaJ!l the bateh and. during; the eooling cycle it is lower.. A
ti:m.e interval sf' two, f'erur:/ or six minutes is selected f'rom
the heating cyele ~d from the eo@li~ cycle and the data
93
used to eale~late
a heat traasf'er eoef'f'icient. The ~0rtions
I
selectecl. are these irTitk the s:m.00th.est set Elf temperature
}3oints..
Tlae length (£)f th.e time interval is selected to give
@
a 10-20 C batch temperature change.
A new run wag usually started shortly after the f'~ish
of the prece9-ing z:tm.. On th.e f'ourtJa run wi th ~ particular
o
in~eller th.e batch was cooled to ~O-25 C, the vessel lid
removed and a new impeller iBstalled.. For fluids other tham
water a sample was takeR to assure the fluia's 'rheological
pr@])erties were remaining eonsta1!l.t..
(For glycerine me
densi ty 'V-TaS cheeked) Thte previous sample was returned to
the vessel to mailataim the fluici!. level..
Tke flai@!. level
was checked aaQ the series of power data taken and the lid
re])laeed.
Then f'0Ul' heating r~s were taken as above and
the cycle repeated until 44 runs using the 11 impellers
For water the h.eating cycle took about ei~t ~utes
and the cooling cycle about 16 gi vin~ a tciltal epera t~ time
of about 24 miNutes. The actual tiMe required f'or a cycle
was about 30 minutes since time vTaS required to drain the
jacket, reset the reeorCiler" take €lata, and turn valves.
The t~e required to make a run with tae more vise0us fluids

94-
was about 40-45 ndmutes ..
Tke impeller speed r~ge was limited both at the IGwer
~d upperspee~s.. The motor itself eould not operate well
below 75 RPM and thus this limited the range.. Often the
lewest speed l!t:sed was considerably ab0Te 75 RPM, however,
beeause lower speeds did not mix the fluid thoroughly and
the hot fluid would stratify at the tep of the bateh.. If
there "ras evidence 0f ineemplete mixing (baton temperatu::t"e
po~ts not on same sm00th e~e) the data taken were dis-
The great~st speed used was also l~ited.. The viscosity
data for tae non-Newtomians was limited te sheap
rates belbw 4zr:~1AX/n where NMAX is 600 RPM, the highest
speed of the v~se0meter. Aceording to Metzmerts results the
shear ~ afl agitated vessel is 11 .. 5 N where N is the RPM at
the impeller.. Smce 4 7r is fairly close to 11 .. 5 the maxi:m.u.nt
rotational speed which eould be used, without exeeediEg the
above shear rate" is lirrl ted to 600-700 RPr-1 ..
The motor and power supply lLmited the top speed
attainable for the very viscous fluids because the power
output of the system vIas exceeded bef'ore the larger impellers
reached 600 RPM ..
Because of these limitations the a.m.otm.t of data.

95
eolleeted r@F the 0.24 ]?ereeRt CarbC'Jpol solution is smae-
1cJhat less than for the ~th$r solutioRs. The mixing quality
of the small impellers was so ~oor
that ma~ gave only one
@1:' even zero acceptable runs. Tae la.r~er il'ltpellers exceeded
the pmJer out]>ut of the agi tatio:rn. system and bl.ew the fuse.
CALCULATIONS
Caleulati0u of Heat Transfer Rate
, _ ;,'',
The net heat transfer rate, qNET' the rate that the
heat is being transfe>pe

96
vThere N is in rev./sec ..
and S is measured in po1..mds.
The heat equivalent, qlvI' of this pOvJer input can be calculated
by multiplying by the proper conversion factor ..
1.286 x 10- 3 Btu = 1 ft. Ib ..
60 sec .. "" 1 min.
Therefore
:: 1.286 x 10-3 P (60)
!'!: 7.72 x 10- 2 P (4-5
Hhere qr1 is measured in Btu/min. and the pOHer is expressed
in ft. Ibs./sec.
The rate of heat transfer into the batch of fluid,
Ql-2' is measured by the fluid's gain in heat content per
unit time.
ql-2 :: HOp dTjdt (4-6
ql-2 is expressed in Btu/min. if
\1 is the 'vJeight of the batch measured in pounds
T
t
is the batch temperature in of
is time in minutes
The net heat transfer rate in the heating cycle is
(L~-7
In the cooling cycle the mech~Ylical
heat as "'Jell as the
sensible heat must be transfered th.-rough the Hall and

97
The heat transfer coefficient, h, can be calculated
from
(~--9
where A is the area for the heat transfer
6T s _ b is the temperature drop between the wall surface
and the batch.
Therefore h = qNET/ A b. TS-b (4-10
ROv-JeVer,6T s _b cannot be calculated since the I'Jall temperature
measured is not the surface temperature but the average temperature
of a 0 .. oL~ inch thicknes 3 of the "t-Jall next to the
surface.
If the temperature drop across the wall is assumed
linear-l:- this average temperature is also the temperature of
a point 0.02 inches from the surface.
For this condition
~TI,.J-b
=-----
l/h +L/kw
(L~-ll
where 6. Ti.J-b is the api tlunetic mean temperature drop between
the point 0.02 inches in the 1-Jall and the batch.
L
k",r
is the thickness of the metal resistance.
is the thermal conductivity of the metal wall.
is the su~
of the heat transfer resistances.
If equation Ll--ll is rewritten fop the resistance of the i-Jall
above it becomes
-It-
Because the vessel is not operating under steady state conditions
the temperature drop is not quite linear. The error
in the anSlrJeI' Has estimated to be betHeen 0 .. 25 and 0.75%.

88
ql\fETI A = 6 T \--T -s
L/kw
(1+-12
1.Jhere l:l T"'I_S is the temperature difference bet1tJeen the
measured point in the wall and the unkn01~
surface temperaturee
If it is assumed that the wall resistance, L/~v'
is
negligible one could calculate the batch film coefricient
using
h' .,. ql-TET
A6T 1 -J_b
(4-13
hf can be calculated since all the variables can be measured
or calcula ted.
If equations 4-9 and 4-12 are equated~Ts_b ~he
unknown
variable in equation 4-10 ,can be calculated •
b,T _ s b
l/b_
III
.6Tw_b
l/h +L!kw
and
b,T s
_ b = .6.T w _ b
l+h L/lt w (4-15
Substituting 6T s _ b into equation L-1-- 1 0
(4-10
+ hL)
~r (4-16
The group in the first set of parenthesis is equal to h'

and if' it is assumed that h' is almost equal to h equation
4-16 can be written
h = hI (1 + h Y L/kw) (4-17
hI is calculated from equation ~--13.
L
is the average distance of the ther.nlocouple junction
from the surface ~
0.02 inches = 0.001667 feet.
y~ is the thermal conductivity of' 316 stainless steel
Substituting the values for L and kw
(286)
h = h' (1 + 0.0001774 hI)
Apparent Vis~2sity
of' the Batch
The apparent viscosity of the batch is needed in the
Reynolds nilluber, Prandtl number, and viscosity ratio. It
can be calculated using equation 2-25.
(2-25
The apparent viscosity is expressed in Ib .. /sec. f't if' K is
expressed in Ib./ft. sec. n and N is expressed in rev. per.
second ..
The apparent viscosity of' the batch could also be expressed
(4-19
based on the theoretical 8.-l1alysis d:i.scussed in Chapte,;,s{~~,Wjo0
\i".2t~;

I {)D
The generalized Reynolds n~mber, NR~' is expressed as
N t D a 2 -r\T (.)
Re:: 1, I
(2-22
a::A
Jia
where Da is the agitator diameter expressed in feet.
N
is the rotational speed of the impeller expressed
in rev./sec.
P is the fluid density expressed in Ibsom/ft.3.
jUa is the apparent viscosity expressed in Ibsf/seco ft.
as calculated by equation 2-25a.
A more theoretical Reynolds number can be calculated
using the apparent viscosity, #d:, defined by equation 1.~-19.
In this case
(4-20
Generalized Prandtl Number
The generalized Pr8..c'1.dtl number, N pl !.' is
(4-21
Hhere C p is the heat capacity of the fluid.
k
is the thermal conductivity of the fluid.
1>Jhere C p
is expressed in Btu .. /l"bm°F •
fia is expressed in Ibf/ft .. sec ..
k is expressed in Btu/ft 2 OF sec./ft.

101
f1'f'.'ldtl nvnber is def:Lnod
U~-22
~iven in Ap~endi~ B.
U30Cl. 8.1'0 i1'c.:111

02.
CHAPTER !2.
RESUI,TS
Many heat transfer runs 1,\fere made '\vith water in the
vessel in order to gain familiarity l..ri th the equipment and
to obtain enough information to formulate the program to
be fol101,-led with the non-Nelvtonian fluids e
To be more
specific, 319 data points ,,,ere obtained using the many
i...mpellers ,listed in Chapter ~_..
163 of these points 1,..Jere
not used for evaluating the constants of the correlations
because the impellers "Jere not at the standard posi tions
listed in Table 5-1. These data, summarized in Table 5-2,
provided much qualitative and quantitative information
about the "Hall temperature, the effect of i...mpeller position,
and the impeller geometry ..
156 of the "\..Jater data points 1-Jere measured at the impeller
heights listed in Table 5-1.
These data, in addition
to 297 data points obtained with glycerine and Carbopol
solutions, "t-Jere used in evaluating constants for the correlations
discussed later in this chapter.

03
TABLE 5-1
INPELLER POSITIONS USED IN TIm i'lAJOR
PORTION OF THE THESIS
Anchor 5 tf clearance HelHL
:: 0.261
Paddle 7 1l center height HeH/HL ::: 0.378
Propeller lOll clearance EelHL = 0" 5}~.o
Turbine 7" center height ECH/EL :: 0.378
Note: At 7 11 center heiGht the impeller is at
1/3 the fluid height and about 1/2 the heat
transfer surface.
t
CLEAR.ANCE
t
f
CENTER I-IEIGI-IT
j

01
TABLE 5-2
sutn~U{Y
OF ADDITIONAL DATA POINTS
HEAE\URED IN THE PRELD1INARY STUDY OF HEAT
TRANSFER TO lrJATER
}}upe lle,r.= Type
Number of Data Points
Anchor
Paddle
Propeller
Reversible Pitch Paddle
Turbines - Disk & Vane - 6 Blades
Turbines - Open - 6 Straight Blades
Turbines - Open - 6 Curved Blades
Total
8
87
24
10
16
10
8
163

lOS
RESULTS:
HEATING AND COOLING vlATER
WALL TEMPERATURE
In all of the batch heat transfel"" Hork to date the
wall temperature has been assumed to be constant over the
entire heat transfer surface at anyone time. The investigators
1vho have measured the vJa11 temperature have done
so only at one point and thus have not confirmed or contradicted
this assumption.
The equipment used in this study
vJaS designed 8.-11.d
constructed 1

108
the batch than the other ticJO thermocouples.
At high iropeller
speeds, the wall temperature became relatively constant
over the whole surface.
It was felt that these data sh~wed
that the local heat
trruLsfer coefficients vary from point to point in the vessel.
In those portions of the vessel v!hich V·Jere best agitated
the heat was conducted from the wall at a faster rate than
in the poorly agitated regions.
Considering a unit area of the wall for any portion of
the vessel the ratio of the driving force to the resistance
is a constant for each of the resistances in series. Thus,.
negle cting the heat capacity of the l

neglecting the heat capaci ty of the 1"all, mus t be transferred
th..rough the wall..
Thus the value of ATs-0/ki.l
must equal Ll.Ts_Yl/h. hm and L/lrw are constant over the
H"hole heat transfer surface and the overall driving force,
~To' is also constant.. Thus h is greater in a well
agitated portion than in a poorly-agitated portion the total
resistance to heat flov! in the former portion l-Jill be less
than in the latter, giving rise to a greater heat flQX in
the well-agitated region.
Since the heat flux is higher in the v.iell-agi tated
regions, the ratio,6Ts-IL/ktl' in that region must be
greater than in the poo:r'ly-agi tated l"egions.
Thus the
driving force across the 1Ajall in the v-rell-agi tated regions
is Greater than in the poorly -agi tated regions..
This phenomena
(Nas manifested by the Hall s1..u"face being closer to the
batch temperature in the \.Jell-agi tated regions.
Experimentally it was found that by proper location of
the impeller the differences in wall temperature could be
virtually eliminated, even at 10VI impeller speeds.
These
positions, surmnarized in Table 5-1, probably gave more
uniform agitation.
It is interesting to note that the Optinlum
posi tion for the paddles and turbines is at the level vJhere
about one half of the heat transfer surface is above and one
half beloH the impeller.
The propeller, v-d th its large axial
flow component had to be positioned somewhat higher. These

108
optimum impeller heights were used in all the subsequent
1.Jork; hO'IJ.!6ver, '.Ihen the more viscous fluids ,.rere in the
vessel the wall temperature differences could not be
eliminated ..
Impeller fIeight
In addition to af:fecting the uniformity of \-1all tem£)­
ex'ature, the impeller height also influenced the heat
trans:fer rate. In general, the greater the impeller distance
from the vessel bottom" the greater the heat trans:fer rate
(1r-Jithin the limits tested, up to 1/2 the vessel height) ..
This phenomenon is pl""obably closely related to the large
wall temperature variations which are present Hhen the
Lmpeller is very close to the bottom of the vessel, (ie. as
the impeller is raised, the agitation of the batch is more
uni:form and thus the wall temperature variations are reduced
and the heat transfer rates increased).
Since the amount of data measuring these effects is
limited the results are only qualitative. They are shown
graphically for the anchor, propeller" and turbine in
Figures 5-1, 2 and 3.
As can be seen on these curves, a
two inch vertical displacement of the impeller changes the
heat transfer coefficient by almost ten percent ..
There 1.

09

10
I r
"'" , •• ,'., "",' """", .... ," 'J : : :::::::
. t,""~r)"'" '::. :::;.~.;,:.,.. :,:,~I.tj .. ii !::'~".':•.
i,;.',!:i!:,',:",
:. .!"IC.
:::l, .. '.i':',;,:;.:,1,;,:,I, ";::: ::::Ii::::::::;::; "., .. ,:::::.:::: ::: ::::':--:,:>::, ,r: ::::,:::-::'.
.. ,!;;,~, .. :,:l".:.:;,,:, i.i, ::;: ::,,:'1' ::::::: ," : ; ;i~l~:~: ':::, """ ""''',' "., '" .'''' .'
" I' ": .. , ... "', .. :""....:. ::1:,:::: ::::::: ':::-:'11:::':::::: ":::1::::!!;'1
:~)!:;j;~\::::i:: :,:;:::': '!:::.'.,::,::.::::,.:::":::::h::'.:,:,:'.:,.,:::::.::.,::. :::::::: :::':::::, ' .
I:"~ : ~ : !:; ~~: 1, ;,1 :,' :,r:, : I"~ :,':, .X,':" :,: ',; ;,': :,': , I····' , ... r " , . ; :: . ,,::,' ',' :: ..!':: I .. I· I
! 11'(. .....,,,.. ",. ,.Ij., ::/:: ::::>' , .... " ," ., . ;
o,,~' '~I:'~'::;li; I::: •••• .••• ...., .. . .... ........... .., ·.rr· ..... : .•.. -:;'
,.. .. " ...... , .. "".,\, , .. ,' :

1/
for:m.ed using:
(a all the paddle data including 241 data points
at twelve different positions; 154 of these
points vJere for one height ..
(b tHO data points for each paddle height.
The i'irst test used all the data available but may have been
biased since 64 percent of th.e data was for one height value
and some heights were represented by only two data points.
Rence the second set of data points was tested using the
same amount of data for each point.
In the first test (all available data) the Nusselt
. (/) 0.32
number was i'ound to be a i'unctlon of HCR HL
where
HCR is the height of the center of the impeller above the
vessel floor and RL is the liquid height..
In the second
test the Nussel t number ·Has found to be a function of
(H CH /H L )O.45. ~lliile neither test is entirely satisfactory
because of the data limitations, the exponent of this impeller
height ratio can be estimated to be somEH-Jhere betl.reen
these two values, or rou&hly 0.4. It is interesting to note
that this effect, not previously studied, is more important
than the Prandtl number or viscosity ratio for equal changes
of the variables.
CORRELATIONS
The major portion of the data collected in tl1.is thesis
(453 data points) 11as used to evaluate the constants for

112
correlations for the prediction of batch side heat transfer
coefficients. These data are summarized in Table 5-3. Two
general types of correlations were evaluated, those based
on the dDJlensional analysis developed in Chapter 3, and
those which are semi-emperical alterations of the present
correlation for Nel,rtonian fluids ..
FO'ur different types of impellers '(-Jere used in this
study: anchor, paddle, propeller, and turbine. Since tl1.e
geometry and flovl patterns for each L.'1lpeller may be different,
the constants of any correlations tested Her'e evaluated
separately for each impeller type.
Only one anchor
agitator was used and therefore the effects of impeller
diameter and ,,,,idth could not be evaluated for the anchor ..
The propellers were geometrically similar and therefore
only the diameter effect was measured.
Results of Dimensional Analysis
The dimensional analysis of Chapter 3 provided
(~~~ra.) a. b )C(: d e
AlMI~C~~ fl!p/t" (~) (g: :;) ~ (3-8.0
as an equation 1:Jhich characterizes the batch heat transfer
system.
The constants of this correlation\labeled correlation
A) Here evaluated and are presented in Table 5-4.
correIa tion ",ri th its constants Has then used to calculate
a "predicted Nusselt number" for each of the data pOints.
The percentage error
The

3
Smll~L4.RY
OF DATA POINTS USED
IN CORRELATIONS
.
Number of Data Points
_Flov.r Behavior Index ::: 1 .. 0
Impel:}..er Type
0 .. 69
0 .. 36 Total
Anchor
16
8
8
7
39
Paddle
Propeller
Turbine
l51~
26
48
48
15
16
~L6
7
15
29
6
277
54
83
TOTAL
87
76
-----------------------------------------~--~--~~--------

TABLE 5 - 4
Correlation Constants
Average Errors
LVJPELLER
C a b c d e p.=lD 0.69 O.I.d 0.)6 O1iet'all
TYPE
..
-~}
ANCHOR 5.52 0.15 0.34
- -.--
.10 6.63 15.6 14.0 22.0 12.7
PADDLE 12.59 0.15 0.31 -.51 0.41 ),31 10.8 8.9 20.1 19.4 12.9
PROPELLER 6.62 0.13 0.32 -.48
-
).69 12.6 8.5 15.1 20.7 12.5
TURBINE 15.16 0.12 0.30 -.14 0.47 P.30 10.7 10.6 20.9 20.7 13.0
* Line under number indicates value not significantly di~ferent from zero as determined
by t test (47),

IS
il'tE"?SUI2£D ~a- PRe:DtCr~o
M..E'"-9s l/( RED Al'NU
~t(
I( 100
(5-2
was calculated for each data point. The average error for
each condition (impeller type and flov-r behavior index) was
calculated. The average error is the aI.'ithrn.etic average
of the absolute values of the percentage errors.
/;{
Average Error ;::;
l2/ %t:RROR/
(5-3
Correlation A is based on a model which very simply
described the flow patterns developed by a marine propeller
in a baffled vessel. The flow patterns developed by paddles,
turbines or anchors are slightly different, but the same
correlation was used to correlate all the data. Correlation
A has only one empirical constant for the measurement of
the Reynolds and Prandtl number effects. To empirically
correct for the oversimplification of the flo\>T model Correlations
B and C were tried. Correlation B has two empirical
constan ts for the Reynolds and Prandtl number effects lilhile
Correlation C has three. Correlation B is
NK({= C N?e %~~;~;)t~n~:t~r.;nf (5-4
and correlatioz.c is )
_ l%tf~tb he, if e I J
~tI- C ~Re Nf'J[ (-~)~ (f1J ~
The calculated constants and average errors are
(5-5
given in

1/6
Table 5-5 and 5-6.
A measure of the significance of the difference betv-reen
tlfJO correlations is determined by using the F test
~'Ilhere
F is the ratio of the variances of the two correlations
(55). The variance is the sum of the squares of the difference
between the measured ~nd
predicted values of the dependent
variable. The significance of the F is dependent
upon the degrees of freedom -of each of the tl-JO variances ..
The number of degrees of freedom is equal to the number of
data points minus the nmnber of constants calculated from
the data. Table 5-7 lists the variances for these correlations.
In testing the significance between correlations A and
C for the anchor agitator~F
is evaluated as follows.
Correlation
Variance
Number of
Data Po.ints
Number of
Constants
Degrees
of Freedom
A
C
963,790 39
537,312 39
4
6
35
33
F35, 33 = ~632790 = 1.80
37,312
(5-6
A table of values for the F distribution ShOHS that for F
to be significant at the 80% limit for 35 and 33 degrees of
freedom,F must be greater than 1.57.. At the 90% limit F
must be greater than 1 .. 79 and at the 95% limit F must be

Average
TABLE 5 - 5
CORRELATION B
f! (a/n+l) It Ii b c f
NNu '" C(N Re ) (N Re Npr) (K/~) (Dt/Da)d(W a /Da)8n
H1PELLER Correlation Constants Errors
. ,~.
TYPE C a b c d e f n-1.0 0.69 0.1.13 0.36 Overall
ANCHOR 0.48 0.74 0.32 0.35 -0.14· 9.6 12.3 9.2 22.1 12.3
- -
PADDLE 2.41 0.73 0.27 0.31 -0.h5 0.h5 0.30 9.4 6.5 lCi.5 19.4 11.4
-.
PROPELLER 0.S4 0.77 0.29 0.32 -0.34 0.68 6.8 8.2 11.1 21.2 9.4
TURBINE 3.35 0.78 0.23 0.31 -0.09*
0.56 0.27 8.5 10.1 19.5 21.3 11.4
-
* See Table 5 - 4

TABLE S - 6
IMPELLER Correlation Constants Average Errors
TYPE C a b c d e f g n=1.0 0.69 0.1.1.3 0.36 Overall
ANCHOR 0.56 1.43 _0.04 1 1- 0.30 0.34 0.54 6.8 S.l 10 .. 7 18. )-+
- -
9.3
PADDLE 2.51 0.96 O.lS 0.26 0.31 -0.46 0.46 0.56 9.4 5.1 17.8 18.9 11.1
-~
PROPELLER 0.55 1.28 0.04 0.30 0.32 -0.40 1.32 7.0 S.4 9.6 20.0
--
8.3
-
.){.
.>
TURBINE 3.57 1.25 0.002" 0.24 0.30 -0.13' 0.61 0.78 8.9 6.S 17.6 19.7 10.5
--
* See Table 5 - 4

19
TABLE 2 - 1
VARIANCES FOR CORRELATIONS
At Rand C
Variances
n- 1.0 ,0.69 i 0.43 0.36 I Overall
Correlation A
I
Anchor 434,764 h49,515 22,762 56,749 963,790
Paddle 12,020,092 530,486 277~796 172.\'211 13,000,5135
Propeller 888,897 100,568 19,995 23,245 1,032 1 705
Turbine L,175,334 27L,633 89,7h3 30,292 4,570,002
Correlation B
Anchor- 1,089,312 291,553 9,126 45,353 1,435.345
Paddle 12,333,246 344,645 232,009 163$478 13,07),)78
Propeller 1,030,u64 59,828 12,721 19 9 600 1,122,613
Turbine 3,L8L,242 216,798 77,7)6 26,750 3,F.05.526
Correlation C
Anchor 42L,58L 32,989 28,002 51,737 537,312
Paddle 12,505,916 209,29L 211,802 179,:'03 1),106,515
Propeller 808~803 10,904 7,442 20,7)6 E7L,685
Turbine 3,641,172 - 79,108 67,894 35,405 3,823,579

120
greater than 2.0. In this case therefore there is a 90%
probability that the difference in variance between correlation
A ~nd
C is significant. Thus correlation C is a better
fit for the anchor data.
It may be seen from this example that in order for a
correlation to be significantly better than another the ratio
of the variances must be about 1 • .5 or gl"eatel", depending upon
the degrees of freedom and choice of probability limits
desired.. Comparison of the variances listed in Table 5-7
shows that the above eXELmple was the only case in Hhich one
correlation 1-laS significantly better than another for all of
the fluids tested. Thus, except for the anchor agitator,
the three correlations fit the data equally v.Jell..
It l

TABLE 5 - 8
NNu '" C(N~e)a
CORRELATION D
(Npr)b (K/Kw)C (Dt/Da)d (Wa/Da)e
IMPELLER Correlation Constants Average Errors
TYPE C a b c d e n= l.0 0.69 0.43 0.36 Overall
ltNCHOR 0.45 0.68 0.35 0.37 10.9 23.0 17.4 22.7 16 .. 9
- -
PADDLE 1.94 0.64 0.27 0.31 -0.40 0.42 9.2 13.4 22.1 22.3 13e4
PROPELLER 0.!.~6 0.69 0.27 0.32 -0.23 11.4 12.3 2B.h 35.5 16.5
TURBINE 2.39 0.63 0.24 0.31 -0.06*
-
O~
O.hOn B.3 15.8 22.9 23.7 13.1
.,l- See Table 5 - 4
-1\)
--

12.2

23
the Nusselt namber predicted using Correlation D ~or
the
propeller data.
The line vIi th slope equal to unity represents
a per~ect
fit of the data. As can be seen the more pseudoplastic
fluids seem to be represented by lines with a greater
slope.
Similar plots for the other impellers shm-l the same
trend. The dimensional analysis of Chapter 3 suggests using
a variable exponent for the Reynolds number and an additional
par8JJ1eter, n.
Correlation D Has thus modified to give
Correlation E ..
NNU" CNR€ %,,' NpJt h{::r(g:r(~:run F (5-7
1ne constants and average errors are presented in Table 5-9.
The measured Nusselt TI1. .. lluber for the propeller data versus
the predicted Nusselt number is plotted in Figure 5-5. Comparison
o~
Table 5-8 and 5-9 and Figures 5-4 and 5-5, shows
that correlation E fits the experimental data better than correlation
D 1"i th the pseudoplastic fluids gaining the most
improvement ..
Treating each ~luid
separately sho"t-led exponent of the
viscosity correction varied with 1/nO.75 . This modification
was incorporated into correlation F:
A I = eN I
0./1(1{ A
I 6 ( j( )C/ n o.75( D2-)d(ZlIa...)€
IV IVV' Re IVp..h KrP Da DC(..m (5-8
The consta.nts and average errors are presented in Table
5-10.. Comparison of the average errors shmoJs that correlation
F is a might improvement over correlation E.
f

TABLE 5 - 9
CORRELATION E
t (a/n +1) ! b d e f
NNu '" C(N Re ) (Npr) (K/Ki.v)C(Dt/Da) (WalDa) n
IMPELLER Correlation Constants Average Errors
TYPE C a b c d e f n-l.O 0.69 0.43 0.36 Overall
ANCHOR 0.47 1.36 0.32 0.3h 1.53 6.9 S.3 10.3 18.1-L
- -
9.3
PADDLE 3.05 1.23 0.25 0.30 -o.hS 0.h7 1.83 9.6 5.7 18.0 19.3 .3
PROPELLER 0.71 1.34 0.29 0.33 -0.58 2.55 10.6 h.l 12.0 19.3 10.0
TURBI1TE 3.47 1.26 0.2)-L 0.30
-
-- --
-~
-0.12 0.6d~ 1.85 8.9 6.8 17.8 19.8 10.6
10.8
* See Table .5 - 4

'
< .' •••• •••• .," ••••
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~ .
/zs
. "-'; ." '.,
. ..... ,
.... "'::l:"
':::r .
..
. . .. .
. 1
~+~~~~~.~. ~~.~. ~~~~~'~'~~-+~'+'~~'~~~--+~~'t-::--
.._, .:: :::: :::: . :j' •. i I
. . . ....... • '--1
~~~~'~:~'~'1'~~--~~~~'~'~"~~~~'~"+' .;:~~:~I~::4:~;;~::r.;~· ~-+·~·~·~.~ .. ~.~~I
,. .......' ........ :... " .. ' 1:... ...,
:::.:: :~ii:-:·::.l::::::::: i::::::::b( ,": :.::iX:: i:i. :,:: .:::: .. , .... , ;1>:-::.:;:~~::1~~i: :;;; ,:: ... j'
.....
'
' '
'.5
,
':. :'.:: '.:'.' ;' .. ;~ :'.:: .... :: ',,:!. ,':'.: .1·.,,:: :' ... :; .. -,
.. •. : .. ::., ... ::., :•.•.
.. ·;i .. .,:: :~ ".,~ "::.;~.::i·ft~.~ :,.::.~
",t.;~_
,j;.'i: :: ... ... ,: ;':' ... :! ... ,.,,: ..
..•.. :; :
:. ..::
, .... :::;.: .. ••• , ,:.: .,';; ',.;:.' ',:' .'.:: .. :: ;: •. •• :; •. .· :i .. : : : ; l ~;; .... ::.:.:.: .. :~.~ .:.:' ".:' .':' ;...• :
.:~ ·':·i:
:l&!l'~ ,:>EL;
.. ::. :;:.:;i;l:!:ll···~:::j !
.. U(2;: .!j: I;·J.: ::.... :~l:
.. :: .:: .... :;
~ : ~ j l; i i 1 l!lTfllW~:ij1m~Uj··~ TWill: }.l.ll\;·IV :::: U:~ ~~I;j;·.; ; ~: ~:;:;:
:; .'. :'. .:' .:' '.: .,: .:, .':' .:' . 1 ·:t
...... -,
· . ...... .
·
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'" ¥+.­
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.........

TABLE 5 - 10
IMPELLER Correlation Constants Average Errors
TYPE C a b c d e f n""LO 0.69 O.Ld 0.36 Overall
ANCHOR 0.146 L37 0.32 0.32 1.55 6.7 7.5 9.).+ 114.0 8.7
- -
PADDLE 3.06 L23 0.25 0.28 -0.148 0.b,7 L85 9.5 5.5 17 .6 16.0 10.8
i
PROPELLER 0.62 L36 0.30 0.32 -0.55
-
2.59 10.2 u.S 9.7 12.8 8.9
TURBTNE 3.27 1.27
>
0.214 0.29 -0.12 0.58 1.88
--
8.8 6.5 15.9 16.5 10.0
--
10.2
* See Table 5 - 14

12
7
In order to simplif'y the correlation some1

TABLE 5 - 11
CORRELATION
G
(1.30/61+1)) (0.28) (0.30/n O . 75 ) (-0.50) (0.50)
NNu '" C (N~e) (N~r) (K/Kw) (Dt/Da) (Wa/Da) n ta
H1PELLER Correlation Constants Average Errors
TYPE C a n"'1.0 0.69 0.43 0.36 Overall I
ANCHOR 0.74 lou3 6.9 8.0 8.5 lu.7 8.9
PADDLE 2.00 1.96 10.0 6.0 17.1 15.8 11.1
PROPELLER 0.86 2.51 10.4 3.8 11.1 13.5 9.0
TURBINE 3.09 2.06 14.2 7.3 10.3 14.8 12.2
--
10.8
Note: For Anchor (Dt/Da)b and (Wa/Da)C are not used.
For Propeller (Wa/Da)C is not used.

129
TABLE 5 ... 12
Correlation D
~ - ~ -
Variances
VARIANCES FOR CORRELArrIONS
~ """,,",'" - - .
D, ,E" F and G
n= 1.0 0 .. 69 0.36 Overall
Anchor l~99,968 816,612 85,009 65,685 1,l~67,2711_
Paddle 13,033,313 1,020,554 350,049 149,878 14,553,794
Propeller 2,378,861 183,678 27,797 33,224 2,623,560
Turbine 3,523,715 498,lW-4 98,968 18,969 4,ll~0,096
Correlation E
''''' $_.' ~ .. _ ._, '1 t 10'_
Anchor
Paddle
Propeller
Turbine
462,132
11,955,325
825,607
3,626,963
64,505 23,365 L~8,108 598,110
171,730 216,953 197,267 12,541,275
9,396 8,560 21,303 864,866
89,211 68,535 35,171 3,819,880
Correlation F
.... ..
Anchor
Paddle
Propeller
Turbine
12,079,618
1,083,141
3,588,125
6.5,386 38,168 28,769 599,806
179,633 215,336 149,272 12,623,859
17,007 4,485 12,991 1,117,624
83,508 51,796 23,842 3,747,271
Correlation G
Anchor 469,778
Paddle 14,791,009
Propeller 941,619
Turbine 6,929,397
99,403 27,708 30,913 627,802
182,~_00 209,375 142,020 15,32l~,804
11,548 5,831 14,168 973,166
~-7,319 21,345 18,086 7,016,1~-7

1.30
of the substantial improvement for the anchor and propeller
correlation E is considered to be a better correlation than
D.
In comparison of correlation E with F there was no significant
improvement for any impeller if all the fluids are
considered.
However, there is significant improvement of
fi t for the anchor and propeller 1

J 31
CRAPTER 6
DISCUSSTON OF RESULTS
Experimental Data
The errors in the measurement of the exper:tmen tal data
1

1.3 2.
The probable error in the calculated heat transfer coefficient
was calculated for a typical rQn (Run 264 for
heating of glycerine) using the method described by Daniels
( 50). The values of the experimental data and the associated
errors are:
Area
6.20 ± 0.04 ft 2
Batch ~\feight
Initial Batch
117.7 ± 0 .. 7 Ibs.
Temperature 59.2 ± 003 °c
Final Batch Temperature 68.2 ± 0.3 °c
Initial Wall Temperature 89.5 ± 7.5 °c
Final Wall Temperature 95.5 ± 7.5 °c
Heat Capacity 0.64L~±' .. 019 Btu/lboF
The heat transfer coefficient was calculated to be 115~
22.1 (or.±. 19 .. 2 percent .. ) The probable error for this run
vJas thus approximately ±.20 percent. This value 1,

133
producibility was about ± 2 percent and for heating about
± 4 .. 5 percent.. ~Jhile this data may not be statistically
significant it roay give some idea of the reproducibility of
the present data.
The merits of calculating the heat transfer rate from
the temperature rise of the batch and the heat transfer
coefficient using wall thermocouples have been thoroughly
discussed in Chapter 2.
The Ne1.,.Jtonian fluid heat transfer data Has compared
to the currently accepted correlations in the literature.
The correlation for anchor agitators developed by BrOi"Jil et
13.1. (32) i>Jas used to calculate predicted Nussel t numbers
for the anchor data developed in this thesis. The actual
measured Nusselt numbers are compared with the predicted Nusselt
numbers in Figure 6-1.
Most of the data points show a good
comparison although on a fe1>J points for the heating of glycerine
the measured Nusselt nU111bers are much greater than predicted.
The arithmetic average deviation of all the points is ± 16 .. 6
percent.. The one factor ""Thich would cause the larger deviations
in the glycerine data ",muld be Bro",m's use of 0 .. 14.
for the viscosity ratio exponent.
The use of a higher exponent
as suggested by Uhl (194) Hould probably reduce the
error greatly.
It must be noted here that Brown did not
measure the effect of viscosity but accepted Chilton's value
of 0.14.

134
.,;'
: :: :::: : ~ !~.
, " . .' ..
!inc 'ill
~.

.3S
The effect of using a 10"1 (0,,1.4-) exponent for the
viscosi ty ratio also increases the error 1"hen comparing the
eight inch by one inch paddle data (geometrically similar
to Chilton) with Chilton's (39) correlation. Comparing the
date to Chilton's equation there is an average error ofl:
16.3 percent. Uhl recalculated Chiltonts data and claLms
that the exponent of the viscosity ratio should be 0 .. 2.4-
instead of 0.14.
Using l;'hl! s modification of Chilton I s
equation there is an average deviation of± 11.1 percent
between the predicted and measured Nusselt numbers.
The
results are plotted in Figure 6-2.
The points are fairly
evenly distributed along the line of perfect agreement.
It ,,,ould be expected that the meaS1.U'ed values vJOuld be
about 10 to 20 percent above the predicted values since Chilton
did not use baffles. However, Chilton measL~ed
the
wall temperature at only one position, just opposite the
impeller. This '--Tould lead to a measured driving force l--Thich
lIms less than the actual value, causing the calculated
Husselt nu.mbers to be greater than they should be.
Naturally
the correlation based on this data would predict Nusselt
numbers which are too high.
The propeller data were compared w~th Brown's (32)
correlation and are plotted in FigLU'e 6-3. The average
deviation is 26 .. 9 percent and thus the fit is not very good.
ROV-lever, Brown t s correlation is only based on limited data,

T." ••••••• ,_ .....
/.3 6
S :.'
1 '
. "
st4-H:HD4f:S++bH++BF+-4+~~. ui-.J::-,-.a~~j~~'-~f4,t-~?:--Tt---~~1(c-,_~t--!4:+ ........... -+_."'7"" ~~--'-".;+..'~ ..:........
~ :L~~ ••.
........
. " ., .
. . .. .
; : ~
: : . : : ; : ~ :
• •• ~ t ' ••
" t"·
.... .... ~"-
, : ::;::' : : :: : : ::: :::: :::: .:: ~
:: :.
.:
-':~" ...
:;: :.'
........ ".
. ::: ::::1. . .,
C'U/LTO/V'J' £QUIITIofl/ (.3!3) MODIFIED BY Uhf (/94)
tfiHv = 0.36 NJ£e ~ IfIpl'e ~ (%'W) 0.:2""

13
7
.. ':!:
;:. : :
::,
• • . •. t" : : : . , : ::: ••..... : .. \
:! ~: ::::~ ::.L:: .. , ~:.:::, .:::.:.: :::: 'f:: "',... I
!Q I, II": ~j_l, ,:. ! I iL '),J1-, '_""j" , ' ,! '.! ___ ~ .. _. ,j I . ,i, .c!~."l,!.! ... , _ .!.~ I
100 1.5 2 2.5 3 4 ;) 6 7 8 9 1000 1.5 2 2.5 3 4 5 6 7 8 9 1 (

38
the cooling of nitration liquors at one speed, and although
it is the only correlation available for propellers its value
is limited ..
The turbine data '!,vere compared I-ll th the correlation of
Brooks and Su (30) and CUYrrrr.d.ngs and it/est (~-9)..
The results
are shown in Figure 6-4..
Compared Hith the correlation of
Brooks and Su there vias an average deviation of 27 percent,
1\1'i th the measured ]')Tussel t numbers being less than the predicted
values.
The largest errors are due to the glycerine
cooling runs and it is felt that these errors I-JQuld be
greatly reduced if the viscosity correction factor exponent
'

.3 9

140
The average deviation of the measured l\fusselt numbers
Hi ~h
the prediction of Cu..rrrmings and \e1est I s correlation is
19.5 percent 1'-1i th the measured values usually higher than
predicted. This is reasonable since the correlation is
based on data taken in an 1L.~baffled
vessel '\

11-1
of variables. A total of 616 data points were taken,
163 of which were used for screening the variables to
be studied and evaluating the effect of impeller height.
The remaining 453 data points were used to evaluate
the constants of the correlations presented in the previous
chapter..
Eleven different impellers representing the
fOl.ll'" major types in common practice 1..Jere used in collecting
the 4.53 points. The range of application is wide since
pseudoplastic as Hell as Newtonian fluids 1,rere used.
The
use of multiple-variable regression analysis Has a
valuable tool in reducing hcunan error and subjectiveness
in the calculation of the correlation constants.
The measurement of the wall temperature at three
different locations gave evidence of the considerable
difference in heat flux in diff'erent positions in the
vessel. Although the ef'fect was not quantitatively studied
it is the f'irst tLme it has been reported; and this opens
the door to a possibly fruitful field of' study.
It has
been shown that the variations in local heat transfer
rates can be minimized by proper location of' the impeller.
The vertical position of' the impeller Has shown to
have a large ef'fect on the Nusselt number in the range
studied, ie. f'or impeller height/liquid heie~t
ratios be-

42
tween 0.25 and 0.58. L~~l had reported ~n 18 percent difference
in Nusselt nu..l11bers for an impeller in hw different locations
a..D.d a fev1 authors had mentioned that hi'>.:her heat transf~r
rates Here achieved for certain impeller locations but the
effect had not been studied qua.nti ta ti vely.
The effect of
height variation may have a considerable signific8~ce
since
changes in the impeller height cause minimal if not neglirible
changes in pOHer requirements.
The model proposed in Chapter 3 results in a dLmensionless
equation which acclJ.rately characterizes the batch heat
transfer system as sh01~m by the good fi t achieved. Thus the
model itself may be inferred to be a fairly accurate portrayal
of the :mechanismof heat transfer in an agitated vessel.
To
be more specific~
the center core of tIle fluid is in turbulent
flm! Hi tll. thorough mixing of the fluj e3 in this region. In
addi tion to tlJrbulence in the impeller region, the impel10r
produces bulk fluid .flow, largely axial. This results in
fluid flov~
alon!:. the cylindrical heat tra..Ylsfer surface in
the vertical direction. At the wall surface the flu:td is
motionless.
There is a velocity gradient in the radial
direction. Heat is transferred across the stagnant fluid
layer at the Hall by conduction 8Jld is then transferred by
diffusion and bulk floH into the turbulent core.
TI'le controllinG
factor in the rate of heat transfer is thus a
stagnant layer at the Hall. An increase in the bulk rImA)"
rate through the eye of the impeller (by increasine; im-

LfJ
peller diameter, l,~idth,
or speed) causes an increase in
the velocity of the fluid near the lfJall..
This results in
greater momentlL111 transfer in the radial direction Itli th a
subsequent decrease in the thickness of t.c"I-J.e stagnant layer ..
Comparison of Correlations
* 1 .. w « ' p ... . _$ ",' -'1' 'M - -"-
The data was correlated by equations representing tvw
different approaches, theoretical and semi-empirical. The
best equation of each type 1~ill
be compared v,Ii th each other
later in this chapter, but first their common characteristics
v-rill be mentioned..
One characteristic is that they both revert
to the cornmonly accepted correlations :for NeHtonian
:fh:tids for the case of n equal to unity..
This is not the
case lvi th ma..ny correlations, an eXE'uuple being the correlation
of Blanchard and Chu (22) for the prediction of batch heat
trans:fer coefficients.
The accuracy of the cOl'"'relation in reproducing the experimental
data is very good, the average error for all :fluids
is in the ra..n8e of 9 to 14 percent Hi th the greatest average
deviation being :for the most pseudoplastic fluid in the range
of 13 to 20 percent. In no insta..nce is the average error
o:f the correlation in representing the data greater than the
error in the determination of the heat transfer coe:f:ficient.
Both the theoretical and semi-empirical correlations
are based on a more fundamental fO~Uldation
than are the
previous correlations :for the prediction of batch heat

144
transfer coefficients to non-Nel A ltonian fluids to
As mentioned
in Chapter 2 Blanchard's viscosi t-y ratio shol,rs a misunderst~nding
of the flow in an agitated vessel since he considers
the shear rate at the l,fall to approach infL""li ty 1.[hile in
actuality it~
is 101,f compared to the shear rates near the
impeller (127). The consistency term used by Sal~mone et
al .. (165), (m:gcKS n - l ) is valid for pipe flow (the "8 11 is
introduced du..ring the development of the equations for
fluid flm>! through conduits); hov.rever, the !lSlI does not
have any significance in a stirred vessel. The semiempirical
development in this thesis shows that the factor
11 .. 5 n - l in equation 2-25 has no fundamental basis but it
does successfully correlate the average shear rate with
the impeller speed and thus has empirical significance.
The correlations discussed progressed from a highly
theoretical correlation (Correlation A) to a highly empirical
correlation (Correlation G).
If the two extremes
are compared by the F test on the overall variances Correlation
A is as good as Correlation G for all impellers
except turbines. Correlation A is sig:..n.ificantly better
than Correlation G for turbines. Hm-rever, these results
are biased in favor of the theoretical equation because of
the large amount of Ne'lAJtonian fluid data, for v.Jhich Correlation
A is slightly better..
If each type of fluid for
each impeller is tested, COl"'rela tion G is significantly
better than Correlation A in five of the tv.Jelve non-Newtonian

11-5
fluid-1m.peller categories..
although not significp~tly
In three others it is better,
better at the 90% level. In
the remaining four categories the correlations have about
the same accuracy..
In the fO'llr Nevltonian fluid categories"
Correlation A is significa..ntly better than Correlation G
for the w.rbines only.
Thus the author believes that
Correlation G is to be recommended over Correlation A, so
far as predictive power is concerned.
Correlation C, a slightly modified form of the theoretical
Correlation A, in the previous chapter was sho~m
to
be the best of the three theoretically based correlations ..
If Correlations C and G are compared by the values of the
errors realized liJhen using them the hio equations are about
equal.
In general correlation C fits the data slightly better
than correlation G although the latter fits the data for n=
0 .. 36 somewhat better than does the former. Comparison of
the var:i,ances shows that there is significant improvement
for this fluid Hhile the remainder of the points are represented
equally 'Hell by ei ther correlation..
The improvement
in this one case is probably due to the variable exponent
on the consistency ratio.
Comparison of correlation C Hith correlation E elbninates
the improvement due to the variable exponent for the consistency
ratio and is a good method for comparing the tI.ro different
apparent viscos i ties..
Comparison of the average errOl'S and
variances shoHS that there :is no difference in the accuracy

16
of fit and it may t...herefore be concluded that bot.h. methods
can be used to characterize the apparent viscosity with equal
success ..
The use of the semi-empirical equation is some1tlhat
easier; because there are only tlNO constants, lNhich vary
from impeller to impeller.
Some of the constants in the
theoretical equation could be averaged but there are large
variations in the Reynolds nu..mber exponents vJhich would lead
to rather large errors if averaged.
It may be argued, h01;J'­
ever, that Hhether theT'e are tlNO or five constan"ts, one l'11"ill
probably have to look them up and thus the actual number
of constants is limnaterial.
The Correlation C has a distinct advantage over Correlation
G since it has a fundamental basis. The use of l/(n + 1)
as a factor in the exponent of the Reynolds number of the
semi-empirical equation has no fundamental basis. The use
of 1/nO.75 in the exponent of the consistency ratio was
purely empirical also.
It is thus the belief of the author
that Correlation C is the better of the two correlations
and is recommended for use.

147
COlllC LUSI ONS
1. The tBeoretieal m0ael proposed i~ ~apter 3 suecess~lly
eerrelates the heat transfer data.
2.. The use of Metzner! s apparent viseesity,A:: K (11 .. 5 N) (n-l),
can be used to successfully characterize the fluid behavi0r
of pC)'I-Jer law pseud0plastics being heated or eeeled
in an agitated vessel.
3. The Nusselt number for Newteni~ fluids ~d power law
pseudoplasties CaB be predicted by ~ 5
N/l/v == C NR~{Yr.m/+')+h) N;~ C(/f) (~) e r-r:tL
) /)1
w u " (E.-I)
where NRg aRd Np~ are calaula ted using ,~«.,. = KN • Th.e
constants vary with the impeller type and for the ~peller
height r~tios 'specified i~
Table 5-1 the values are:
C a b c d e f g
Anchor 0 .. 56 1 .. 43 -0 .. 04 0.30 0 .. 34 0 .. 54
Paddle 2.51 0.96 0.15 0.26 0.31 -0 .. 46 -0 .. 46 0.56
Propeller 0.55 1.28 0 .. 04 0 .. 30 0.32 -0.40 1.32
Turbine 3.57 1 .. 25 0 .. 002 0 .. 24 0.30 -0.13 0.61 0.78
4. For the specified heights the Nusselt number can also be
pr/l61:ic:ed
C b: 1
/1/ A/I/ fVR Alp-"'i € f( w LDa..! (bttl )
I (.3Ycot7V+ 1)) I 0. 28(1( )o.3ojm 1 (Dt 1-D..50;'W~J:: .v
1 . ( ~ )n-l
where N Re and Np~ are calculated using~ :: K 11.7N ..
The exponent 6f the Dt/D a
term is net applicable to tae
anchor agitator and ti~ exp~nent of· the WalDa term is
mot applicable to the anchor or propeller because there

148
'tvas insufficient data to evalua.te these constant.s ..
The value of C and a V'a:J!'Y with the impeller type and
c ..
Anchor 0 .. 74 1 .. 43
Paddle 2.00 1.96
Propeller 0.86 2.51
Turbine 3.09 2.06
5.. The above correlations predict the batch side heat
transfer coefficient lNi thin + 20 percent :for all pO't

149
REe Ol'ifHENDAT IONS
1.. The correlations given in the Conclusions should be
used ror the prediction or batch heat transfer coefficients
provided the situation has been covered by
the range of variables stUdied.
2. A thorough study should be made regarding the variations
or local heat tr~nsrer
rate and the variables arfectLng
the same ..
3. The range or the present study should be extended to
include unbarrled vessels and systems using coils as the
heat transrer surrace ..

50
A :::
Apr ...
B :::
C p
:::
CPr :::
D :::
TABLE OF NOIVJE1'l,CLATURE'
ENGLISH ALPHABET
----------~' . .
Heat Transfer Area
Constant in Prandtl eq. 2-18
Constant in Powell-Eyring equation
Heat capacity
Constant in Prandtl equation, eq. 2-18
Pipe or tube diameter
Da
:::
Dc ==
Impeller dim.~eter
Diameter of coil tubing.
DR
:::
Dia~eter
of coil helix
Dt ""
F =.
Vessel diameter
Statistical parameter
gc :::
Dj~ensional
(ft/sec. 2 )
conversion factor, 32.17 (lbm!lbr)
gz : Acceleration due to gravity in z direction
HC ::: Clearance betv.reen bottom of agi tator and vessel
bottom
H CH
::: Height of center of impeller (vertical direction),
above vessel bottom
HL ::: Height of liquid
HV = Depth of vortex (inches)
h ::: Average heat transfer coefficient of batch
lit = Pseudo heat transfer coefficient defined in eq. 4-13
hb ::: Height of bob or spindle of rotating cylinder viscometer
h f ::: Beat transfer coefficient of fouling material

lSI
:::
...
:::
Local heat transfer coefficient
Heat transfer coefficient of' jacket medium.
Conversion factor for mech&~ical to heat energy ~
2.39 x 10- 8 cal/erg
K
Fluid consistency index, pOi-ver lal-J equation
:::
=
::
=
::::
Oonstant in eq. 2-19
Fluid consistency index evaluated at wall temperature
Thermal conductivity of batch fluid
Therm~l
conductivity of the metal wall
Thickness of metal resistance
:::
Torque
=
Function of fluid consistency index, m ::::
m evaluated at l.rall temperature
K
8 n - l
Number of data points
N :::
:::
n ...
:::
Rotational speed in revolutions/sec. or revolutions/min.
11aximum rotational speed of viscometer (RPI'1)
Flm1 behavior index in power la1AT
Slope of logarithmic plot of \Forque versus RPI'1
'If
TIa
::: Number of blades on impeller
= Reference number of blades on impeller
Number of baffles
Neference number of baffles
::: P01AJer
p ::: Pressure
:::: Dimensionless pressure defined by eq. 3-14
::: Pressure at a particular position

52.
Q ::. Average heat transfer rate
QL ... Local heat transfer rate
ql'1 :: Rate of mechanical heat input
qNET :: Net heat tra.11.sfer rate through heat transfer
s'tlrface
:: Rate of heat input to batch
:: Radius of vessel
:: Radius of bob
:: Radius of cup
~ :: Pulley radius (Dynrunometer)
:t'R .,. Sum of all heat transfer resistances except
batch resistance
I:;Rc :: Sum of all heat transfer resistances except batch
resistance in cooling cycle
::
Sura of all heat transfer resista.nces except batch
r
r ~~
.. ~(~Cr
S
S
T
~~
T"
Tb
Ts
Ts
::
::
:::
...
""
::
::
=
::
::
resistance in heatine; cycle
Value of radical coordinates
Dliuensionless radius defined by eq. 3-38
Dlffiensionless radius defined by eq. 3-10
Dynamometer scale reading (lbs)
Ratio of cup radius to bob radius, Rc/Rb
Temperature at any point
Dimensionless temperat'tITe defined by eq. 3-16
Temperature in bulk of fluid
Torque
Hall surface temperature

5..3
T,.J
= Tempera tUre ax thermocouple
.6T o ::: Temperature driving force betHeen batch and heat
transfer mediu:m
hTs-b = Temperature drop be~~een
wall surface and batch
A T w
_ b
::: Temperature drop bet1rJeen measured point in wall
and the batch
l) T\:Ar_s = Temperature drop bet"reen measured point in ",raIl
and wall surface
~Tl_2:::
Change in temperature of batch over time interval
1-2
t
"
t'~
~
U
V
V
Vb
Ve
Vr
Vr *.
·~,~it-
Vr
V z
.. ~~ ..
V z
H
1'1'
'a
T.:Jb
= Time
::: Dliaensionless time defined eq. 3-15
::: Terminal blend time (seconds)
= Overall heat transfer coefficient
= Average velocity in pipe or tube
= Characteristic velocity = 11])&
::: Linear velocity of bob
= Velocity in angular direction
::: Velocity in radial direction
::: Dimensionless Vr defined by eq. 3-39
= DL~ensionless Vr defined by eq. 3-12
::: Velocity in vertical direction
= Dimensionless V z defined by eq. 3-13
= Height of batch
= Width of agitator
= Width of baffles

Xc = Function of Reynolds nL:l.m.ber, eq. 2-4.4
X·
J = Function or Reynolds nmnber, eq .. 2-1t5
z .. Value of height coordinate
~~
z = eq.
DL'11ensionle ss height defined by 3-11.

ISS
GROUPS
-- ~ - - .' - --,
:DIHEl~SIONLESS
11 Fr
NNu
NPe
Npo
N pr
N' _lpr
=
:::
=
=
Froude nUInber ::: V 2 /g z Da or DN 2 /g c
Nusselt nmnber = ~~/k
Peclet number (Cp V P Dalk )
Power nur.1ber ::: Pgc/ p N3Da5
Prandt.l number, Cpft/k
Generalized Prandtl n~mber calculated using
apparent viscosity = K (11.5 N)n-l
N II
Pr
- Generalized Prru1.dtl number calculated using
apparent viscosity::: Klf-- l
2
= IvIixing Reyno Ids number, D ).1 e
= Generalized Reynolds nrunber, calculated using
apparent viscosi ty ""
K (11 .. 5N)n-l
::: Generalized Reynolds number calculated using
apparent viscosity = KN n - l
= Generalized mixing Reynolds number defined by
eq. 2-27

IS6
G REE:>{ ALPHABET
0 ::: Value of angle of rotation coordinate
JL ::: Newtonisn viscosity
/La.
::: II c' n-1
Apparent vis cosi ty defined by 1I1etzner,t-OW
f
,.. :::
"'-W
1;tz
?'Z.z.
Infinite shear-rate viscosity evaluated at wall
temperature
;:::
Density
Shear stress
,., Shear stress at wall
::: Shear stress in z direction at constant radius
c
Shear stress in z direction at constant z
~
lOt Shear rate
iw
::: Shear rate at i

A,PPENDIX A
FLUID PROPERTIES
Th~ d~ensi@~less g.ro~ps used to correlate seat
t·ransf'er data include i'0U.:i? fluid :properties; viscosity II
ther.mal conductivity, heat eapaeitys amd &ensity. Literature
values i'or these properties were used when they were
available and the remainder 'i'lfere m.easured.
The tem.pera~eaependent
i'luid properties were expressed as a i'unetion oi'
temperature.
VISCOSITY
.. I
For Newtoniaa correlations the rheological behavior
of' the fluids is expressed im terms of~ s the viscosity
coefficient. Since this study includes n0n-Newtoni~
fluids for which the term viscosity is meaningless, the
rheological behavior is described by the two constant,
power law equation. The fluid properties which are
measured are the flow behavior index, m" and the fluidconsistency
index, K.
The apparent viscosity for all the
fluids used is thus given in teJ:"'l1ilS of :m. and K.· For use
n-2
in. the dlmensionless groups K has the umits Ibo m
sec. /i't.
and n is dimensionless.
NewtoniaE. Fluids
r '1 f
The flew behavior index for all Newtonian i'lui~s
UNity and thus does not have to be determined. The i'luid
eOl1lsisteney iRdex is equal to the Newtonian viscosity
is

158
coefficient. Thus, for the water and glycerine it was
only necessary to evaluate the viscosity coefficient and
express it in the correct units.
The viscosity of l-Iater \·ras determined from Bingham t s
equation for the fluidity, ( ¢ ), of water as a fUl~ction
of temperature (17).
¢ = 0.021~-B2 [(T-8.L~35) + j8078.~. + (T-8.435)2] - 1.20 (A-l
\.Jhere ¢ is expressed in centipoise -1 and
T is the temperature in degrees Centigrade.
The relationship betl-Jeen fluidity and viscosi ty is
jl = l/¢
(A-2
The fluid consistency index in the proper units is obtained
by multiplying the viscosity in centipoise by
6.72 x 10-4
K = 6.72 x 10-4p
(A-3
The viscosity of 93.7 percent clycerine was graphically
interpolated from data of Segur and Oberstar (177) and is
given in Table A-l.

S9
TABLE A-l
VISCOSITY OF 93.7 PERCE1~
GLYCERIN~
Temperature
(oC)
Viscosity
(Centipoise)
0 2760
10 982
20 413
30 193
L~O 99
50 56.5
60 34 .. 1
70 24 .. 7
80 15.3
90 10 .. 9
100 7.9
trhe data vrere assumed to fit an equation of the type e
(A-4
and Here plotted as the logarithm of f/ versus the reciprocal
of the absolute temperature $
The curve 'L,ras not linear
but a straight line viaS drm·m through the firs t
three
points (corresponding to 100, 90 and 80 °C) and extended
as Sh01·ffi on Figure A-l.
The difference be tvJeen the data and the stl"aight line
for any temperature \Vas measured and defined as f to give
equation A-5.
These differences are given in Table A-2.
jJ :: A10 B / T + f
(A-5

160
,
., I ..
: I :. '. • • !. ::! ::; : II' : ',':: :::! ~::: lfi I : 1 : ~ . f ., :;': ~!: I: ':. : ::: j :::, :! i 1 ",' !,: :,: :. :1'
. " ., • ., ' .! • ," " .'. ':,1'
" ..
1 :." • ,.. ".. '. ".' '. '.',
j .: , ... , , . " i." . i·1 . ' 'j
~.
., .. ! .. ··'JI·l·; ,1" I' ,,;.,.
!:'" !,:
i'l' " "
:T :::;.;
,I-. ... , ,. .... '.
t;..: .;:' ., ., ,. ." '1'" .. :., . ,,1·£
" V::
;
~. ;. j I ..... ,
. .!. ,.
I . . :. ..'. . : ! ; l , . .. . l' . 1 , ~ j :
~ 1" :::1: :~ ::i ;iI;i;; '. ! ::'1 ;,'1' ": . ,. i:J
: ~ ': , .. . I . : , V ' ; " ;:. i ;'
: ',' : : j 1
... , i i' . . .. ..
~ .:, .:):/: ::'h li: J
l :ij 'I: il":'I·!::.i,,; :,;:'~'. ":':1:,1
~

6/
TABLE A-2
CORRECTION FACTORS FOR GLYCERINE VISCOSITY
EQUATION
Temperat1Jll:'@l liT f'
(eC) (ex- 1 ) (eeJ5lt-1~(l)is$)
100 2 .. 68 x 10- 3 0
90 2 .. 75 x 10 -3
0
80 2 .. 83 x 10- 3 0
70 2.91 x 10- 3 0 •.5
60 3 .. 00 x :LO -3 3.0
,50 3 .. 09 :x 10- 3 9 .. ,5
L~O 3 .. 19 x 10"'3 27
30 3.30 x 10- 3 '71
20 3.41 :x ].0 -3 222
10 3 .. 53 x. 10- 3 6:>67
~e eerreetion f'aeter was p10tted versus liT ~d
f'ouad to deseribe a straight liJ5le on semileg pa~er (Figure
A-2). It eould thus be expressed
i' := C 10 D/T
(A-6
T1:le i'our eonstaJ.fl.ts were evaluated as
A ::: -4.14.5
B ::: 1.88 x 10 3
C ::: -12 .. 23

162
I ,
. I .
"I
'1
I
i
I
1 I
1· '; I
I
II
ii
I
. I
I
10 J
.
I·
"
i·:::
::
1:::
I .... .., , , , :V:: I' '.. :'::1:
I : J:::
i ., .
I
j:IY;':,:
,;: ,! I ;, :
I, II I '!, : .
: iii
9 :1': : .. ' :1.: :j:.', ,I::' ........ 1
. '1;
i: , ,
t, !
1:
3
L:
'.
. !

6..3
expressed as
-5 1880 13 h270
7.17 x 10 x 10 T + 5.81 x 10- x 10 ~ {A-7
1-Jhere ft is expressed in centipoise and T in degrees Kelvin.
Expressing the viscosity in the proper tel~s ru~d converting
the temperature term to degrees Centigrade gives
K = 6.72 x 10-4 [ 7.17 x 10- 5 x 10
4270 Jl
10 273+ rt
1880 13
273 +T + 5 .. 81 x 10- x
{A-8
This equation was solved for the temperatures listed in Table
A-I and reproduced the data to Hi thin ± three percent.
Non-Newtonian Fluids
Carbopol solutions have been reported to be well represented
by the pov.Jer lavr (63, 165) but the fluid consistency
index and flolN behavior index have not been determined for
a ll1Tide range of concentrations.
Furthermore, the Carbopol
resin seems to vary slightly. The method of solution preparation
and the degree of neutralization seem to effect
the values of the flmr! behavior properties. Thus it was
necessary to measure these properties.
"
The flow properties Here measured using a Brookfield""
LVT-5x-600 Synchro-Lectric Viscometer equipped vd th cylindrical
spindles.
This model has eight different speeds
of rotation; 3, 6, 15, 30, 60, 120, 300, and 600 revolutions
-l~
Trademark of Brookfield Engineering Laboratories

64
ncr --~iIluto e
torque of the ins trDI'10n t, 1Jl-:.:i.cll for t1:, i s nodal 336P.5
d-:rne centi:'leters. The fl~:cicl contLineI' used UD"l [' 600 "'ill.
The shenr roto 2~ ~10 8vrf 0 cP of t~o opindlo c~n bo
c[llcnlntod from
w~ere N is t~e rotn~ion~l 8pcod of tho snindle o~pr0330d
8.3 r0vC',J;'.tions por :r1innte (or 38 conel depondin2; npon the
V,(,. A']" lOr< .J th0. .l. _~ "'l"pe '_-J • ~) __ ~-' ".0 \....Jl. ("
10~nriUTIic Dlot of tho tor~ue
verSHS tho rototionnl speed of tl,o s}JindIe.
nec;l:L sible A.nd oClun.tion 2-11 :11'l;{ be .'3 :iJllplif i e d to
(2-12
(2-5
1-!hore Ts , l8 tho torql.l.e
• 1
renUlroc, to rot8.to the sp:i.mlle
Bb is the r'Jdi'18 ,)f tho sp in ell e 01'"
bob

6S
some R~en~ ~t the onds of t~8 suindle 2nd therefnro the
, ., -l-. 1
310 l ~n '-', l.le' 2.8 disCU3'Jnc 1 in Chaptor 2. Theref-:;re
(A-9
dr~ 'J cri bed in Cho.pter 29 ·US inr; n Droolcfii31d vi s cos :tty
8t'~n(lcrd,
L-3, of ,Thich the visco8i ty 1Tas repnrtod to be
dI'll ro:::dlnS In perc~nt,. X, ',-188 V'on c~tlc111['ted for e"eh
snindle usinc the eff'ectivo hei rr ]:1t.
T8.ble A-3.
These 2.n' list0d in
TriBLE A-3
CI;:AnAC':L'ERLj';.'ICS c.:;t' B~OOEF'ISLD
SFIFDLES
CYLID) fUCAL
3FIlTDLE Il.."lDILJS lIEIG1S EF:!?EC~IVE I=EI1J.JIJ; :3~~:S!l.R
( dpl.o S / cn )
(~r~"'f1.nr< ... ,
o .l.l'Li2.J0 '~.J
rTU: iLsn ( e:'1 ) ( cn) (err:, ) / 2
1 0.9L12 6 c::?
"/'- 7. 7L~ 0.782X
2 0.513 5.30 6.11 3.35x
3 o. 29L~ Lt .• 28 L!._ 95 12.52X
4 0.159 3.10 3.62 53.6ox
rrornue - 'c - V'''''''''l)''' .~~,-, •.•). ro+-' 10.'. t·; J. 0-- L·. 1 "1 °p"od ,,-, 'G ("0 ,.), 0, LO 120 :II J ')00 8.nc 1
600 RPM) dnta was taken in triplicate for each fluId at

166
rive different temperatures; about 17~
25, 40, 60 and 82 °e.
The fluid Has maintained at the desired temperature by
iramersing the 600 ml ..
beaker in a constant temperature
bath..
The constant temperature bath was placed on a magnetic
stirrer (the stirring bar Has in the 600 ml.. beru-rer)
which was run l'lhile bringing the fluid up to temperature,
but Has shut off while rheological data 14ere being taJcen.
The temperature could be held constant 1AJ"ithin 0.1 degree
Centigrade,
A grooved cast acrylic lid was also fabricated
to cover the 600 mI. beaker Hhile the Carbopol solutions
were at the higher temperatures to prevent evaporation
losses..
The apparatus is sh01m in Figure A-3.
The average of the three readings of torque 1...ras used
to calCUlate the shear stress. nn, the slope of the logaritlLmic
plot of torque (or shear stress) versus rotational
speed, ""'las needed to calculate the shear rate. n ll v-Jas evaluated
for each fluid at each temperature using a linear regression.
The actual calcu~ations Here performed by the IB}1
1620 digital computer. The computer programs are enclosed
at the End of this Appendix.
The slope for each condition
is listed in Table A-4.
The shear rate at each point was then calculated using
equation 2-12.
The apparent viscosi t·y Has calculated using
(2-23

VISCOMETeR
LID
~ODML BKAK€R
TO CONSTANT
TEMP CIRCULATOR
SPINOLE
-
CONSTANr
T€MP BArN
-
.5T1RRIIVG
BAR
rlf'OM CONSTANT
TEMP CII(t:tJLATOR.
MAGNETIC
STIRRER.
riG 4-3
COfJSTANT TEMPERATURE APPARATt/S FoR j//S(,O#67c/?

168
TABLE A-4.
SLOPE OF "LOG SHEAR STRESS VERSUS ROTATIONAL
SPEED II
FLUID TEMPERATURE SLOPE
0 .. 15% Carbopo1 18.5 0.656
25.0 0 .. 651
41 .. 3 0 .. 681.
63 .. 0 0 .. 720
82 .. 0 0 .. 717
0 .. 20% Carbcpol 17.5 0 .. 433
25 .. 0 0 .. 436
~.2.7 0 .. 422
61.7 0.427
83 .. 8 0.457
18.6 0 .. 370
25 .. 0 0 .. 366
41.8 0 .. 363
59 .. 5 0.374
83.5 0.341

The results are tabulated ~ Table A-5.
The flow behavior index~ ~, am~ fluid 00nsisteRey
logarithm of the shear stress and Shear rate. T~e results
are listed ~ Table A-b. Since the fluid properties were
needed as functions of temperature, the fluid eonsistency
index was p10tted versus the temperature on semrllogarithmie
eeordinates; as suggested by Ferment (63).
The poi~ts
deseribed a straight line vJhiel3. CaE. be expressed as
IGg K :: A + B (T)
(A-IO
The constamts~ 'A ~d BI were calculated using a linear
regression. The flew behavior index was mot very temperature
dependent but eould be expressed as
m :: C + D (T)
(A-II
vrhere C and D Here evaluated using a linear regression.
The results are given in Table A-7.
TABLE A-7
CONSTANTS FOR EQUATIONS A-IO ~d A-il
A~;'
Fluid B C D
C"C- l )
(oC-l)
0.15% Capbopol 0 .. 702 -0 .. 00947 0.631 0.00117
0 .. 20% Carbo])ol 1 .. 607 -0.00bl0 0.423 0.00027
0 .. 24$& CarbQPol 1.906 -0.00308 0.378 -0.00034
,:. Tke use of tl'il.ese e0l1lsta:mts gives K in. d'J1llles see. Ja jelii1. 2

TABLE 11.-5
RHEOLOGICAL DATA FOR CARBO POL SOLUTIONS
0 .. 15% CARBOPOL
SHE ... ffi ST~SS ROTATIONAL SHEAR APPARENT
(liple'ls/e:m) SPEED RATE VISCOSITY
(RPM) (sec- 1 ) (eentipoise)
II J
93
t • ".
..
63 .. 0
-, - $1. ,
82 .. 0
14 .. 2 30 9 .. 55 1.49
22.5 &0 19 .. 1 118
36.2 120 38 ..:2 95
. 64 .. 7 300 95 .. 6 68
. 101·2 600 191.2
" "~"1 t , r .a 53 .
13 .. 1 30 9 .. 63 136
21 .. 3 60 19 .. 3 111
32 .. 7 120 38.5 85
59.3 300 96.3 62
1 600
" ,- ~t , ... 19,,2 .. 6 48
!r !"f ~ t -,rr9 "- r
•
9 .. 7 30 9.21 105
15 .. 0 60 18 .. ~ 81
24.5 120 36. 67
45~8 300 92 .. 1 50
. 73~8 .• 600 , 1.84",.1 40

TABLE A-5 (e011t .. )
/7'
0 .. 20% CARBOPOL
TID-fPERATURE SHEAR ST~SS ROTATIOJlTAL SHEAR APPARENT
(GC) (dynes/em) SPEED RATE VISCOSITY
(RPM) (see-I) (eentipo ise )
17 .. 5 97 .. 6 30 14-.. 5 674
128 .. 8 60 29 .. 0
170 120 '57.9
255 300 ~8 17
~~
359, " .. , 600 ,a ,Q;6 124
25.0 91.3 30 ~.5 635
122 .. 6 60 2,.8 42~
160 120 51.5 278
241 300 1%3 .. 8 168
.. ..,.341 600 2. 7.6 11;9 , .
I :it
42 .. 7 7'5 .. 2 30 1.4 .. 9 ~O6
97.8 60 29 .. 7 329
127 .. 8 120 59·t 215
193.5 300 1Q.8. 130
26~ 600 2~:Z .. 2 82
61.7 59 .. 7 30 14.7 407
76 .. 8 60 29 .. 4 262
99 .. 8 120 58 .. ~ 170
151 .. 5 300 146 .. 103
j t ..
.21,2 600
\ I ' 223.7 13
83 .. 8 39.3 30 13 .. 7 286
53.3 60 27 .. 4 194
68 .. 3 120 54 .. 9 124-
107.7 300 137 .. 2 78
156,,3 600 274 .. 4 57
. b
rt

TABLE A-5 (eollt. )
/12
o . 24;;& CARBOPOL
TEMPERATURE SHEAR ST~SS ROTATIONAL SHEAR APPARENT
(®C) (d-yE.es/em ) SP"RED RATE VISCOSITY
(RP~.iI) (sec-I) (®ellltiJloise)
18.6 205 30 17~O 12tO
259 60 33.9
358 120 67.8 J2%
462 300 169..;5 272
. 628 ..
6,00
v IIIIILdI 4''''1
338 .. 2 .185:
25 .. 0 197 30 17 .. 1 1150
247 60 34.3 721
312 120 68.5 455
438 300 171 .. 3 256
593 600 342 .. 6 17~
. . •
41.8 172 30 17 .. 3 996
215 60 34 .. 6 622
2~1 120 69.1 392
3 3 300 172.7 222
... 51g 600 345 .. 5 , ,lJA,8
d
59 .. 5
, ,
30 16.8 859
~
60 33.'5 537
235 120 67.'1 350
327 300 167 .. 7 195
.W±2 600 3.35 .. 3 132
83 .. 5 130 30 18 .. ~ 707
157 60 36 .. 42~
197 120 73 .. 8 26
274 300 183 .. 9 149
359 600 367.7 98

TABLE A-6
FLOW BEHAVIOR INDEX AND FLUID CONSISTENCY INDEX
OF CARBOPOL SOLUTIONS
FLUID
TEJ:1PERATURE
(@C)
K
(dynes
18.5 0.656 3.25
2.5.0 0.651 3.05
41.3 0 .. 681 2 .. 11
63.0 0 .. 720 1 .. 19
82.0 0.717 0.87
0.20% Carbopo1 17 .. 5 0.433 30 .. 1
25 .. 0 O.L~36 28 .. 1
~.2 .. 7 0.422 23 .. 5
61 .. 7 0.427 18.3
83 .. 8 0.457 11.6
0.24% Carb0po1 18 .. 6 0.370 72.0
25.0 0.366 68 .. 2
41.8 0 .. 363 59 .. 7
59 .. 5 0.373 L~9 .. 2
83 .. 5 0 .. 341 46.7
sE!\e:rljem2)

'11
The flow behavior index and fluid consistency index
expressed i~ the proper units are given iE. Table A-8. The
data are pletted in Figures A-4, A-5 and A-6.
li~es
The solid
are the values for the shear stress calettlated using
equations A-9 and A-IO with the constants in Table A-6 while
the plotted points are the data from which the constants
were es.leulated ..
The effects of turbulence were noticed when measur~
the 0.15% Carbopol at high speed. H.:noJever, these r'llE.S were
then redone using a smaller diameter spindle as suggested
in. Chapter 2.. . The data Has also che eked .for tem]5erature
rise due to heat generation..
The heat generated per unit
vol~ can be calculated using equation 2-16.
""""',..}J
Heat Generation = / ~ (2-16
The most viscous fluid at the highest shear rate generated
8 .. 31 x 10- 5 cale/see.. A series of measurements at aay one
tem.1gerature at any s]'ced took about five minutes at the
longe s t. This amoUJ:71.ts to a maximum temperature rise of
0.025°0. which is negligible. Not only was this rise
calculated on the basis of the conditions most prone to give
I
hi~~ rates of heat generation, but alsG the system was considered
to be adiabatic, whiCh is untrue..
did not influence the rheological :m.easurem.emts ..
Thus, heat generation
The torque required to rotat~
the spindle at a constant

f7S
TABLE A-8
FLOW BEHAVIOR INDEX A1TD FLUID CONSISTENCY
INDEX FOR CARBOPOL SOLUTIONS
0,.1,5% CA,RBOP,oL
n a
0.631+ 0.OOl17T
0.20% CARBOPO~
n- 0 .. 423 + 0.000267T
K= 6 .. 72 x 10-2 x 10 (1.607 - o .. oo610T)
0,.24$ CftRB.oT!,oL
. (
B= 0 .. 378 - 0.00034T
K= 6 .. 72 x 10-2 x 10 (1.906 - O .. 00308T)
K is given in 1~aeen-2/ft. amd m is dimensi0nleas ..
T MUst be eXFreased 1m degrees Centigrade.

i .f.C
·F
s o 6 1 6 I

177

· . . .
" ,
· . :::11" ':
"'" ~ .' . ,
· , j
" .;
.. ,
::1:",
j
"" J
"':'1
::1:
."
. . ,
"': v: "" , :1~
" ie-­
--,--,-,-~,'-.--'-t--7-~,-j-'~'-,-' ~-+--,--1r--M-:-'b:+. -:~ ~-- -+-,,-,',~ 'c..c

179
speecil. did Rot eha:mge td tk i:m.ereasim., times @f skear..
Carb0:fJ®1 s01'U.tiollS therei"@!l'e we~ net t:i.l¥!.e-cii.epemGl.emt.
The
The
retatimg shaft of the spindle aE.Cl.
als@ ue impeller sha.f't
were checked to see if' the f'luid (t.rept up the shaft.. Tlaere
WillS aJ!l absence of' creep and tkerei'ore the f'luiCl.s were assum.ed
to he ROB-viscoelastic.
THERMAL CONDUCTIVITY
.. nf1t .. 1 it I
The thermal eonductivity, k, is used in beth. the Nusselt
number a:m.d the Pr~dtl llumber.
Bates (11) reports the
thermal eOllcil.uctivity of' both water ~d glycer:i:m.e..
Tke
thermllll eellduetivity of' water is ex~ressed
as
(A-12
:ror k iIt caL./em. 2 0C see./em. and T in degrees Centigrade.
Tkis is multiplied by 242 to give the thermal conductivity
im tae desi~ed umits ..
k = 0.325+ o.ooo888T
(A-13
TRe ~ermal
eoncil.uetivity of glyeeriae does not vary
with temperature above a eomeentratien of' 90 percent. Tke
taer.mal eonauetivity is 0.00072 ~d 0.00070 at 90 &na 95
percent pure respectively. The thermal conductivity of'
93.7 percent glyeerille was inte~olated to he 0.00071 cal./
8m. 2 8ee.oC/e111.. or 0.172 Btujhr. :rt. 2 ~/tt. The aceuraey

180
Tke thermal e€l1'!ciluetlvity CDf.'
tile Carbop~aratu.s built by
tlae a.utk®l' and €l.esel"ibed in ref'erel'lee 83. Tlae aee'a!'ae.,-
of' the instrt'll'ael11t was esti..'l1l1ate€i to be ± .5.0~e The ex­
~erimem.ta.l va1u.es are presented i:m. Ta.b1e A-9. Wlthm the
accuracy of.' tBe data there is mo signif.'ie~t dlf.'f'erel1lee
betl.reen the values for the dif'f'eremt solutioRS. A regressiol1t.
analysis was performed, usin~ all the data points to obtain
a linear relationship between the tRer.mal conductivity of.'
the solutior.J.s and temperature. Tb.e rela tioP.l.ship "t-TaS f.'0und
to be
(A-14
2 ®
for k in Btu./Br .. ft. (F/f't .. ) an.d T in degrees Centigrade ..
Tb.e thermal cemductivity of' the solutloD.s was about the same
as water at 20°C ~d about 10 percent l0wer at 80@c ..
HEAT CAPAC ITY
1 1
The heat capacity of' water (given in Perry (143) at
several diff'erel1lt temperatures) varies yery little with
t~perature. A eOl1lst~t value of' 1.003 Btu/lb.@F C0vers
t~ range between 0° &Rd 100Ge vnth a Max~ of' 0.6 per-
TRe heat capacity CDf' glycerine so,lutioE.s crua be expressed
by (130)

18/
TABLE A-9
EXPERIt1ENTA~
VALUES FOR THE THEID'!IAL CONDUCTIVITY
OF CARBO POL SOLUTIONS
CARBOPOL
CONCENTRATION
0.15%
0 .. 20%
0.24%
18 .. 9
41.8
62.2
80 .. 6
17.7
4_0 .. 5
60 .. 5
80 .. 1
18.4
L~0.5
60 .. 6
80.6
0 .. 340
0 .. 355
0 .. 363
0 .. 353
0 .. 342
0 .. 350
0 .. 348
0 .. 362
0 .. 348
0 .. 365
0 .. 345
0 .. 358

182
Heat capacity data for 100% glycerine is reported at many
temperatures (49, 95, 1~.3)
and can be expressed as
Cp(lOO% GLYCERINE) :: 0.535 + 0.00132T
for C p
in Btu/lb.op for T in degrees Centigrade.
(A-16
Substituting
the above value for water and equation A-16 for
100%, glycerine in equation A-1S yields
Cp(SOLN) :: (1.003) (0.063) + 0 .. 937 (0.535+0.00132T)
(A-I?
or
Cp (93.?% GLYCERINE) ... 0.565 + 0.0012LI·T
(A-IS
with an estimated accuracy of ± 3 .. 0 percent.
The heat capacity of Carbopol solutions of approximately
the same concentrations used in this thesis Here reported
by Ferment (63) to be the same as for water.
Ferment
estimated the accuracy of his measurements to be ± 5.0 percent.
Thus the heat capacity of the Carbopol solutions vIas
1.003 ~ 5.0% Btu/lb.Op.
DENSITY
Values of the density, f ' of water at various temperatures
are reported by Badger and McCabe (10).
The data
l,.Jere ass1Lrned to be represented by an equation of the form.

183
{A-19
3 -4 Z
f= 62.12 -1.6tfSx/o- T- 2.1-8 x/o T (A-20
where f is expressed m lb.m/ft .. 3 8.l!ld T is expressed m
degrees Ce~tigrade.
represent the data to witlaL-q T 0.3% ..
~e use of this equatio~ was found to
TJn.e density Elf' 93.7 1E>ereent glyeerim.e was gral!>hieally
interpolated from data supplied by the Glycerine Producers'
Assoeiati0R (74). Tke Eiensity WitS f®'U:l:ad t® va:r'Y linearly
with. tem.pEIlrature aJ3.a coulcil. be representea. 't.J"ithb ± O.35b by
(A-2l
where f is expressed in lb.m/f't. 3 fer T i~ degrees Centigrade ..
The density of tae Carbo~0l solutions was determimed
experimentally using ealibrated pyenemeters. Tome data
listed in Table A-lO were obtained ~rlth an estL~ated aeeuraey
of' ± 0 .. 1%.. Tl1.te dens i ty was ilie s rune Hi th1:a experimen tal
aeeura~y
fer all three solutions ~d was eonsistently about
0.1% above the eorresponding values for water. Multiplying
the equation fer the density of' water by 1.001 yields
(A-22

IB4-
wkiek ex~resses the aensity e£ tae Carbe~el s@lutions witk
run estbuated err0l? 0£ ± 0 .. 35~ ..
TABLE A-lO
DENSITY OF CARBOPOL SOLUTIONS
19 .. 9
40 .. 8
60 .. 7
79 .. 9
2
DENSITY (g/em)
0.15% Carbop01 0 .. 20%
Carb0}!'01
0 .. 999 1 .. 000
0 .. 993 0 .. 994
0.984 0.986
0 .. 973 0 .. 972
0 .. 24%
CarbeF>Gl
1 .. 000
0.993
O .. 98~
0 .. 972

ISS
NOMENCLATURE FOR APPENDIX A
E:t~GLISH
ALPHABET
A
B
C
G p
C
~SOLN)
::::: Constant iJa eq. A-9 aJ!I.Gl eq. A-IO
::::: C0nstant in eq. A-9 and eq. 11.-10
::: Constant in eq .. A-6 ara.d eq .. A-ll
1111 Heat capacity
::: Heat capacity of an aquE!lcs)''as glycerine
s01uti0l'l.
G]l
(H20 )
c
11009&
D
::: Heat ea1'laci ty of water
• Heat capacity of 1009& ~lyeeriRe
glycerine) -
::::: Colltstant in eq. A-6 and eq .. A-ll
hb ::: Height of spinale
K
k
N
-
=
, I
Effective height of spindle
C~nver~iom
factor of mechanical energy to heat
energy 2.39 x 10- 8 cal./dyne-em.
Fluid consistency index
Thermal conductivity
Rotational s]leed of spindle (Revolutions per
minute or second)
n ::: Flow behavior ~dex
n" = Slope of logarithmic plot of the torque versus
R
e
IiIII
rotational speed of spindle
Radius of cup
Rb
11111
.-
Radi~s of spindle
T ::: Temperature

186
Ts - Torque
X :: Peree~t 0~ full seale readim~ en viseemeter
A ::
ft

18 7
Computer Programs For
Evaluating Rheological Data

Phase I Calcu13tiJ~ of Slope of !oGarithnetic ~lot of
i.)he~1.r· ....itress Versus ap:t:
3 REAO,N,M
4 EN=N ',(i0
EM=M
Sx=O.
Sy=O.
SXY=O.
sx2=O.
Sy2=O.
D051=! .N
REAO.TEMP.SHST.RPM
X=.4343*LOGCRPM)
Y=e4343*LOG(SHST)
sx=sx+x
SY=SY+Y
SXY=SXy+x*Y
SX2=SX2+x*x
5 SY2=SY2+Y'~Y
XBAR=SX/EN
YBAR=Sv/EN
CX2=SX*sx/EN
CXy=sx*sv /EN
VX2=SX2-CX2
VXY=SXY-CXY
BcVXy/vx2
A=YBAR:-B*XBAR
C=SXY/SX2
R=CC(EN*SXY-SX*SYl**2!/( (EN*sx2-SX*SX)*(EN*SY2-SY*sY»i~*.5
IF(R)6.7.7
6 RA=-R
GO TO 8
7 RA=R
B S2SX=(EN*SX2-SX*SX)/CEN*(EN-l.»
S2SY=IEN*SY2-SV*SY)/(EN~(EN-l.)1
YGX=(CEN-l.)/(EN-2a»)*
·CI }
, ,(J (t
JC ~~f
, le!fl,
: l(ll)
',f) I
,(I' J
'.lor
J~)O '"}
~ ., () 1
)'
~ ,f J j
',i1 I
"i)
, ,\) '~)

189
NOIVlENCLATURE FOR PHASE I
B II Tfle l('i)gari tlimUe slope of shear stress versus
DF2 II
N ..
RA ;:
RPM
Il:
SHST ;:
SB :::
TA
II
rotatie)llal speed of viscem.ett:llor ~€ib
Degrees of' freedom
Number of data poimts
,
Correlatio~
coeffieient
Rotational speed of viscometer bob 1m rev./mime
Shear stress 1m dYRes/~2.
Standard error in B
T of the T test
TEMP ;:
DATA
Tke first card of a set of data had the values for N and
M. M was a constant with value 2.0. Tke next N cards
each had ~ree nttmbers corresponding to the temperature,
s'fu.ear stress~ !':U'td'retati0na1 s:peed of' a particular run.
The temperature w~s not needed 1m this program but was on
the eard fer later use.

3 REAL). N. ti •• D
4 cN=N
E'I'1 = [·1
SX=Lo.
'SY=W.
SXY-o.
SX2=,O.
Sy2=O.
D051=1.N
--~---RE·AtS'.~TE:lqp~ SHST. RPtC---------
Z= ~209*RPI'l/D
SX2=SX2+X*X
5 SV2=SV2+V*V
XBAR=SX/EN
YEIAR-SY7EN
'j
i
---~------,~-~--- ---------------,5"'0"'o",.-+\
.. , -------------~ --------------:S=-C=-=-O-li
500
500
500
~. ---- -·--·------~-~-----------;=5-;;:0-;;:O-l
500
.... - ..... -------------1
W=ShST/Z ------------.---------------------------------------~;
PUNCH. TEji,P. r.(Pf.1. Z. Vi
----·X- .4343*LOG IZ)
Y=.4343*LOGISHST)
--,------ -SX=SX+X
SY=SY+Y
SXY=SXYtX*V
6
CX2=SX*SX/E"!
ex,' -:3X*S i ; EO!'"
VX2=SX2-CX2
VXy=SXY-CXy
d=VXY/VX2
A=YL,AR-8*xaAR
C=SXY/Sx2
R=
~------... -, ,--_ .... -_ ...
7
8 S2SX=IEN*SX2-SX*SX)/IEN*CEN-l.) I
S2SY-IEN*SY2-~y*SYI)(EN*C~N I.})
YGX=IIEN-l.I/(EN-2.»*CS2SY-d*O*S2SX)
SYGX-YGx**.S
se=SYGX/I(S2SX*IEN-l.)I**.51
!F(B)9.10.1C ·__ n ---- ~oo
~~~ I'
500
500 I
~~~ I
~oo (
5'00 !
50
500 1
500 '
500 I
----.------------~
500
500
9 i3A=-B 500
;,a GO TO II SOo
' ,7 ( 10 BA=8 500
~'6 --·!·1-·....,.-:s-A"'/"'s"8:r-------------·---- -- 500
15 IFIT)12t!3.13 500
I ,'· 12 TA=-T 500
1~'
12 14 DF 2=EN-2. 500
'\
500 {
___________ ~~G~O~~T~O---1-4----------------------~-----------------------------------------______ ~5~0~,O~
13 TA-t 500
(
,'1 ( SEX- ( !Sx2-Sx*Sx7ENj7 tEN I. I )**.::>
':
SEY.=((Sv2-SY*SY/EN)/(EN-l.)I**.S
1 1''-'" xK=IQ**A
'76el.____\ __ ~P~U~N~C~H~.~T~E~M~P~.~8~.~.~X~K~----------------________________________________________________________ __
POi

191
A - Leg @f f1uid eonsiste~cy ~dex
B IIlII Fl0W behaviGr index
D .. Sle~e of logal"ith:m.ie £llet 0f shear stress Versus
DF2 -
N ::
11 ::
RPM (B at PJ:lase I)
De~rees
of rreeaom
Number of data ~oints
C@nstamt equal te 2
£leI' set
RA ::
RPM ::
SB :::
SHST :::
SXGX ::
TA ::
TEl'-1P :::
Xl{
-
Correlatien coefficient
Rotational speed of impeller bob
Standard error in computed B
Shear stress (dynes/em,2)
Standard errer in Y
i
T of T test
Temperatulte
Fluid e~nsisteBey
DATA
TRe first eard of a. set of data had the values at H, M
and D.
The l'lext H cards each l:.Lad three values cerres]lo:ading
to the temperature, shear stress, and shear rate.

~~-- ~---- --~--~ ~~~------------------------------
Phase- III Calculation of Fluid __ G.nnsl stency ___ _
----~
Index as Functiou of Temperature ______ _
LQg K = B(~emp.)
3 READ.N.M
4 EN-~N~------------------------------------~
EM=M
Sx=o.
Sy=o ..
---_.-- -~------
SXy=o.
Sx2=O.
Sy2=O.
D05I=1.N
-- ---- --~ ------._-----------
READ.CONC.TEMP.XINT.XSL
X=TEMP
'"--- -'- -- ----~---.--.---.----
Y=XINT
SX=SX+X
SY=SY+Y
SXY=SXy+x*y
Sx2=SX2+X*X
5 SY2=SY2+Y*Y
- . -----------.----------~-
XBAR=SX/EN
YBAR=SY /EN
CX2=SX*SX/EN
CXY=Sx*sy/EN
VX2=SX2-CX2
VXY=SXY-CXY
B=VXY/VX2
A=YBAR-B*XBAR
-----~----------~-- ---------- ----
C=SXY/SX2
+ A
-- -------~~---------
-------------------------------------
R = ( ( (EN*SXY-Sx*SY )**2 / ( (EN*SX2:-~X~~X ) * (EN*SY_?-=-~_!'~::;~LL:liI"_~.. 5 _____ _
IF(R)6.7,7
6 RA=-R
GO TO 8
7 RA=R
8 S2SX=(EN*SX2-SX*SX)/(EN*(EN-l.»
S 2 S Y = ( EN* S Y?= ?Y_*5,_'('_!~~N'lE-~ N- l_!_ ~L ____
YGX=«EN-l.)/(EN-2.»*(S2SY-B*B*S2SX)
11 T=BA/SB
IF(T)12.13.13
12 TA=-T
GO TO 14
13 TA=T
14 DF2=EN-2.
-------- ----- ----- -----------~--- ----
~EX:: (LSX2____ SX *5 XLEI"L1L---LE~_._LL*~5
SEY=«SY2-SY*Sy/EN)/(EN-l.»**.5
PUNCH .. CONC.A.B
---
PUNCH.RA.TA,DF2
PUNCH.SB.SYGX
-- - -"."'- -- - ----
GO TO 3
------~----~-- -~--
----------- ~-----
------

NOMENCLATURE FOR PHASE III
.... t -
A
A
B
= B 1m aO@Te eq~ati0B
CONC = Coneentra tion o:f Carb0:pol (used :for identif'i~ation
N
}!
TEMP
XINT
XSL
;;
=
=
=
::
l''1.lJ:'Iposes)
Number o:f sets o:f aata :for each :fluid
C@nstant equal te 2.0
Tellq3eratui"e
L0g K
Flew behavior index (used in Phase IV)

Phase IV
Correlation of Flow Behavior Index
With Temperature
3 READ.N.M
4 EN=N
500
EM=M
SX=O.
n
500
B(Temp.) + A
SV=O.
500
SXV=O.
500
-----------------------------------S-oo-·
SX2=0.
Sv2=0.
500
(Nomenclature Same as
0051 = 1 .N
506
READ.CONC.TEMP.XINT.XSL
X=TEMP
V=XSL
SX=SX+X
Phase III except A
and B are defined --.----soo--
Sv=sv+v
500
as above)
SXY=SXy+x*y
500
Sx2=SX2+X*X
5 sv2=Sv2+v*Y
XBAR=SX/EN
YBAR=Sv/EN
CX2=SX*Sx/EN
CXY=SX*sv/EN
VX2=SX2-CX2
vxv=sxv-cxv
B=VXY/VX2
A=VBAR-B*XBAR
C=Sxv/SX2
R= ( (

I!JS
APPENDIX B
~
1. Heat Transfer Data
2. Computer Programs For Calculating Heat
Transfer Results
3. Heat Transfer Results

96
HEAT TRANSFER DATA
FOR WA'fER
USING NON-STANDARD
Ifc1PELLER POSITIONS

DATA
137
'tfATER
Batch Weight
94.0 Ibs. 'rime 2.0 min.
Run
Heatine;
47
48
49
50
Diameter
x Height
(inches x
inches)
9.0
9.0
9.0
9.0
RP~I Are:J. 2
(ft. ) Dynamometer Temperature (oC)
Scale Batch Aa11
(lbs) 1 2 1 2
Ancho:!: -
50
go
1 ')5
210
Clearance = 3.0 inches
6.20
6.20
6.23
6.3S
0.?7
1. "?8
4. ')5
8.73
61.0
74.7
73.1
66.0
78.0
88.7
88.6
84.1
77. 1 +
tl.5.1
C32.3
74.9
89.2
95.7
94.0
'90.0
Cool~n.£
47
48
49
50
9.0
9.0
9.0
9.0
50
90
15')
210
6.20
6.20
0>.27;
6.'S')
0.37
1.38
'-1.55
8. T5
8'S.5
58.1
73.3
51. 9
69.6
49.0>
60.2
1+3. ')
70.3
51.0
66.0
l't-7.7
59.6
/~.L~. 0
54.5
40.0
!:!eati~
55
54
53
52
51
Cooling
55
5L~
53
52
51
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
9.0 x 0.7
llO
170
242
365
445
llO
170
21+2
)65
445
6.20
6.20
6.23
6.23
6.27
6.20
6.20
6.23
6.

DATA
/98
Batch \'ieight '" 94 •. 0 1bs.
PADDLES
Time = 2.0 min.
Run Center Diameter RPJ'v! Area 2
Dynamometer Temperature COC)
Height x Height (ft. ) Scale Batch Wall
(inches) (inches x (lbs) 1 2 1 2
inches)
Heatin~
60 4.5 8.0 x 1.0 126 6.20 0.53 71.0 84.5 85.8'95.5
61 4.5 6.0 x 1.0 127 6.20 O~15 68.1 S1.3 sri

'"
Run Center Diameter RP}! Area Scale Temperature cOe)
Height x Hei~ht Batch 'rlall
1 2 1 2
43 9.0 8.0 x 2.0 250 6.35 7.70 '15.8 90.6 82.9 94.5
108 9.0 5.0 x 1.5 104 6.20 0.16 75.0 86.5 88.8 95.7
109 9.0 5.0 x 1.5 190 6.20 0.48 77.3 89.7 87.1 95.7
110 9.0 5.0 x 1.5 =535 6.23 1.76 70.7 86.3 80.3 92.5
111 9.0 5.0 x 1.5 515 6.2'/ 4.23 63.0 81.2 71.7 87.6
56 10.0 8.0 x 4.0 49 6.20 0.43 60.7 77.8 75.5 88.2
57 10.5 8.0 x 1.0 125 6.20 0.56 68.0 134.3 82.2 93.0
Cooli!lli
60 4.5 8.0 x 1.0 126 6.20 0.5"-> 87.5 7~).1 76,,3 62.3
61 4.5 6.0 x 1.0 12'7 6.20 0.10 57.1 49.3 L~5.0 38.9
28 5.0 ,-~. 0 x 2.0 100 6.20 0.03 1i4.8 39.5 33.5 28.6
29 5.0 '4-.0 x 2.0 luO 6.20 0.03 43.3 37.8 3~.7 30.2
30 5.0 4.0 x 2.0 190 6.20 0.09 1~5 .2 39.0 35.9 29.3
31 5.0 4.0 x 2.0 :s :~5 6.23 1.00 57.6 48.0, 51.0 '+1.9
32 5.0 4.0 x 2.0 53~ 6.2-; 2.10 '+0.0 ~jl • • (.; 35.8 31.7
33 5.0 4.0 x 2.0 620 6.27 2.8') 56.0 i·7.6 50.6 43.0
38 6.0 5.0 x 2.0 92 6.20 0.15 53.7 46.5 '4-2,7 37.2
37 6.0 5.0 x 2.0 185 6.20 0.55 75.8 62.7 64.3 53.5
36 6.0 5.0 x 2.0 2'1-2 G.20 1.00 51. 5 43;9 46.7 39.9
35 6.0 5.0 x 2.0 390 fl,23 (~. 85 54.1+ '-1-6.0 ~9,2 41.8
34 6.0 5.0 x 2.0 1+75 6.27 4.70 46.'1 39·7 11-0).2 36.'1
59 6.5 8.0 x 1.0 125 6.20 0.57 8'3.7 69.6 71.4 58.8
63 6.5 6.0 x 1.0 125 6.20 0.15 60.7 52.3 48.7 41.7
66 6.5 i •• O x 1.0 125 6.20 0.02 83.8 72.3 65.5 54.5
116 6.63 5.0 x 0.75 120 6.20 0.11 65.0 56.5 49.5 42.8
117 6.63 5.0 x 0.75 '320 6.20 0.40 5?0 1+5.6 ll-S,8 39.3
118 6.63 5.0 x 0.75 515 6.23 1.28 68.4 57.'+ 59.4 51. 3
119 6.63 5.0 x 0.75 715 6.2;; 2.63 56.0 46.9 50.2 42.3
112 7.63 5.0 x 0.75 l:.)U 6.20 0.05 54.9 413.8 41.6 36.8
113 7.63 5.0 x 0.75 315 ':'.20 O.4:S 53.9 4b.4 46.5 40.0
114 7.63 5.0 x 0.'75 5l? 6.23 1. 31 54.8 46.9 48.2 41.5
115 7.63 5.0 A 0.75 705 6.23 2.56 60.8 5L3 54.8 46.8
21" 8.0 7.0 x 2.0 7H 6.27 0.24- h6.6 il-0.6 41.B :56.3
t::2~ 8.0 7.0 x 2.0 117 6.27 0.85 65.5 56.1 S'7.3 50.0
23" 8.0 '7.0 x 2.0 184 6.27 2.20 51.2 44.0 46.7 40.1
24' 8.0 7.0 x 2.0 220 6.27 ? .1+3 't7.5 1+1.0 43.0 37.9
25' 8.0 7.0 x 2.0 260 6.27 4.93 82.0 68.0 74.0 62.0
27' 8.0 7.0 x 2.0 285 6.20 6.1'7 61.0 51.6 55~8 47.8
58 8.5 B.O x 1.0 125 6.20 0.58 69.7

zoo
Run Center Dia!!1ec;er Ri'M Area Scale TemDerature COO)
Heip,-ht Batch \'Iall
1 2 1 2
44 9.0 B.O x 2.0 190 6.27 4.28 78.2 65.7 71.3 60.0
43 9.0 fl.. 0 x 2.0 250 6.35 7.70 l1-2.5 36.5 39.0 33.7
108 9.0 5.0 x 1.5 101~ 6.20 0.16 41. 3 36.6 34.9 31.3
109 9.0 5.0 x 1. '5 190 6.20 0.48 51.1 44.2 44.9 38.6
110 9.0 5.0 x 1.S 33S 6.23 1.76 [I-LI- o 9 '59.0 40.8 35.3
111 9.0 5.0 x 1.5 515 6.27 4.23 60.9 51.1 56.3 47.2
56 10.0 8.0 x 4.0 49 6.20 0.43 71.0 60.5 60.8 52.8
57 10.5 8.0 x 1.0 125 6.20 0.56 :;'4./ 47.7 48.0 41.7
• Batch '1leir;ht

WATER -
Batch i'ieight = 94.0 Ibs.
DATA
PROPELLERS
Time", 2.0 min.
Run Clearance Diameter RPf'l Area? Dynamometer Temperature (oC)
Cinches) (inches) (ft.·- ) Scale Batch viall
(lbs) 1 2 1 2
Heating
147 6.0 5.2 110 6.20 0.04 73.0 85.1 90.6 97.8
148 6.0 5.2 350 6.20 0.32 64.8 81. 5 79.2 91.0
149 6.0 5.2 540 6.20 0.79 6'?6 81.3· 76.3 89.4
150 6.0 . 5.2 765 6.20 1.74 f.i6.8 84.3 '77.1 91.2
151 8.0 5.2 105 6.20 0.02 71.6 83.8 89.7 96.3
152 8.0 5.2 315 6.20 0.26 64.3 80.5 79.0 90.3
153 B.O 5.2 535 6.20 0.86 70.8 84.8 81.0 91.2
154 8.0 5.2 768 6.20 1.84 77.8 92.2 87.0 97.4
161 12.0 5.2 116 6.20 0,04 56.4 72.1 79.5 88.0
164 12.0 5.2 327 6.20 0.32 63.3 80.1 76.8 89.4
162 12.0 5.2 335 6.20 0.28 56.2 82.4 78.8 90.8
163 12.0 5.2 628 6.20 1.25 6l~.3 82.3 74.2 89.5
Cooling
147 6.0 5.2 110 ().2u 0.04 l~9. 7 43.7 38.8 -53.5
148 6.0 5.2 350 6.20 0.32 l~6.4 40.0 40.0 35.0
149 6.0 5.2 540 6.20 0.79 52.2 .44.5 46.6 39.7
150 6.0 5.2 765 6.20 1.74 62.7 52.3 56.8 47.7
151 8.0 5.2 105 6.~0 0.02 4'7.8 42.5 35.8 31.8
152 8.0 5.2 315 (').20 0.26 '+6.5 1.0.2 40.0 34.9
153 8.0 5.2 )35 h.20 0.86 53.9 '-1-5.9 48.2 40.9
154 8.0 5.2 7613 6.20 1.84 39.7 33.8 36.2 31.0
161 12.0 5.2 116 6.20 0.04 49.0 4,.5 3.9.4 35.0
164 12.0 5.2 327 6.20 :).32 54.8 47.4 '+8.3 42.0
162 12.0 5.2 335 6.20 0.28 85.9 71. '5 75.5 62.2
163 12.0 5.2 628 6.20 1.25 62.0 52.0 5,:0.5 47.3
2tJ/

DATA
20l.
WATER - TUHBINSS
Batch Weight = 94.0 Ibs.
Time = 2.0 min.
Run Center Diameter RPi'l Area2 Dynamometer Temperature (oC)
Height x Height Ut. ) Scale Batch 'liall
(inches) (inches (lbs) 1 2 1 2
x inches2
HeatinG
Disk & Vane 'l'urbines
132 5.0 6.0 x 1.25 85 6.20 0.28 5~.2 ~6.3 77.1 88.3
133 5.0 6.0 x 1.25 145 6.20 0,86 6 .8 0 •. 0 76.6 ·89.2
134 5.0 6.0 x 1.25 260 6.23 3.14 76.0 90.7 85.3 96.1
135 5.0 6.0 x 1.25 338 6.27 5.64 '17.8 91.7 85.5 96.2
136 9.0 6.0 x 1.25 80 6.20 0.24 62.2 77.8 77.5 -87.2
137 9.0 6.0 x 1.25 155 6.20 1.16 73.7 88.3 83.8 94.9
138 9.0 6.0 x 1.25 255 6.23 3.31 58.7 77.7 67.8 84.7
139 9.0 6.0 x 1.25 330 6.27 5.70 65.3 84.0 73.1 89.5
Six-Blad~d - Open Bladed 'l'urbine - 3trai6ht Blades
177 7.0 4.0 x 0.75 III h.20 0.05 52.0 68.2 77.7 86.4
178 7.0 4.0 x 0.75 235 6.20 0.23 67.8 83.2 82.2 93 •. 7
179 7.0 4.0 x 0.75 320 6.20 0.48 69.3 81~.4 82.3 93.4
180 7.0 4.0 x 0.75 505 6.20 1.38 69.3 85.0 81.0 92.3
lEll 7.0 4.0 x 0.75 705 6.23 2.73 ;:)6.9 83.7 76.0 90.1
Six-Bladed ~n Bladed Turbine - Curved Blades
182 7.0 4.0 x 0.50 218 6.20 0.25 73.0 85.3 88.1 96.0
183 7.0 4.0 x 0.50 453 6.20 0.51 69.0 84.1 80.8 92.7
184 7.0 4.0 x 0.50 710 6.20 1.41 68.1 84.? 79.4 92.1
185 7.0 4.0 x 0.50 940 6.20 2.68 65.6 83.0 75.9 89.8
Cooling
Disk & Vane Turbines
132 5.0 6.0 x 1.25 85 6.20 0.28 47.8 41.7 40.0 35.5
133 5.0 6.0 x 1.25 145 . G.20 ,) .86 49.1 42.1 42.9 36.9
134 5.0 6.0 x 1.25 26,; 6. ,~3 3.14 54.5 46.0 49.0 41.7
135 5.0 6.0 x 1.25 33['. (.,.27 5. ;.',4 51.0 L~2 .8 46.8 39.4
136 9.0 6.0 x 1.25 80 6.20 0.24 68.7 58.1 58.1 50.2
137 9.0 6.0 -x 1. 25 155 6.20 1.16 41.3 40.7 L~2. 7 36.7
138 9.0 6.0 x 1.25 2')5 6.,23 3.31 52.7 44.7 48.7 41.2
139 9.0 6.0 x 1.25 ?:,O 6.27 5.70 49.6 42.4 45.8 39.7
Six-Bladed - Open Bladed I.'urbine -·otrai[.!;ht rllades
177 7.0 4.0 x 0.75 111 6.20 0.05 61.7 54.3 48.0 41.8
178 7.0 4.0 x 0.75 235 6.20 O.d L~J.j.. 1 -j8.L~ 37.7 32.8
179 7.0 4.0 x 0.75 320 6.20 . 0.48 !14.0 ?ti.O 38.1 33.0
180 7.0 4.0 X 0.75 505 6.20 1. 38 54.5 lj·6.3 4tL7 41.7
181 7.0 4.0 x 0.75 705 G.2~ 2.73 45.5 313.7 41.3 35.7

Run
Center
Height
Six-Bladed -
182 7.0
183 7.0
184 7.0
185 7.0
Diameter
x Heicht
Open Bladed Turbine -
4.0 x 0.50 218
4.0 x 0.50 453
4.0 x 0.50 710
4.0 x 0.50 940
Area
Curved
6.20
,S.20
0.20
6.20
Dynamometer -Temperature (°0)
Scale Batch Wall
1 212
Blades
0.25 51.3 44.4 41.9 36.9
0.')1 56.7 48.3 49.6 42.2
1.41 5'1.5 48.'1 51.7 44.1
2.68 61.8 52.0 56.2 47.2

204-
HEAT T'rtANSFEH DATA
USED IN CORRELATIONS

DATA
ANCHOR
2. OJ
~'IA:l'ER
Batch Weight = 94.0 Ibs.
Clearance = 5.0 inches
Run Diameter RPl"l Area2 D;}'TIamometer Temperature (oC) Ti:ne
(inches) (ft. ) Scale Sutch Wall
(lbs) 1 2 1 2
Heating
67 9.0 55 6.20 0.56 .">7.;') 7"'5.1 72.7 8'5.6 2.0
68 9.0 90 6.23 1.58 77.4 89.0 85.8 94.2 2.0
69 9.0 150 6.27 4.68 ('9.5 92.7 86.2 97.0 2.0
70 9.0 207 6.38 8.83 67.3 84.3 75.2 90.1 2.0
Coolin[3:
67 9.0 55 6.20 0.56 42.2 36.6 36.7 31.7 2.0
68 9.0 go 6.23 1. S8 40.1 34.8 36.2 31.4 2.0
69 9.0 150 6.27 4.68 L~7. 3 40.7 4":.L!. 37.2 2.0
70 9.0 207 6.38 8.53 59.5 49.5 54.5 45.8 2.0
93.7% GLYCERINE
Batch Weight 117.7 Ibs. Clearance 5.0 inches
!:!~atinfl:
235 9.0 56 6.20 0.6-') :)'5.9 64.0 96.4 97.8 2.0
236 9.0 96 6.20 2.15 59.3 71.6 92.8 97.2 2.0
237 9.0 152 6.20 5.4-0 52.7 66.3 81.g 30.0 2.0
238 9.0 196 6.23 ;;.25 5,.0 :")0.8 79.9 68.3 2.0
CooliQ15.
235 9.0 56 6.20 0.63 62.9 55.7 26.4 23.1 2.0
236 9.0 96 6.20 2.15 09.8 58.7 36.1 29.1 4.0
237 9.0 152 6.20 5.40 68.2 56.? 1+0.6 31.4 L~. 0
238 9.0 196. 6.23 9.25 45.3 38.2 ;~5.2 20.4 4.0

DATA
ANCHor;:
206
Batch :'Ieight = 94.4 1bs.
CARnOPOL :::;OLU ~'ION3
C1e8.rilnce = 5.0 inches
Run Diameter RPf\~ Area;? ;)ynHmOr.1eter Tempp.I":--=-.ture CoC) Time
(inches) (ft. ) 0cf11e Batch I'lall \r:lin)
(lbs) 1 c:. 1 2
---------- ... _- ------- ~.-.
0.1 ';, :r'crce!'1t CATrF',O?OL
!!~~tinr:
373 9.0 5B h.20 0.h7 53.2 6'>. C; 8R.8 9/).6 2.0
374- 9.0 97 6.20 1.8": 56.) 68.1 83.8 90.5 2.0
375 9.0 1')8 '.20 ':>.0;) 52.7 G0.? '10.3 82.(\ 2.0
376 9.0 ,'06 6.27
:~ _ 9 'I
:)/·1-.5 GEl.7 69.5 Hl.2 2.0
Q£()ling
373 9.0 5t3 6.20 (J. ;',7 58.6 50. L~ :,8.1 -,2.'> le.O
374- 9.0 97 6.20 1.S'i ,6.5 5'-1.2 '+7.7 59.4 4.0
375 9.0 158 6. ,:0 5.03 59.2 4·6.d 47.5 '>7.2 11-.0
376 9.0 =0(; 6.27 8.9'> ,,6.0 50. '3 5 L I.8 41.8 4.0
0.c.0 re~£ent
Q~RJOPO~
Heo.t:i!l3.
415-2 9.0 .8 38.2 11-.0
Heating
~24 ~~~ceg!_f~~TIQ?OL
1~56 9.0 157 6.20 5.2l~l 50.3 60.8 :-,d. (-) Cj2.1 2.0
455 9.0 186 6.20 6.6:'; 4.c:l.7 61.3 8').4· ClO.l 2.0
Lj·54 9.0 20 L I- 6.20 B.O:S 40.d 54.1 '79.0 8').2 2.0
Cooling
457-2 9.0 138 6.20 3.36 ll-'l. ~~ 42.7 27.8 211-.8 6.0
4·56 9.0 167 6.20 5.28 5'i·O 1+4.3 -3'L5 28. l j- 6.0
,'- r- 'Z
455 9.0 186 6.20
~) .. 8) 60.1 118.7j 42.5 =53.6 6.0
454 9.0 2()L, 6.20 8.0'; 52.U 11-2.1 37.3 )0.7 l) .0

DATA
PADDLBu
207
:?lJl.'J'ER
Batch ',,{eight 94.0 lbs. Center Heie;ht = 7.0 inches
Run Diameter RPf~l Area 2
Dynamometer 'rern!)ersture (oC) Time
x Heic;ht (ft. ) Scale Batch Wall (min.)
(inches x (lbs) 1 2 1 2
inches)
------------- -~
iIeatinr;
124 L~. 0 x 1.0 llO 6.20 0.07 56.6 71.0 79.8 90.0 2.0
125 L~. 0 x 1.0 3l~0 6.20 0.3? 65.0 80.5 bO.6 91.0 2.0
126 L~. 0 x 1.0 525 6.20 0.87 72.9 86.8 83.5 93.9 - 2.0
127 4.0 x 1.0 724 6.23 1.84- 82.0 9l~. ::; 89.3 98.8 2.0
120 LJ-.O x 2.0 105 6.20 0.15 67.6 eO.7 84.5 92.4 2.0
121 4.0 x 2.0 304 6.20 0.59 64.7 80.7 n.5 H9.? 2.0
122 4.0 x 2.0 472 6.,23 1.69 69.7 85.7

2.08
Run Diameter RP!'1 Area Dynamometer I'empcrature CoC) Time
x Height Batch \;,Iall
1 2 1 2
84 7.0 x 3.0 75 ;:'.20 0.50 '71.1 8').0 82.7 92.8 2.0
85 7.0 x 3.0 120 6.20 L "38 61.7 79.8 74.1 '38.2 2.0
86 7.0 x 3.0 195 6.2-5 3.98 62.3 8L3 72.7 88.6 2.0
87 7.0 x 3.0 270 6.27 8.0:;; 63.7 E12.5 72.3 (58.5 2.0
75 8.0 x LO 78 6.20 0.17 76.7 87.8 ()9.7 96.8 2.0
76 8.0 x 1.0 77 6.20 0.15 82.8 92.3 94.0 99.0 2.0
77 8.0 x 1.0 150 (:,.20 0.82 76.0 87.6 8h. l l- 95. 1 + 2.0
78 8.0 x 1.0 260 6.2>; 2.85 59.0 78.0 70.7 86.7 2.0
79 8.0 x 1.0 360 6.27 5.:>8 72.7 88.? 81.2 94.0 2.0
71 8.0 x 2.0 58 6.20 0.25 63.3 83.0 83.1 92.7 2.0
72 8.0 x 2.0 105 6.23 1.15 64.1 81.4 77.1 90.1 2.0
73 8.0 x 2.0 194 6.23 4.25 83.0 9i~ .. 2 89.5 97.9 2.0
74 8.0 x 2.0 260 6."31 8.28 79.0 92.2 85.6 96.3 "2.0
80 8.0 x 4.0 60 6.20 0.53 4·5.3 65.4 61.9 ;8.9 2.0
81 8.0 x 4·.0 92 6.20 1. 59 58.() 76.1 70.7 85.3 2.0
82 8.0 x 4.0 l L I-8 6.23 1+.75 58.6 77.2 68.7 84.5 2.0
83 8.0 x 4.0 200 6.'55 9.03 62.3 al.'5 70.0 87. 7 , 2.0
Coo line;
124 4.0 x 1.0 llO 6.20 0.07 66.9 58.5 49.1 112.8 2.0
125 4.0 x 1.0 340 S.20 0.33 55.7 47.9 47.0 41.2 2.0
126 4.0 x 1.0 525 6.20 0.87 48.3 LI-1. 3 42.3 '56.7 2.0
127 4.0 x 1.0 724 6.23 1.8a 56.7 48.8 50.7 43.2 2.0
120 4.0 x 2.0 105 6.20 0.15 66.9 50.6 46.2 1-l·0.·3 2.0
121 4.0 x 2.0 304 6.20 0.5'3 66.8 57.0 58.1 50.0 2.0
122 4.0 x 2.0 472 6.23 1.69 52.7 1+5.2 1+7.8 40.3 2.0
123 4.0 x 2.0 598 6.23 2.89 52.6 [1-4.8 4/.6 41.1 2.0
lll-3 5.0 x 1.0 96 6.20 0.05 4·9.8 4 1 +.2 40.3 36.1 2.0
146 5.0 x 1.0 112 6.20 0.11 6LI-.2 55.5 52.3 .45. 1 1- 2.0
144 5.0 x 1.0 295 5.20 0.70 56.5 48.3 50.4 42.8 2.0
14·5 5.0 x 1.0 475 6.23 1.38 49.5 42.2 45.0 38.5 2.0
104 5.0 x 1.5 98 6.20 o.n 42.0 36.9 34.1 29.7 2.0
105· 5.0 x 1.5 185 6.20 0.40 i1-6.0 33.9 39.8 3L~. 7 2.0
106 5.0 x 1.5 356 6.23 1. 73 4'7.3 [j·0.6 112.6 3to.5 2.0
107 5.0 x 1.5 540' 6.27 4 •. 28 T5.8 61.3 66.8 55.8 2.0
100 5.0 x 2.0 107 6.20 0.25 47.4 42.1 39.8 35.1 2.0
101 5.0 x 2.0 11'35 6.20 0.33 44.0 3(:,.2 38.8 53.8 2.0
102 5.0 x 2.0 335 6.2"3 2.03 54.3 4·6.2 l~9. 0 42.2 2.0
103 5.0 x 2.0 455 6.23 3.88 73.3 60.4- 66.3 55.3 2.0·
96 6.0 x 1.0 112 6.20 0.21 61.9 53.4 4 ).5 il·,.O 2.0
97 6.0 x 1.0 190 6.20 0.47 ')0 .. ') 43.5 42.7 37.5 2.0
98 6.0 x 1.0 358 6.20 1.9, 51.8 44.3 46.5 3).5 2.0
99 6.0 x 1.0 478 6.23 "')."73 51.6 43.7 47.0 40.0 2.0
33 6.0 x 2.0 85 6.20 O.!? 49.5 4'5.3 42.1 36.2 2.0
40 6.0 x 2.0 130 6.20 0.55 62.7 52.9 54.0 46.0 2.0

209
Run Diameter RH1 Area !)ynamometer Temperature (oC) 'rime
x Height Batch 1:lnll
1 2 1 2
41 6.0 x 2.0 260 6.23 2.59 5Lj .8 47.1 50.1 L"3.1 2.0
42 6.0 x 2.0 350 h.27 5.08 60.7; 50.9 55.6 47.0 2.0
92 7.0 x 1.0 108 6.20 0.24 67.8 57.3 55.7 46.5 2.0
93 7.0 x 1.0 1'76 6.20 0.61 61.5 52.2 53.7 45.5 2.0
94 7.0 x 1.0 305 6.23 2. ::s6 68.2 57.1 60.7 50.8 2.0
95 '1.0 x 1.0 407 6.2'S L". -;; 3 50.1 42.4 45.9 ')9.0 2.0
88 -7.0 x 2.0 77 6.20 0.29 76.R 64.4 65.8 55.2 2.0
89 7.0 x 2.0 l?5 6.20 1.16 51.8 44.5 46.0 -)-l. 6 2.0
90 7.0 x 2.0 225 ,:;.23 3.58 77.7 67.0 69 •. 5 57.2 2.0
91 7.0 x 2.0 326 6.27 7.88 53.7 44.8 49.8 42.0 2.0
84 '7.0 x 3.0 75 6.20 0.50 70.2 ,')0.0 61.7 52.7 2.0
85 7.0 x 3.0 120 6.20 1. 58 61.7 52.3 55.':> 47.1 2.0
86 7.0 x 3.0 195 6.23 3.98 49.2 L~1.6 l>5.1 38.2 2.0
,r ~
87 '7.0 x 3.0 270 6.27 8.03 .(") • .? S I I.8 60.7 50.8 2.0
75 8.0 x 1.0 78 6.20 0.17 50.4 !;·3.5 LI-2.0 36.0 2.0
76 8.0 x 1.0 '77 6.20 0.15 43.9 78.4 76.9 32.3 2.0
'77 8.0 x 1.0 150 6.20 0.82 54.4 46.8 48.0 41.0 2.0
78 8.0 x 1.0 260 6.d 2.85 59.1 50. L " 53.6 45.6 2.0
79 8.0 x 1.0 360 6.27 5.58 46.4 39.4 42.8 36.1 2.0'
71 8.0 x 2.0 58 6.20 0.25 58.5 50.3 49.8 11-2.6 2.0
72 8.0 x 2.0 105 6.23 1.15 46.7 40.0 4] .2 35.3 2.0
73 8.0 x 2.0 194 6.23 4.25 8'1.0 /0.9 7-).5 (')4.9 2.0
74 8.0 x 2.0 260 6.71 8.28 4').3 :;i6.8 40.Lj- ':>4.4 2.0
80 8.0 x 4.0 60 6.20 0.53 i32.2 67.9 70.1 59.0 2.0
81 8.0 x 4.0 92 6.20 1. 59 62.2 52.') 55.7 47.2 2.0
82 8.0 x 4.0 148 6.2') 4-.75 'j5.0 44.B 4£3.7 41.1 2.0
83 8.0 x 4.0 200 6.35 9.07 60.0 l19.9 55.0 4-6.4 2.0

DAT_':
210
"i'ADDI,ES
9:5.7'10 GLYCERINE
Batch ':!eie;ht 117.7 lbs. Center Height = '1.0 inches
Run Diameter R?t'i Area 2
Dynamometer 'l'emperature COC) Time
x Heie;ht (ft. ) ;Scale Batch \'la11 (min)
(inches x (lbs) 1 2 1 2
inches)
----------------------
He§:~i!!E
262 4-.0 x 1.0 2L~0 h.20 0.23 4-4-.S 53.2 96.0 96.S 2.0
261 4-.0 x 1.0 11-65 0.20 0.69 53.3 64.3 94-.2 96.0 2.0
260 4-.0 x 1.0 70S 6.20 1.80 54-.8 67.5 90.7 94-.8 2.0
259 4-.0 x 1.0 935 6.20 '5.35 bl.8 74-.8 gO.8 95.4 2.0
258 4.0 x 2.0 22lJ. 6.20 0.37 48.2 5';.7 gil-. 2 96.8 2.0
257 4.0 x 2.0 520 6.20 0.81 (-)4-.1 73.9 95.8 QS.3 2.0
256 lJ..0 x 2.0 4-25 6.20 1. 1 1-5 53.5 66.0 a8.S 96.3 2.0
255 4-.0 x 2.0 570 6.20 2.60 59.7 72.'+ 90.3 95.S 2.0
253 6.0 x 1.0 105 6.20 0.15 LI-0.2 i~j. LI ')5.2 97.2 2.0
254- 6.0 x 1.0 198 6.20 0.68 56.5 66.7 96.5 97.8 2.0
252 6.0 x 1.0 333 6.20 1.d8 69.3 79.5 96.8 ?9.2 2.0
251 6.0 x 1.0 1+98 6.20 4-.'75 55.5 69.7 BS.2 93.5 2.0
250 6.0 x 2.0 S5 6.20 0.25 Y?9 Lj.9.8 96.1 96.7 2.0
24-9 6.0 x 2.0 152 6.20 1.10 58.1 67.0 93.1 93.2 2.0
24-S 6.0 x 2.0 280 6.20 3.25 ')9.7 '72.1 89.13 95.3 2.0
21.1·7 6.0 x 2.0 355 6.20 5.60 1~-6.8 53.2 SO.) 91.0 2.0
246 8.0 x 1.0 90 6.20 0.37 i1-9.8 59.3 95.8 98.2 2.0
24-5 8.0 x 1.0 Fi4- 6.20 1.11 lJ.9.8 61.3 92.8 95.7 2.0
244- 8.0 x 1.0 260 6.20 ;;.50 '.00. 1 1- 7"'5.2 -n.9 95.7 2.0
24·3 8.0 x 1.0 336 6.?0 ':"i. 95 48.0 64.1 83 .(~ 90.3 2.0
242 8.0 x 2.0 78 6.2(; 0.55 50.6 GO.8 95.7 97., 2.0
24-1 8.0 x 2.0 122 6.2u 1.67 \-)f,.0 76.0 9').2

2JJ
DATA
PADDLES
93.7'}6 GL'!CEfUNE
Batch \'ieight 117.7 Ibs. Center Height = 7.0 inches
Run Diameter RPM Area 2
Dynamometer Temperature (oC) Time
x Height (ft. ) Batch \'iall (min)
(inches x 1 2 1 2
inches)
-----.--- - --------------
Q~~l~~g
262 1~. 0 x 1.0 2L~0 6.20 0.23 60.3 55.1 23.3 20.1 4.0
261 4.0 x 1.0 465 6.20 0.69 66.8 5t3.2 30.8 24.2 l~. 0
260 4.0 x 1.0 708 6.20 1.80 65.0 55.2 35.2 26.3 4.0
259 4.0 x 1.0 935 6.20 3.35 5g.7 49.7 32.2 211.4 4.0
258 4.0 x 2.0 224 6.20 o. )7 57.6 51.9 22.7 20.5 4.0
257 4.0 x 2.0 320 6.20 0.81 64.6 56.5 29.9 25.3 4.0
256 4.0 x 2.0 425 6.20 1,1+5 '-';5.8 76.3 32.Q 27.6 4.0
255 4.0 x 2.0 570 6.20 2.60 64.0 53.7 3S.6 28.2 4.0
253 6.0 x 1.0 105 6.20 0.15 60.6 55.8 21.3. 19.4 4.0·
254 6.0 x 1.0 198 6.20 0.68 62.5 55.':: 25.2 23.5 4.0
252 6.0 x 1.0 1'33 6.20 1.Ba 65.8· 55.8 34.8 27.0 4.0
251 6.0 x 1.0 498 6.20 4.55 60.7 50.5 35.0 2'7.2 1~.0
250 6.0 x 2.0 85 6.20 0.25 (;1.2 55.7 22.8 21.6 1+.0
249 6.0 x 2.0 15.:: 6.20 1.10 56.L~ ')0.0 2L~. 7 21.2 L~. 0
248 6.0 x 2.0 280 6.20 3.25 58.Li l~9. 5 31. 5 24.7 4.0
247 6.0 x 2.0 355 6.20 5.60 5E.2 11·8.4 34.0 25.2 4.0
246 8.0 x 1.0 90 6.20 0.37 57.8 52.2 19.8 18.7 4.0
245 8.0 x 1.0 154 6.20 1.11 ;:)4.0 55.7 28.0 23.2 4.0
244 8.0 x 1.0 260 6.20 3.50 6/+~6 54'03 34.7 27.2 lj·.O
243 8.0 x 1.0 336 6.20 5.95 80.9 71. 3 57.3 43.3 4.0
2LI2 8.0 x 2.0 78 6.20 0.55 61.3 54.8 23.7 21.2 4.0
241 8.0 x 2.0 122 6.20 1.67 66.4 56.8 33.3 27.1 4.0
240· 8.0 x 2.0 192 6.20 4.60 65.7 52.4 ;>6.8 29.5 4.0
239 8.0 x 2.0 2:;'5 6.23 8.10 64.3 52.7 38.9 30.Lj· L~. 0

212
DATA
PADDLES
0.15 PEHC:::N'r CARBOPOL
Batch Weight 94.4 l'bs. Center Height = 7.0 inches
Run Diameter RPt'l Area 2
Dynamometer Temperature cOe) Time
x Height (ft. ) Scale Batch Wall (min)
(inches x (Ibs) 1 2 1 2
inches)
Heating
345 4.0 x 1.0 224 6.20 0.17 48.6 57.1 94.8 96.5 2.0
346 4.0 x 1.0 j24 6.20 0.20 56.8 66.0 92.13 95.2 .2.0
=547 '+.0 x 1.0 540 6.20 0.83 53.8 65.2 8i).7 93.1 2.0
348 4.0 x 1.0 696 6.20 1.45 49.5 61.8 76.2 87.9 2.0
31.19 4.0 x 2.0 216 6.20 0.25 55.3 64.5 89.8 92.8 2.0
350 4.0 x 2.0 320 6.20 0.61 56.9 67.5 88.1 93.4 2.0
351 lj-.O x 2.0 494 6.20 1. 71 62.0 7,.3 88.3 93.7 2.0
352 4.0 x 2.0 622 6.20 2.78 51.7 65.0 73.3 86.8 2.0
357 6.0 x 1.0 103 6.20 0.15 38.7 47.7 92.3 94.3 2.0
358 6.0 x 1.0 272 6.20 1.05 58.9 69.8 89.5 93.6 2.0
359 6.0 x 1.0 416 6.20 2.63 58.3 70.7 83.7 91. 3 2.0
360 6.0 x 1.0 526 6.20 4.33 53.8 67 .L~ 73.4 86.3 2.0
361 6.0 x 2.0 93 6.20 0.31 L16.7 56.9 '-;9.7 92.7 2.0
362 6.0 x 2.0 167 6.20 0.85 51.6 63.1 86.7 93.0 2.0
363 6.0 x 2.0 292 6.20 2.93 60.7 73.2 84.3 92.7 2.0
364 6.0 x 2.0 390 6,20 5.28 54.7 68.7 72.9 85.8 2.0
365 8.0 x 1.0 94 6.20 0,4') 4Q.7i ')9.0 QO.2 94.8 2.0
366 8.0 x 1.0 11~3 6.20 0.77 50.S 62.2 86.0 93.0 2.0
367 8.0 x 1.0 280 6.20 3.35 45.8 60.2 73.3 84.2 2.0
368 8.0 x 1.0 _354 6.20 5.63 (')3.7 76.5 84.8 92.0 2.0
369 8.0 x 2.0 70 6.20 0.43 L1-8. ') 59.2 87.7 92.2 2.0
370 8.0 x 2.0 121 6.20 1. 35 52.9 6l1-.8 83.8 90.8 2.0
371 - 8.0 x 2.0 206 6.?O ll-.38 59.2 72.3 80.2 90.3 2.0
372 8.0 x 2.0 254· 6.27 7.03 53.8 67.8 70.3 82.2 2.0

i!.IJ
DATA
PADDLE::;
0.15 PERCENT CARBOPOL
Batch ~Ieight 94.4 lbs. Center Height = 7.0 inches
Run Diameter RPM Area Dynamometer Temperature (oe) Time
x Height (ft. 2) Scale Batch Wall (min)
(inches x (lbs) 1 2 1 2
inches)
---.~----------------
Cool~
345 4.0 x 1.0 224 6.20 0.17 62.8 56.6 37.6 32.3 4.0
346 4.0 x 1.0 324 6.20 0.20 61.0 53.3 38.8 32.2 4.0
347 4.0 x 1.0 54-0 6.20 0.83 64.8 54.3 45.0 37.7 4.0
348 4.0 x 1.0 696 6.20 1.45 60.2 50.2 43.0 36.7 4.0
349 4.0 x 2.0 216 6.20 0.25 55.8 49.7 36.1 31.3 4.0
350 4.0 x 2.0 ':>20 6.20 0.61 60.7 52.0 42.2 36.2 4.0
351 4.0 x 2.0 494 6.20 1.71 61. 3 50.7 44.8 38.2 4.0
352 4.0 x 2.0 622 6.20 2.78 61.3 49.7 47.0 37.7 4.0
357 6.0 x 1.0 103 6 •. 20 0.15 68.8 52.8 32.8 30.2 4.0'
358 6.0 x 1.0 272 6.20 1.05 67.8 56.':> 46.7 39.8 4.0
359 6.0 x 1.0 416 6.20 2.63 61.3 49.9 45.7 37.7 4.0
360 6.0 x 1.0 526 6.20 L~. ':>3 71.8 55.8 55.5 1+4.0 4.0
361 6.0 x 2.0 93 6.20 O. ':>1 61. 7 54.7 35.3 30.7 4.0
362 6.0 x 2.0 167 6.20 0.85 60.7 51. 3 40.3 33.1 4.0
363 6.0 x 2.0 292 6.20 2.93 60.2 48.8 44.8 36.3 4.0
364 6.0 x 2.0 390 6.20 5.28 60.9 1+8.3 4-8.0 38.4 4.0
365 8.0 x 1.0 9 l !- 6.20 0.45 56.7 49.8 34 .L~ 30.7 4.0
366 8.0 x 1.0 143 6.20 0.77 59.7 50.7 39.7 '33.0 4.0
367 8.0 x 1.0 280 6.20 3.35 58.3 47.3 l~/+ .1 '35.7 4.0
368 8.0 x 1.0 354 6.20 5.63 60.2 47.7 47.4 37.9 4.0
369 8.0 x 2.0 70 6.20 0. 1 +3 62.2 53.8 37.9 34.4 4.0
370 8.0 x 2.0 121 6.?O 1. 7j C; G1. 'J '31..2 1+2.5 35.9 4.0
371 8.0 x 2.0 206 6.20 1+.38

211-
D!~ 'I'l\.
PA-:JDLES
0.20 PERCENT CAR BOPOL
Batch ',)eic;ht 9l~.4 1bs. Center Height = 7.0 inches
Run Diameter RPJVj At'ea2 Dynamometer 'I'emperature (oC) Time
x Height (ft. ) Scale Batch \va11 (min)
(inches x C lOs) 1 2 1 2
inches)
Heati!!!l
395 4.0 x LO 556 6.20 0.86 49.3 57.0 95.7 96.3 2.0
394 L~. 0 x LO 626 .,i,20 1.05 ')4.2 1+3.d 89.7 9L6 2.0
397 4.0 x LO 714 6.20 l.l~3 49.3 58.4 92.3 95.0 '2.0
392 1+00 x 2.0 340 6.20 1.n 42.':> 4B.3 90.3 94.2 2.0
393 4.0 x 2.0 412 6.20 1.21 5".2 60.5 92.1 93.0 2.0
"01 L~. 0 x 2.0 496 6.20 2.13 52.2 61.8 9L7 94.2 2.0
390 4.0 x 2.0 618 6.20 2.83 11-2.2 5 1 1-.2 82.3 87.7 2.0
402 6.0 x 1.0 278 h.20 1.11 /11.2 49.3 92.9 9'1-.9 2.0
403 6.0 y. 1.0 376 6.20 2.0? Ij.Fl • Po S;~. Pi '-\;. ': (1';;.7 2.0'
P') ('\
404 6.0 x 1.0 432 6.20 2.73 50.7 61. '5 Do' .0 ')L7 ,-.J
405 6.0 x 1.0 532 6.20 I~ .• ? '} 57.2 68.1 8G.b 0~ -;Jr... '" ,j 2.0
399 c-.O x 2.0 240 6.20 2.1') 51.1 61.] 92.0 95.3 2.0
398 6.0 x 2.0 290 6.20 3.08 38.5 51. 7 8ll'.7 88.8 2.0
400 6.0 x 2.0 342 6.20 4.33 ')(').3 6(').3 8').3 90.4 2.0
401 6.0 x 2.0 370 (').20 5.15 ')3.8 66.2 83.4, g1.1 2.0
411 8.0 x 1.0 163 6.20 1.13 52.5 ')9.5 96.6 97.7 2.0
410 8.0 x 1.0 220 6.20 2.13 37.7 48.8 87.3 91.8 2.0
412 b.O x 1.0 272 6.20 3.33 ')2.7 63.2 90.3 94.3 2.0
413 8.0 x 1.0 358 6.20 S.68 50.4 G1.9 80.7 .B9.2 2.0
407 8.0 x 2.0 130 6.20 1.65 46.3 53.8 95.7 98.1 2.0
406 8.0 x 2.0 182 6.20 3.08 11-8.8 59.8 87.4 90.7 2.0
408-2 8.0 x 2.0 216 6.20 4.48 61.1 70.0 85.7 92.2 2.0
409 8.0 x 2.0 265 6.20 7.1'3 f,2.7 73.9 87.h 93.9 2.0

DATA
PADDLES
0.20 PEHCENT CARSOPOL
Batch \veight 94.4 lbs. Center Height = 7.0 inches
21$
Run Diameter RPt'-l Area 2
Dynamometer :i:'emperature
-
COC) Time
x Height (ft, ) Scale B!3.tch Wall (min)
(inches x (lbs) 1 2 1 2
inches)
Q£oli~
395 LI-.O x 1.0 556 6.20 0.86 54.9 47.7 30.2 26.2 6.0
394 4.0 x 1.0 626 6.20 1.05 49.3 42.9 27.8 24-.3 6.0
397 4.0 x 1.0 714 6.20 1.4'5 ')0. E3 h8.2 ')2.3 27.9 6.0
392 4.0 x 1.0 340 6.20 1.13 53. l l- L1-6.8 26.6 25.2 6.0
393 4.0 x 1.0 412 0.20 1. 21 54.1 46.3 '50.4 26.7 6.0
391 1+.0
... ........-\
x 1.0 LI-96 \-:>,.::'-" 2.13 60.4 50.2 3ELll- 30.8 6.0
390 1-1-.0 x 1.0 618 6.20 2.83 57.3 4G.3 37.1 31.8 6.0
402 6.0 x 1.0 271:\ 6.20 1.11 52.9 40.3 2b.a 2h.l 4-.0
403 6.0 x 1.0 376 6.20 2.02 60.7 5'5.3 39.1 32.6 4.0-
4-04 6.0 x 1.0 432 b.20 2..73 59.7 51. ? 39.7 33.8 11-.0
405 6.0 x 1.0 5?2 6.20 4-. ")3 67.9 56.7 48.7 l!-0.2 4.0
399 6.0 x 2.0 2LI-O 6.20 2.15 58.2 51.2 37.2 31. El 4.0
398 6.0 x 2.0 290 6.20 7).OB 60.0 SloB 42.,> 35.2 4.0
400 6.0 x 2.0 342 6.20 4. '53 59.2 49. 0 4-2.6 7,0).7 4-.0
401 6.0 x 2.0 370 6.20 5.15 63.7 53.0 46.4 39.3 4.0
411 8.0 x 1.0 163 6.20 1.13 55.7 50.7 29.9 28. 1 1- 4.0
410 8.0 x 1.0 220 6.20 2.13 52.4 46.7 31.8 28.7 4.0
412 8.0 x 1.0 272 6.20 3.?3 53.7 46.8 >\'5.2 30.2 I~_.O
413 8.0 x 1.0 358 6.20 5.68 ')5.2 46.7 4-0.3 33.5 4.0
407 S.O x 2.0 130 6.20 1.65 57.9 52.5 29.6 26.8 1+.0
406 8.0 x 2.0 182 6.20 3.08 57.7 50.2 38.8 33.7 4-.0
408 8.0 x 2.0 216 6.20 4.4-8 62.1 52.3 43.8 36.9 4.0
409 8.0 x 2.0 265 6.20 7.13 62.8 52.2 47.0 39.2 4.0

~;:. 'I'A
3.16
P.;'DDLES
0.24 PEHCEl'!'r CArt::BOPOL
Batch Weight ')4.4 Ibs. Center Height = 7.0 inches
Run Diameter HPI"! Area 2
Dynamometer Temperature (oC) Time
x Heir:;ht (ft. ) Scale Batch \

DAi'A
217
P::10?;;;LL :i~S
WA'P'SR
Batch = 94.0 Ibs.
Cleo-trance = 10.0 inches
Run Diameter RP~l Area2_ Jynamometer 'l'empera ture (oC) Time
(inches) (ft. ) l:::)cale :Batch \'iall (min)
(lbs) 1 2 1 2
Heating
155 5.2 135 6.20 0.01 73.1 84.9 89~2 96.4 2.0
159 5.2 319 6.20 o.:n 68.0 83.5 80.2 92.5 2.0
156 5.2 332 6.20 0.26 79.2 91.3 88.5 97.4 2.0
157 S.2 545 6.20 0.88 71.0 86.8 81.9 93.5 -2.0
158 5.2 765 6.20 1.86 82.5 95.0 89.8- 98.8 2.0
Coolin[?;
1';15 5.2 135 6.20 0.01 55.4 48.7 45.2 39.9 2.0
159 5.2 319 6.20 0.31 67.9 56.4 58.6 48.7 2.0
156 5.2 332 6.20 0.26 47.8 41.1 42.1 %.6 2.0
157 5:2 545 6.20 0.88 46.8 40.0 42.3 36.3 2.0
158 5.2 765 6.20 1.86 46.9 40.0 43.i 36.9 2.0
Heating
93.7% GLYCERINE
Batch \'ieight 117.7 Ibs. Clearance 10.0 inches
278 4.1 253 6.20 0.12 43.3 51.2 96.7 97.3 2.0
277 4.1 L~94 5.20 0.35 54.3 64.2 94.2 96.2 2.0
276 4.1 835 (').20 0.92 48.2 61.6 87.0 93.9 2.0
275 4.1 1035 6.20 1.45 42.3 57.2 83.8 90.2 _ 2.0
274 n.O 120 6.20 0.14 1+3.6 51.8 95.4 96.9 2.0
273 6.0 234 6.20 0.43 4-6.3 57.5 91.7 95.2 2.0
272 6.0 420 6.20 1.40 5">.0 66.3 88.4 94.2 2.0
271 6.0 62,? 6.20 "'i.20 61. 3 74.9 8(3.,) 94.3 2.0
Cooling
278 4.1 253 6.20 0.12 58.3 54.7 J 9.3 19.4 4.0
277 4.1 4g4 6.20 0.'i'3 h1. p. C;C,.0 25.5 24.1 4.0
276 4.1 835 6.20 0.92 67.2 57.5 35.3 29.0 4.0
275 4.1 1035 6.20 1.L~5 63.9 54.1 35.4 28.2 4.b
274 6.0 120 6.20 0.14- 61.8 56.6 22.3 20.7 4.0
273 6.0 23L~ 6.20 0.43 61.1 51~. 3 2:,.5 24.2 4.0
272 6.0 420 6.20 1 ;1+0 60.1 _51.7 32.2 26.0 4.0
271 6.0 625 6.20 3.20 60.1 49.8 36.3 28.5 4.0

2/8
DATA
PROPELL:SH3
0.15 P:~RCEN'l' CARBOPOL
Batch Weigbt 94.4 Ibs. Clearanc"
~
10.0 inches
Run Diameter RPM 'u'ea 2 Dynamometer 'l'emperature (oC) Time
Cinches) (ft. ) Scale T:l;d;ch VIall (min)
(lbs) 1 2 1 2
------ --
Heati~G
341 4.1 372 - 6.20 0.17 47.7 ')7.8 91.7 94.2 2.0
342 4.1 482 6.20 0.21 58.2 1)7.2 91,5 95.2 2.0
343 4.1 596 6.20 0.27 54.0 (;4-,9 f\8.9 92.8 -2.0
3L~4 4.1 766 6.20 0.55 L~9. 2 (-)1.5 82.8 89.8 2.0
353 6.0 113 6.20 0.11 53.8 61.3 95.3 97.2 2.0
35L~ 6.0 315 6.20 0.55 55.G ()6.7 84-.8 91.7 2.0
355 6.0 496 6.20 1.43 53.8 (:'7.1 77.7 88.9 2.0
356 6.0 630 6.20 2.43 55.8 69.0 '7'-1-.7 87.7 2.0
Q2.01~~
341 4.1 372 6.20 0.17 59.9 53.5 35.2 31.7 4.0
342 4.1 482 6.20 0.21 61.0 53.2 38.2 38.8 4.0
343 4.1 596 6.20 0.27 60.6 52.1 39.8 34.2 4.0
344 /-1-.1 766 6.20 0.55 58.7 1-I-9. l e 40.0 35.3 4.0
354_ 6.0 315 6.20 0.55 66,0 55.4- Le7.0 39.9 4.0
355 6.0 496 6.20 1.43 58.8 1-1-8.2 45.3 37.5 4.0
356 6.0 630 6.20 2.43 64.0 50.8 50.7 41.2 4.0

DATA
PROPELJ,SRS
219
CARBOPOL SOLUTIONS
Batch Weight 94.4 lbs. Clearance = 10.0 inches
Run Diameter RPM Area2 Dynamometer 'remperature COC) Time
(inches) (n. ) Scale Batch Wall (min)
(lbf?) 1 2 1 2
Heatine;
0.20 Percent CARBOPOL
381 6.0 324 6.20 0.73 43.3 49.7 88.8 91.8 2.0
382 6.0 396 6.20 0.88 37.8 47.0 90.1 92.8 2.0
383 6.0 572 6.20 2.08 51.2 62.1 85.3 90.7 2.0
Cooli!!E;
385-2 4.1 766 6.20 0.55 38.2 34.1 22.7 20.7 6.0
381 6.0 324 6.20 0.73 55.7 49.4 30.9 27.3 6.0
382 6.0 396 6.20 0.b8 ':;6.3 48.7 35.0 29.2 6.0
383 6.-0 572 6.20 2.21 62.1 49.7 43.3 33.8 6~0
0.24 Percent CARBOPOL
Heatine;
427. 6.0 500 6.20 1. 58 45.7 52.8 94.3 96.2 2.0
428 6.0 572 6.20 2.08 49.8 57.9 94.9 95.8 2.0
L~29 6.0 650 6.20 2.65 48.8 58.3 88.3 90.2 2.0
Cooline;
427 6.0 500 6.20 1.58 51~ .3 48.7 30.8 27.8 6.0
428 6.0 572 6.20 2.08 56.3 49.2 34.9 30.1 6.0
429 6.0 650 6.20 2.65 52.4 44.8 34.6 29.3 6.0

DATA
DISK & VANE 'l'URBINE
\'iATER
Batch Weight 94.0 Ibs. Center Height = 7.0 inches
2.2.0
Run Diameter RPf>1 Area2 Dynamometer Temperature (oe) Time
x Height (:ft. ) Scale Batch Wall (min)
(inches x (lbs) 1 2 1 2
inches)
Heating
173 4.0 x 0.75 118 5.20 0.06 57.1 71.0 75.2 85.8 2.0
174 4.0 x 0.75 ::>12 6.20 0.61 73.'+ 87.5 83.8 94.1 2.0
175 4.0 x 0.75 492 6.20 1.64 66.3 83.1 76.0 89.7 2.0
176 4.0 x 0.75 712 6.23 3.68 67.8 85.1 76.3 90.8 2.0
169 5.0 x 1.0 102 6.20 0.14 74.1 87.0 87.8 96.4 2.0
170 5.0 x 1.0 268 6.20 1. ~2 66.8 83.5 '16.8 90.1 2.0
171 5.0 x 1.0 402 6.23 .~.17 (',7.2 84.3 76.2 90.0 2.0
172 5 .• 0 x 1.0 L~98 6.23 4.88 72.8 139.0 BO.2 93.3 2.0
128 6.0 x 1.25 70 6.20 0.21 72.3 84.7 86.2 94.2 2.0
129· 6.0 y: 1.25 145 6.20 0.97 50.7 77.4 73.3 86.5 2.0
130 6.0 x 1.25 254 6.23 3.15 0,5.5 82.9 74.5 89.0 2.0
131 6.0 x 1.25 346 6.27 5.98 78.7 93.2 85.8 97.7 2.0
165 7.0 x 1. 375 70 6.20 0.48 67.0 82.3 80.5 91. 5 2;0
166 7.0 x 1.375 113 0.20 1.20 63.8 81.0 74.6 89.0 2.0
167 7.0 x 1.375 202 6.20 4.33 65.2 82.2 73.7 88.6 2.0
168 7.0 x 1. 375 273 6.27 8.18 68.1 85.6 76.2 91.0 2.0
CoolinEi
173 4.0 x 0.75 118 6.20 0.06 65.8 56.5 53.0. 46.1 2.0
174 4.0 x 0.75 312 6.20 0.61 84.7 69.2 74.0 61.3 . 2.0
175 4.0 x 0.75 492 6.20 1.64 51.3 43.6 46.0 39.3 2.0
176 4.0 x 0.75 712 6.23· 3.68 53.5 45.3 49.8 42.1 2.0
169 5.0 x 1.0 102 6.20 0.14 53.2 46.3 44.9 39.6 2.0
170 5.0 x 1.0 268 6.20 1.32 47.0 40.2 42.2 36.7 2.0
171 5.0 x 1.0 402 6.23 3.17 51.2 43.5 47.0 39.8 2.0
172 5.0 x 1.0 498 6.2"') 4.88 50.3 42.6 4f>.5 39.6 2.0
128 6.0 x 1.25 70 6.20 0.21 49.9 42.9 41.4 36.5 2.0
129 6.0 x 1.25 145 6.20 0.97 82.3 67.5 72.5 60.2 2.0
130 6.0 x 1.25 254 6.23· 3.15 61.0 51.3 55.3 46.7 2.0
131 6.0 x 1.25 346 6.27 5.98 L~5. 5 38.6 41.8 36.4 2.0
165 7.0 x 1.375 70 6.20 0.48 67.7 57. 1 + 58.9 49.6 2.0
166 7.0 x 1.375 11') 6.20 1 •. ?0 4g·9 IL) .7 4L~. 0 38.2 2.0
167 7.0 x 1.375 202 6.20 11.,? :)2.3 44.0 48.1 40.7 2.0
168 7.0 x 1.375 273. 6.27 8.18 49.3 41.4 45.7 38.7 2.0

DATA
221
DISK 8"-
VANE TURBINES
93.7% GLYCEitINE
Batch WeiGht
Center HeiGht = 7.0 inches
Run Diameter RPI'1 Area2 Dynam.ome te r Temperature (oC) 'rime
x Height (ft. ) deale Batch l>Jall (min)
(inches x (lbs) 1 2 1 2
inches)
Heating
270 4.0 x 0.75 226 6.20 0.3~ 48.5 59.0 96.8 97.1 2.0
269 4.0 x 0.75 412 6.20 I.E> 57.7 69.6 9').1 95.6 2.0
268 4.0 x 0.75 560 6.20 2.30 55.8 69.1 89.5 94.0· 2.0
267 4.0 x 0.75 730 6.20 3.80 45.2 61.4 81.7 89.1 2.0
266 6.0 x 1.25 93 6.20 0.37 l~7. 5 58.3 94.3 97.3 2.0
265 6.0 x 1.25 158 6.20 1.18 53.5 65.2 91.7 95.7 2.0
264 6.0 x 1.25 276 6.20 3.75 59.2 68.2 89.5 95.5 2.0
263 6.0 x 1.25 345 6.20 6.25 50.3 61.2 84.2 90.8 2.0
Cooli!!;8
270 4.0 x 0.75 22~ 6.20 0.:;;:0; h4.g 57.7 2"".1 22.1 4.0
269 4.0 x 0.75 lH2 6.20 1.13 62.8 54.2 31.8 26.2 4.0
268 4.0 x 0.75 560 6.20 2.30 63.3 53.3 34.7 29.1 4.0
267 4.0 x 0.75 730 6.20 3.80 60.0 49.9 35.0 28.3 4.0
266 6.0 x 1.25 93 6.20 0.37 57.7 52.2 20.8 19.8 4.0
265 6.0 x 1.25 158 6.20 1.18 67.8 58.3 32.4 26.2 4.0
:264 6.0 x 1.25 276 6.20 3.75 60.7 51.1 .32.8 25.2 4.0
263 6.0 x 1.25 345 6.20 6.25 61. 7 50.2 36.6 27.2 ll-.O

2.22
DATA
Tu.'i:SINES
0.15 PERCENT CARBOPOL
Batch \veight 94.4 Ibs. Center :iei(l;ht = 7.0 inches
Run Diameter RP~1 Area2 DJ'namometer Temperature (oC) Time
x Heicht (ft. ) Scale Batch ~/al1 (min)
(inches x (lbs) 1 2 1 2
inches)
Heating
337 4.0 x 0.75 216 6.2u 0.21 46.6 57.2 89.3 89.7 2.0
338 4.0 x 0.75 326 6.20 0.57 51.5 (.,2.7 85.8 90.7· 2.0
339 4.0 x 0.75 498 6.20 1. 57 61.2 72.7 86.3 92.7 2.0
340 4.0 x 0.75 684 6.20 3.13 65.0 77.1 84.9 93.6 2.0
333 6.0 x 1.25 104 6.20 0.35 50.6 61.2 89.8 92.8 2.0
334 6.0 x 1.25 152 6.20 0.87 51.2 63.0 85.0 92.7 2.0
335 6.0 x 1.25 266 6.20 :>i.17 57.5 70.7 79.4 89.7 2.0
336 6.0 x 1.25 348 6.20 5.73 54.7 68.6 71.8 84-.3 2.0
Cooling
337 4.0 x 0.75 216 6.20 0.21 61.9 ')4.3 37.8 32.7 4.0
338 4.0 x 0.75 ?26 6.20 0.57 G1.8 52.3 l~l. 7 35.B 4.0
339 4.0 x 0.75 498 6.20 1. 57 68.4 55.2 50.5 40.9 4.0
340 4.0 x 0.75 684 6.20 -? .13 64.2 50.9 49.7 40.1 4.0
333 6.0 x 1.25 104 6.20 0.'>5 '35.8 49.2. '33.2 30.4 4.0
334 6.0 x 1.25 152 6.20 0.87 53.7 l~5. 8 ;;5.6 '51. ;; IhO
335 6.0 x 1.25 266 6.20 3.17 68.5 54.3 51.6 41.7 4.0
336 6.0 x 1.25 ')48 6.20 5.73 63.7 49.9 50.8 40.7 4.0

DA'rA
22.J
'l'LlTIBINES
CAR30POL SOWl'IONS
I3atch "'ieight 94.4 lbs. Center Height = 7.0 inches
Run Diameter ~~PM .tu:ea,;) -:ynamometer :.re:nperature CoC) Time
x Height (ft.-) Scale Batch \'lall (min)
(inches x (lbs) 1 2 1 2
inches)
0.20 P~~cent_Q!g~Q?OL
Heati!l5.
31)9 4.0 x 0.75 4 L W 6.20 loll 56.6 63.5 92.8 94.9 . 2.0
387 4.0 x 0.75 518 6.20 1. 55 49.4 58.2 91.2 94.5 2.0
386 4.0 x 0.75 645 6.20 2.58 42.6 55.2 85.3 87.8 2.0
419-2 6.0 x 1.25 187 6.20 1.28 51.2 58.5 97.7 98.2 2.0
418 6.0 x 1.25 230 6.20 2.05 4-2.3 53.2 91.8 92.0 2.0
420 6.0 x 1.25 275 6.20 3.13 53.2 64.0 8'7.8 92.3 2.0
421 6.0 x 1.25 350 6.20 5.48 53.0 65.2 83.1 90.8 2.q
QooliJ.:!f!l
389 L,.O x 0.75 4AO 6.20 1.11 60.2 51.6 35.3 30.7 6.0
3d7 4-.0 x 0.75 5Hi 6.20 1. 55 57.0 48.5 3 1 1-.8 29.7 6.0
j88 4.0 x 0.75 592 b.20 1.93 43.1 37.1 28.0 24.7 6.0
386 4.0 x 0.75 645 6.20 2.58 59.7 48.7 42.3 ?3.6 6.0
'+19 6.0 x 1.25 187 6.20 1.28 '56.3 4ii.7 30.3 27.2 6.0
1+18 6.0 x 1.25 230 6.20 2.05 50.) 43.0 30.8 26.1 6.0
1+20 6.0 x 1.25 275 6.20 3.13 62.3 50.5 43.4 34.5 6.0
421 6.0 A 1.25 350 6.20 ';',48 62.2 48.3 4-5.7 35.7 6.0
0.21+ Percent CARIlOPOL
He~!ini5
459 6.0 x 1.25 342 6.20 4-.65 4-9.2 59.0 90.2 93.8 2.0
i}58 6.0 x 1.25 365 6.20 5.43 36.5 49.2 84.1 89.2 2.0
Cooling
459 6.0 x 1.25 - 3 1 Q 6.20 I~- .65 52.8 4i~.9 31.3 27.3 6.0
458 6.0 x 1.25 =)65 6.20 5.4.3 49.6 41.7 32.8 27.8 6.0

CALCULATION OF HEAT TRANSFER
AND PRANDTL NUIVlBERS
1. Program for calculating dimensionless groups based
on apparent viscosity derived by dimensional analysis
2. Program for calculating diQensionless groups based
on Metzner1s apparent viscosity
3. Fluid properties used in above programs. (STATE:1ENTS
12-30)
4. Nomenclature

• _________ H ___ -.5_J
n __ 41._
_._._-_.
5 REAO.N.DA.W.T!~E
- ______ h n.Q65-L=-l-J..I-----------------------------------
59 PUNCH,DF,OME,QNLT,HP
_ 6it 2UNCH,.J::1...LhJ\JNU-, Xl'-.L~E.-"1M2.Q ___________________ _
61 PUNCH.oV,XNPR.VCFl.VCF2
. [:; ::'_~l..JNC~H._-"LC::£_3_j,jj_CF_4-,-' L' --,,-V-,C,,-,-F_-=~:....:.,-,X~R,-"c=..!K--,,--________________
70 GO TO 5
____ ~~JLOJe _______________________________________
72 END
_
----------------.. ------~---~
---- .
Note; . AhmlB __ p-ro.grams lNxitt-en. £o.I'--conl:i:ng-runs.-
For heatingjstatement 36--illUSt. read-
_________ ~ 36 QNET
=: QDT ""-QM.K--------

________________ ~parent viscosity deri veQ.~v dimensional analysj s
6 D06SI=1.N
7 REA~.RUN.RPM.A.~CAL.LTl.~T2. Tl. T2
8 dTAV=(UTl+bT2,*C.5
9 liJ T A V = ( l.c-'Tl.+ iJJ_",,?~) -x,-,-'~-"C,-,-e!'-='S'---______________
10 DF=AOSIWTAV-HTAV)
--- ---------_/
_ _ _ ____ ll~_.I_C:i=_A U SId T 2 --,o=--T-=l-,-_
----------------------~
--------------- ----
-------------------------- ------------ ----------------- ------------ ----.--~
31 XPOW=12H.3E-3,*SCAL*PPM
___ --"3"-!2=---"OfY1E::: ( 7 " 7 2 Ec_--'L=-'-'-)-.:*:...:x"'/'-P-->OL':::c,\! ________________ _
33 DENO=IRPM**3I f CDA**51*DENS
:3 4 >3"-0",,c---,-H~:::-,-H",-,-'
P~*-,I~l,--,,-G -'.;O,-+,-,H-,-,-p_",_L-=-1-=,,'-.7L..7-'.-4,--,L=-_-_4,-',-'_____________
39 XNNU=1.1b6*H/TC
f+ l_tL,£:::_X_I

. ________ ---'F"'-l uid prope-rty statements for water
12 VIDA=dTAv-o.435
13V LLlLt::;b,-'7B .... A+\j~lLliUt'\LLLR _____
14 VltJC=Vlhdi< I:-JW =.L~': _~__ ~.
26 DENS=62 .. 42-(1 .. 645L-3l*UTAV-(2.4HL-4)*DTAV**2 .. 0
~ ____ ~2~_-~7_T~C~-~u-,.,-,3~2~5~,~'~D~·T~A~\L/~~;

------------------------ -_._--------------'
--____ -Rluid-J].I'operty statements Tor 93" 7 percent 8;1 ycerj ne
. _____ 2.2...8--./
--.. ---------~
12 _DENS.= 7 u ... ~.3_=L!_IAVJLL..4...aj _ 4 b ic_c::::2J, _____________ _
-------_---./
14 TC=0.172
______ ~1~~L_~(~~ _________________________________________ /
16 CP=O&~6~+uTAV*( I .~4~-JI
___. __ L1 __ C PW := Q." :).6?t ~ILT lL\L}LU_~? 4 E:. - .:.tL.____________
18 LXUl=lbHO./(273.+0TAVI
_ J_.?_. _.E:XtjZ-==.9-'?' 7l)_!!LC2_7.J " + L:l T A V )
---------.---/
20 VI~=(7.17E-5)*1: .• L**Lxbl+(~.8~E:.-13)*ln.~**~xu~
_______ ~21~~X~K~~. (6.72E:.==-~4~'~)~*~V~I~~~____________________________ /
LXWl=18HC./(273.+~TAV)
__ ;;:_~ ___ C;.X "il; = 4 L -L~L(.Z_7 :;;-,-' '!." 2+..."1-,,--, -,-T.:.:./~~V'!....!.) ____________________ _
24 VI~~=(7.17c-~)*lO.C**~X~I+(~.81C-1J)*1~.n**cX:L
_____ ...f:'.2 __ X!

12 D~NS=6~.48-(1&G61E-3)*0TAV-(2~48E-4)*wTAV**2.C
_____ L~± __ I~=_~~t+_L+d J_A \I * 2.3 I L ~

~--~, ~
---- ---- -----------~---------
___ 2..3--",O,--~
--------------~
12 DE f,S::: 62 e 4 G- ( 1 .06 1 L -,3 ) ~~L~ T A V

lfJ1]ld p.rD.p£..:C.Ly statements for 0./4- percent C.arbopo]
"---
-------------
1 2 Dc i'-J::' = 6 L " 4 U - ( 1 "b 6 1 c:.. - -.5 ) ~< u T ;'., V - ( 2 •

232
NOMEliCLATURE FOR BEAT TRANSFER GALC1J1A TIONS
.", 'i J c· •• .... --'''-" -,,;' .' ,
A
BTl
BT2
OP
DA
DENS
DF
II
If
= Heat transfer area
III
::
::
=
iii
::
::
::
First bate~ temperature
Seeo~a
~aten temperature
Heat capacity
Impeller diameter inches
Density
Driving f0ree. ($e)
Batek heat transfer coeffieient (Btu/hr @F ft2)
QWT
RPM
RUN
SOAL
TO
VCF2
W
WTl
WT2
XX
XN
XNNU
XNPO
XNPR
XNRE
::
::
::
::
IIIiiI
::
l1li
..
::
::
::
::
::
::
::
items on first eard
Net heat transfer rate (Btu/mi~)
Impeller speed (rev./min.)
Rua number for identifieati0B
DJ~aaometer seale reading (lbs)
Tftermal conductivity
,
Viseosity rati
Batch weight (lbs)
First 1-rall tem}!lerature
Second wall temperature
Fluid e0nsisteney index
F10wbehavior index
Generalized Prandtl Number
Generalized Reynolds N~ber

2.33
CALCULATED RESUVrS
FOR \\fArrER RUNS
UNDEH
NON-STANDARD CONDITIONS

2.34-
CALCULATED RSSULTS
WATER
Run Diameter h NNu N po N N Re
K/K
x Height
Pr w
(2tu_ )
(inches x of hr ft2
inches)
Anchor - Clearance 3.0 inches
~eat~~
47 9.0 517 1861 2.01 104,265 2.57 1.19
48 9.0 828 2430 2.33 218,092 2.13 1.11
49 9.0 1126 3309 2.59 371,921 2.16 1.09
50 9.0 1295 313'34 2.70 LJ-70 ,007 2.35 1.10
C0S2.li!2E;
47 9.0 599 1777 2.02 113,986 2.30 0.85
48 9.0 676 2115 2.30 149,991 3.36 0.90
49 9.0 106L1 3228 2,57 311,592 2.68 0.91
50 9.0 1145 3636 2.66 316,819 3.77 0.93
!::!eat~~
B~ve~in~
Pitch Paddle - Center Height = 6.0 inches
55 9.0 x 0.7 556 16:;'8 O. »2 261,793 2.18 1.13
5 L I- 9.0 x 0.7 685 2071 0.32 347,996 2.62 1.18
53 9.0 x 0.7 832 2528 0.34 483,526 2.70 1.17
52 9.0 x 0.7 1107 3~Jl8 0.56 785,678 2.47 1.12
51 9.0 x 0.7 1196 3500 0.37 938, :::'18 2.53 1.12
Cooling
55 9.0 x 0.7 609 1802 0.32 255,508 2.25 0.86
54- 9.0 x 0.7 638 1961 0.32 316,071 2.95 0.89
53 9.0 x 0.7 690 2252 0.34 299,129 4.75 0.93
52 9.0 x 0.7 909 2808 0.35 657,2»1 ».06 0.91
51 9.0 x 0.7 1042 3155 0.37 905,470 2.64 0.91

CAl/jULATED REBULTS
23S
""A'l'!m
PADDLES
?un Center Diameter h NNu Iii N N- A/K
Height x Height
Po Re rr w
( Btu )
(inches) (inches x of hr ft2
inches)
!i~~!::\:'~
60 4-.5
61 4-.5
S.O x 1.0
6.0 x 1.0
517
3-)1
1531
1164-
0.82 230,279
0.96 125,,(8?
2.26 1.17
2.36 1.22
28 5.0 Ll.O x 2.0 7,75 111L~ 2. :s6 44,785 2.31 1.21
29 5.0 4.0 x 2.0 361 1100 2.54 38,852 2.75 ·1.30
30 5.0 LI-. () x 2.0 531 1551 1.97 93,258 2.06 1.13
31 5.0 4.0 x 2.0 766 2253 5.08 198,696 2.00 1.10
32 5.0 4.0 x 2.0 9::;::; 2707 5.81 271 ,644 1.98 1.08
33 5.0 4.0 x 2.0 945 2755 5.86 306,0=)4- 2.05 1.09
38 6.0 5.0 x 2.0 1+50 1328 /1-.57 66,193 2.24- 1.17
37 6.0 5.0 x 2.0 673 1986 4.15 134,060 2.22 1.12
36 6.0 5.0 x 2.0 8W:S 24-68 4.4-2 182,14 5 2.11 1.09
35 6.0 5.0 :( 2.0 1019 2983 '+ .85 293,876 2.11 1.09
34 6.0 5.0 x 2.0 1264 368::;

2,36
Run Center Diameter h NNu Npo
Height x Height
p
-'Re
r~Pr
K/Kw
108 9.0 5.0 x 1.5 493 1l~4B :'.82 /6,931 2.16 1.14
109 9.0 5.0 x 1.5 806 2'>54 3.44 145,059 2.08 1.10
110 9.0 5.0 x 1.5 1037 3063 4.05 241,318 2.23 1.10
111 9.0 5.0 x 1.5 12

23
7
Run Center Diameter h NNu N N N K/K
Height x Eeight
llo Re
Pr \~
108 9.0 5.0 x 1.5 390 1265 3. 7L~ 41,482 4.51 0.89
109 9.0 5.0 x 1.~ 584 1857) 3.38 88,397 3.78 0.90
110 9.0 5.0 x 1.5 T?2 2484 3.97 141,165 4.24 0.93
111 9.0 5.0 x 1.5 1239 3855 4.06 273,834 3.23 0.93
56 10.0 8.0 x 4.0 ")85 1780 4.37 76,779 2.73 0.88
57 10.5 8.0 x 1.0 547 1723 0.87 157,826 3.53 0.')0

2.38
CALCULAT'ED ~E~:UL'rS
?!ATER
PROPELLi':RS
Run Clearance Dia:neter h NNu II! N
Po Re
l~Pr K/K
Iv
(inches) Cinches) ( 3tu )
of hr ft.2
Iieating
lL~7 6.0 5.2 387 1143 0.70 86,267 2.21 1.19
148 6.0 5.2 70~) 2119 0.55 255,5 0 6 2.Lj·2 1.16
149 6.0 5.2 882 2641 0.57 390,513 2.4') 1.1l.J
150 6.0 5.2 107b 320 1 + 0.63 575,105 2.53 loll
151 8.0 5.2 387 11'45 0.38 81,028 2.20 locO
152 8.0 5.2 667 1998 0.55 227,655 2.45 1.17
153 8.0 5.2 873 2582 0.6 L • 413 ,356 2.26 loll
154 8.0 5.2 1055 3074 0.66 644,973 2.03 1.09
161 12.0 5.2 391 1193 0.63 75,223 2.80 1.29
164 12.0 5.2 751 2255 0.63 234,224 2.lj.8 1.16
162 12.0 5.2 791 2358 0.53 24 7,974 2.38 1.14
163 12.0 5.2 1121 3252 0.67 459,066 2.42 1.U
CooliQ.g
147 6.0 5.2 271 863 0.69 54,4'72 3.85 0.82
14-8 6.0 5.2 55g 1792 0.54 163,118 4.13 0.90
149 6.0 5.2 757 2398 0.57 274,931 3.73 0.91
150 6.0 5.2 1051 3260 0.62 450,040 3.14 0.92
151 8.0 5.2 221 705 0.313 50, 63 L j. 3.97 0.81
152 8.0 5.2 529 1697 0.55 147,196 4.12 0.90
153 8.0 5.2 765 2416 0.63 279,440 3.62 0.91
154 8.0 5.2 990 3227 0.65 317,816 4.74 0.94
161 12.0 5.2 2'31 926 0.62 57,005 3.88 0.85
164 12.0 5.2 62L I. 1965 0.63 174,158 7,.'73 0.90
162 12.0 5.2 765 2260 0.53 261,321 2.23 0.88
163 12.0 5.2 1038 3221 0.66 366,680 3.17 0.92

CALCULA'l'BD RE.::iUI/I'S
2.39
DISK ,'I".
'4A'.PSR
VANE 'l'URBINES
Run Center Diameter h NNu Fipo N . Re N K/K
Height x 'ieight
Pr w
(~~-
(inches) (inches 2)
x of hr ft.
inches)
~~tine;
132 5.0 6.0 x 1.25 569 1724 3.99 76,972 2.6 I i· 1.21
133 5.0 6.0 x 1.25 764 2293 4.22 1)7,744 2.49 1.16
134 5.0 6.0 x 1.25 1051 ';072 1+.83 285,357 2.08 1.09
135 5.0 6.0 x 1.25 1209 3522 5.14 376,860 2.04 ,l.07
136 ).0 6.0 x 1.25 633 1906 3.87 74,6'51 . 2.54 1.17
137 9.0 6.0 x 1.25 907 26h4 5.02 165,587 2.15 1.10
138 9.0 6.0 x 1.25 1269 3838 5.25 232,306 2.62 1.11
139 9.0 6.0 x 1.25 15 L ,4 J,I599 5.42 326,635 2.37 1.09
Cooline;
132 5.0 6.0 x 1.25 425 1359 3.95 5L, ,194 LI-.OO 0.88
l?3 5.0 6.0 x 1.25 (',16 1964 4.17 93,818 3.98 0.90
134· 5.0 6.0 x 1.25 899 2836 4.74 181,838 3.59 0.92
135 5.0 6.0 x 1.25 1148 3651 5.04 223,599 3.83 0.93
136 9.0 6.0 x 1.25 569 1741 '5.85 68,25? 2.84 0.87
137 9.0 6.0 x 1.25 785 2514 4.92 97,540 4.06 0.92
138 9.0 6.0 x 1.25 1134 3592 5.20 173,E~57 3.70 0.94
139 9.0 8.0 x 1.25 1181 3765 5.34 21 L I·,9B6 3.90 0.94

CALCULA'rED 1-{E8iiLlJ. 1 S
\.;!\.'fER
TURBINES
2.10
Run Center Diameter h NNu
N N N Re pr K/K
Height x Height
Po
w
(~l~_ ;;)
(inches) I.inches x of hr ft.-
inches)
Heating
Six Bladen - O~n Bladed iJurbines -
:Straight Blades
177 7.0 4-.0 x 0.75 ;';56 1098 3.16 40,151 'S.OO 1. 35
178 7.0 4.0 x 0.75 620 1844 3.27 104,472 2.">4 1.16
179 7.0 4.0 x 0.75 695 2060 3.69 1 /+4,627 2.29 1.14
180 7.0 4.0 x 0.75 853 2527 Le.26 ~29,071 2.,28 1.12
181 7.0 4.0 x 0.75 1151 '5424 1+. ',2 312,644 2.34 1.10
Qooligg
177 7.0 4.0 x 0.75 269 83 Ll- 3.16 38,929 3.11 0.81
178 7.0 4.0 x 0.75 4b6 1504 3.22 62,581 4.30 0.89
179 7.0 4.0 x 0.75 547 1764 3.62 84,1330 4.32 0.90
180 7.0 4.0 x 0.75 En2 2561 4.20 157,354 3.58 0.91
181 7.0 4.0 x 0.75 980 3152 4-.25 190,643 4.22 0.93
§ix_Bladed =--Q£~n BleLded i'urbines - Curved Blades
.!:~eating
182 7.0 4.0 x 0.50 4-68 1380 4.15 101,283 2.21 1.16
183 7.0 4.0 x 0.50 755 2240 1.96 203,993 2.30 1.13
IB L e 7.0 L~ .0 x 0.50 866 2573 2.20 318,167 2.31 1.12
185 7.0 4.0 x 0.50 1075 ')207 2.38 411,720 2.38 1.11
Q2-0lin U;
182 7.0 4.0 x 0.50 397 1259 4-.07 65,129 3.76 0.86
183 7.0 4.0 x 0.50 64-0 2009 1.93 14-5,992 3.4-4 0.89
184 7.0 4.0 x 0.50 880 2756 2.17 230,997 3.40 0.92
185 7.0 4.0 x, 0.50

CALCULATED RESULTS
USED FOR CORi{ELATIONS

CALC:_:LA'i'ED _12:-)ULTS
24c.
ANCHOR - 5.0 inch Clearance
Run Diameter h NNu Npo N N pr K/Kw
x Height
He
( Btu
')
(inches x
)
of
inches) hr ft.'-
\J.jATEH
Heatine;
67 9.0 \:,02 1834 2.':>1 108,,624 2.74 1.19
68 9.0 gbO 2571 2.67 221,871 2.0B 1.08
69 9.0 1287 ;!j7-;'B 2.86 381,98'1 2.00 1.07
70 9.0 1437 L.2·~7 2.81 469,317 2.31 1.09
Coolinr;;
67 g.O 534 172(3 2.48 71 ,675 4.47 0.90
68 g.O 7% 2;)f., 2.61 113,068 l~. 66 0.93
69 9.0 921 29C,1 2.79 212,385 4.06 0.94
70 9.0 1208 37T5 2.G8 34H,485 3. ')2 0.93
93.7 Fercent GLYCERIN'E
Heatin!?i
235 9.0 98 ',63 2.19 1596 3.';)5 4.23
236 9.0 157 10b5 2.55 36ll!- 2.56 2.98
237 9.0 193 1306 2.55 fl.l~'38 ::S.27 2.83
238 9.u 213 144J!- 2.63 ,)821• :-S. -.?1 2.61
Cooling
235 9.0 38 258 2.19 1621 3.30 0.13
236 9.0 65 ll,lj-2 2.55 3438 2.68 0.19
237 9.0 8l~ 5572 2.55 5001 2.9'1 0.26
238 9.0 67 456 2.60 2367 7.70 0.28

CALCULATED REdULTS
ANCHOR - CLE.~.RA';CE .. 5.0 inches
CARBOPOL SOLUTIONS
Z..,.J
Run Diameter h NNu Npo N' N' K/Kw Nil
Re Pr Re N"
(inches)
Pr
( Btu )
oJ;' hr n. 2 , ,
HeatinE,i
0.15 Percent CARBOPOL
373 9.0 147 484 2.69 728 468 2.05 349 976
374 9.0 225 737 2.63 1523 373 1.72 739 768
375 9.0 388 1276 2.72 2736 339 1.45, 1317 704
376 9.0 504 1655 2.84 4002 301 1.35 1938 622
Coolin~
373 9.0 99 326 2.68 678 505 0.66 ,22 1064
374 9.0 173 567 2.63 1473 386 0.69 '111 800
375 9.0 280 924 2.71 2444 382 0.79 1155 ,809
376 9.0 386 1271 2.84 3774 321 0.81 1810 669
0.20 Percent CARBO POL
Heatins
415-2 9.0 101 331 2.39 193 2559 1.64 49 IJ,080
414 9.0 105 352 2.45 206 3026 1.98 52 12,085
416 9.0 200 656 2.61 550 1'139 1.47 140 6848
41'1 9.0 247 810 2.61 851 1483 l.l~2 216 5837
Coo1in~
415 9.0 58 192 2.39 193 2562 0.70 ' 49 10,095
414 9.0 61 202 2.45 222 2798 ·0.79 56 11 ,130
416 9.0 156 513 2.60 534 1798 0.81 135 7089
417 9.0 205' 676 2.60 811 1562 0.83 206 6165
0.24 Percent CAR130POL
Heatin5
456 9.0 141 /.1-65 2.55 2L~4 4042 1.28 51 19,329
455 9.0 167 556 2.58 291 3774 1.26 . 61 18,047
454 9.0 181 598 2.59 317 3824 1.28 67 18,165
Coolin~
457-2 9.0 51 170 2.37 165 4972 0.87 35 23,592
456 9.0 79 261 2.54 231 4298 0.89 49 20,592
455 9.0 115 378 2~58 288 3818 0.89 60 18,239
454 9.0 120 396 2.59 316 3837 0.91 67 18,224

CALCULATEDR3SULTS
PADDLE - CENTER H;':IGHT = 7.0 inches
WATER
244-
Run Diameter h I\ Npo N N Re K/K 1 "
x Height Btu
Nu
Pr
(
(inches x
2)
of hr
inches)
ft.
Heatine;;
124 4.0 x 1.0 328 1003 4.52 41,9'+lj- 2.82 1. 32
125 4.0 x 1.0 . 593 1775 2.24 146,046 2.44 1.18
126 4.0 x 1.0 806 2374 2.49 245,940 2.19 loll
127 4.0 x 1.0 1090 3152 2.78 372,433 1.95 1.07
120 4.0 x 2.0 . 448 1338 10.69 45, L~2 3.49 70,131 2.25 1.17
105 5.0 x 1.5 535 15'/2 3.02 137,088 2.16 1.13
106 5.0 x 1.5 845 2L~')5 3.52 256,292 2.23 loll
107 5.0 x 1.5 1164 3408 3.77 359,4 L·5 2.46 loll
100 5.0 x 2.0 526 1605 5.59 65,134 2.'74 1.23
101 5.0 x 2.0 784 2306 2.49 1'36,609 2.10 loll
102 5.0 x 2.0 988 2d84 4.69 257,356 2.06 1.08
103 5.0 x 2.0 1101 330L~ 4.82 300,740 2.48 1.11
96 h.O x 1.0 497 147~ 1.73 114,032 2.29 1.16
97 6.0 x 1.0 662 1942 1. 35 203,449 2.15 1.12
98 6.0 x 1.0 913 275~ 1. 55 331,140 2.57 1.15
99 6.0 x 1.0 1057 .3179 1.68 '+48,539 2.53 1.13
39 6.0 x 2.0 613 1805 1.87 89,435 2.19 1.13
40 6.0 x 2.0 766 2220 3.40 149,003 1.97 1.08
41 6.0 .c. 2.0 927 281L~ 3.95 231,513 2.69 1.15
42 6.0 x 2.0 1124 -';')25 4. :.sO 360,026 2.26 1.09
92 7.0 x 1.0 494 14

24S
:lun Diameter h hi
-, "0 N,-, H
' t,e I\jI\,r
x Heie;ht
Pr
84 '7.0 x 3.0 729 2155 4.27 105,323 2.25 1.13
85 7.0 x 3.0 905 2720 4.58 153,864 2.51 1.14
86 7.0 x 3.0 1141 3421 :;.00 253,433 2.47 1.12
87 7.0 x 3.0 1395 L~171 5.27 356,'758 2.42 1.10
75 8.0 x 1.0 493 111~)0 0,69 150,292 2.11 1.14
76 8.0 x 1.0 526 1 S2L~ O.G) 15'7,412 1.96 1.11
77 8.0 x 1.0 642 ldS? 0.30 28},S31 2.13 1.11
78 8.0 x 1.0 ':373 29L~0 L03 1+22,769 2.61 1.14
79 8.0 x 1.0 1163 3'+1') 1.06 679,140 2.17 1.09
71 8.0 x 2.0 600 1784 1.83 103,329 2.3."3 1.16
72 8.0 x 2.0 816 2441 2.56 180,409 2.1+4 1.15
73 8.0 x 2.0 1169 3".)78 2.80 401,123 1.93 1.06
74 8.0 x 2.0 1315 3823 3.03 520,265 2.02 1.06
80 8.0 x 4.0 674 2102 3,58 80,864 3.27 1. 25
81 8.0 x 4.0 854 2=)89 4-,59 146,722 2.67 1.16
82 8.0 x 4.0 1135 34:i5 5.30 238,739 2.63 1.12
83 8.0 x 4.0 1500 41+99 5.5--; :>39,502 2.47 1.09

CALCULATED HESULTS
216
PADDLES - CENTEI~ HEIGHT 7.0 inches
'rJA1'ER
Run Diameter h NNu N N Re
N pr K/K
x Height
Po
w
(Bt~_ )
(inches x of hr ft.2
inches)
--------------------------------------
Cooling
124 4.0 x 1.0 238 728 4.51 41,301 2.87 0.77
125 4.0 x 1.0 500 1570 2.22 108,360 3.49 0.88
126 L~. 0 x 1.0 667 2133 2.44 148,B98 4.00 0.91
127 4.0 x 1.0 756 2:S71 2.73 2j3,514 3.L~4 0.91
120 4.0 x 2.0 287 897 10.57 3l~, 512 ':;'.36 0.84
121 4.0 x 2.0 627 1923 4.98 112,852 2.91 0.89
122 L~. 0 x 2.0 829 2fl23 5.88 lLJ·3,618 3.68 0.92
123 4.0 x 2 .. 0 937 2gf,6 6.26 181,205 3.70 0.93
143 5.0 x 1.0 305 970 1.38 Lj4,177 3.83 0.85
146 5.0 x 1.0 384 118'5 2.24 6"5,071 3.01 0.84
144 5.0 x 1.0 718 2255 2.05 148,314 3. Lj·8 0.91
145 5.0 x 1.0 927 2955 2.23 214,345 3.91 0.93
104 5.0 x 1.5 325 1052 3.43 39,45 1 -1- '+ .1+7 0.86
105 5.0 x 1.5 530 1702 2.96 79,362 Lj .• 15 0.90
106 5.0 x 1.5 777 2490 3.46 155,438 4.07 0.92
107 5.0 x 1.5 1051 3183 3.76 338,673 2.65 0.91
100 5.0 x 2.0 350 1120 5.54 47,376 4,00 0.87
101 5.0 x 2.0 605 1950 2.44 76,768 4.31 0.91
102 5.0 x 2.0 903 2849 4.60 162,702 3.59 0.92
103 5.0 x 2.0 1138 3451 '-1-.80 282,688 2.68 0.92
96 6.0 x 1.0 360 1117 1.72 87,918 3.13 1.83
97 6.0 x 1.0 500 1591 1. 33 125,905 3.83 0.88
98 6.0 x 1.0 760 2411 1. 54 241,455 3.'/5 0.92
99 6.0 "J 1.0 1002 3181 1.67 320,238 3.78 0.93
39 6.0 x 2.0 417 1327 1.83 55,755 3.87 0.88
40 6.0 x 2.0 631 1955 3.34 102,277 3.12 0.88
41 6.0 x 2.0 920 2i:S96 ).91 183,913 3.54 0.93
42 6.0 x 2.0 1164 3625 4.25 266,353 3.25 0.93
92 7.0 x 1.0 Lj·49 137f, 0.98 123,922 2.88 0.84
93 7.0 x 1.0 64 5 2004 0.93 185,801 3.18 0.89
94 '7.0 x 1.0 826 2529 1. 21 350,460 2.8'7 0.90
95 '7.0 x 1.0 1076 3427 1.23 362,445 3.88 0.93
88 7.0 x 2.0 615 1850 2. 3L~ 98,538 2.52 0.87
89 7.0 x 2.0 691 2190 3.01 12 1 -1-,138 3.'74 0.91
90 '7.0 x 2.0 1115 3356 3.38 287,001 2.53 0.91
91 '7.0 x 2.0 1464 1.~630 3.50 305,288 75.6f:, 0.94·

:Run Diameter h Np .,u
N N Re
N pr K/K
x Height
Po w
2.1-7
84 7.0 x 3.0 650 1980 4.23 89,176 2.76 0;89
85 7.0 x 3.0 836 2595 4.54 126,969 3.17 0.91
86 7.0 x 3.0 1072 :Slj·~3 4.94 171,139 3.95 0.94
87 7.0 x 3.0 1294 3983 5.23 301,058 2.98 0.93
75 8.0 x 1.0 424 1349 0.68 91, Enl 3.83 0.87
76 8.0 x 1.0 410 1321 0.61 81,872 4.31 0.88
77 8.0 x 1.0 627 1975 0.88 187,564 3.57 0.90
78 8.0 x 1.0 875 2'729 1.02 347,186 3.30 0.92
79 8.0 x 1.0 lu74 yi.50 1.04 395,001 4.16 0.94
71 8.0 x 2.0 49~ 1539 1.80 77,031 4.16 0.94
72 8.0 x 2.0 659 2114 2.52 116,131 4.12 0.91
73 8.0 x 2.0 1260 3710 2.78 363,951 2.19 0.91
74 8.0 x 2.0 1325 4286 2.96 270, ~1l~8 l~ .41 0.95
eo 8.0 x 4.0 689 2051 3.62 106, 1()l.~ 2.3"5 0.87
81 8.0 x 4.0 886 2748 '+' 57 127,621 3.16 0.91
82 8.0 x 4.0 1086 3437 5.25 179,982 3.69 0.93
83 8.0 x 4.0 1263 3938 5.48 267,892 3.29 0.93

248
CALCULATED RESULTS
PADDLES - CENTER HEIGHT 7 • .0 inches
93.7% GLYCERINE
Run Diameter h N Npo N Re
N pr KIT{
x Height
Nu
w
( Btu )
(inches x of hr £t.
inches)
2
Heatins.
262 4 • .0 x 1..0 64 lj·32 2.5.0 843 528 6.66
261 4 • .0 x 1..0 112 759 2.01 26.0.0 337 3.99
26.0 4 • .0 x 1..0 15.0 1.016 2.26 4389 3.05 3.32
259 4 • .0 x 1.0 199 1348 2.42 78.09 228 2 •. 49
258 4 • .0 x 2.0 44 ,.01 4.62 868 481 5.86
257 4 • .0 x 2 • .0 132 896 5 • .0.0 2749 222 2.75
256 4 • .0 x 2 • .0 142 961 5 • .05 2478 323 3.51
255 4 • .0 x 2 • .0 178 12.05 5 • .05 4345 25.0 2.72
253 6 • .0 x 1..0 64 433 1.12 667 654 8.25
254 6.0 x 1..0 1.07 723. 1.44 2524 332 4.21
252 6.0 x 1.0 166 1121:) 1.42 .7941 ·182 2.29
251 6.0 x 1..0 189 128.0 1. 52 7392 287 2.93
21:).0 6 • .0 x 2 • .0 69 465 2.84 541 652 8.28
249 6 • .0 x 2 • .0 1.08 734 3.95 2252 288 3.17
248 6 • .0 x 2 • .0 116 1193 3 .L~4 4773 251 2.69
247 6 • .0 x 2 • .0 199 1346 3.67 3756 398 3.44
246 8 • .0 x 1..0 82 554 ·.0.9.0 1658 4.06 5.17
245 8 • .0 x 1..0 1.09 74.0 .0.92 2972 389 4.5.0
244 8 • .0 x 1..0 18.0 1218 1 • .02· 8175 242 2.7.0
243 8 • .0 x 1..0 193 13DB 1.03 6635 38.0 3.lj-4
242 8 • .0 x 2 • .0 92 621 1.77 1516 386 4.81
241 8 • .0 x 2 • .0 149 1DC9 2.22 4537 2.06 2.5.0
24.0 8.0 x 2 • .0 185 1254 2.46 4938 294 2.96
239 8 • .0 x 2 • .0 197 1336 2.45 6672 289 2.3.0

PADDLES -
CALCULATED RESULTS
CENTER HEIGHT = 7.0 inches
249
93.7 :;'::>ercent GL ':,"CL~~INE
Run Diameter h 1')"
-'Nu
x Height ( Btu )
(inches x of hr ~t 2
I •
inches)
Npo 1'1
'Re N pr K/K w
Cooline;
262 4-.0 x 1.0 26 178 2.51 1227 353 0.11
261 4.0 x 1.0 45 308 2.01 3055 288 0.14
260 4.0 x 1.0 62 420 2.26 4193 319 0.20
259 4.0 x 1.0 65 4:1)8 2.40 4235 413 0.22
258 4.0 x 2.0 31 211 4.6» 1041 4-03- 0.13
257 4.0 x 2.0 45 306 4.98 1933 313 0.16
256 4.0 x 2.0 57 387 5.05 2623 306 0.19
255 4.0 x 2.0 71 480 5.03 :S194 336 0.23
253 6.0 x 1.0 23 156 1.13 1286 346 0.10
254 6.0 -x 1.0 39 262 1.44 2496 336 0.13
252 6.0 x 1.0 62 419 1.40 4575 309 0.20
251 6.0 x 1.0 77 523 1. 52 -5418 388 0.25
250 6.0 x 2.0 28 Hi7 2.86 1053 342 0.11
249 6.0 x 2.0 38 260 3.93 1477 432 0.15
248 6.0 x 2.0 63 427 3.42 2820 418 0.22
247 6.0 x 2.0 76 517 3.67 3467 430 0.25
246 8.0 x 1.0 28 192 0.90 1693 398 0.10
245 8.0 x 1.0 44 301 0.92 3608 322 0.14
244 8.0 x 1.0 67 453 1.02 5985 527 0.21
243 8.0 x 1.0 144 976 1.04 15,188 171 0.33
242 8.0 x 2.0 33 _226 1.'15 1687 3[1-8 0.12
241 8.0 x 2.0 56 382 2.21 308L~ 299 0.18
240 8.0 x 2.0 84 569 2.45 4152 3L~8 0.26
239 8.0 x 2.0 90 - 611 2.45 5627 341 0.28

CALCULATED RE:>ULTS
2. So
PADDLf~S - C!~NT'E'~ E;;;IGHT = 7.0 inches
0.15 Percent CARBO i 'OJ,
Run Diameter h r~Nu N po N Re
l~
x Heir.;ht (~~ )
(inches x of },:r ft. 2.
inches)
I
i\jK Nil l~ 11
, Pr w ~'Re Pr
geatigg
345 4.0 x 1.0 92 0:-05 ~.6J) 760 344 2.54 "359 729
346 4.0 x 1.0 1'52 ll-3/+ 1.Lf8 2~,4 2fA 2.04 \S86 546
3 i l'7 4,.0 x 1.0 17'7 581 2.22 2fi6R 2'55 1. 9 1 + 1284, 4-87
348 4.0 x 1.0 221 72H c.:";, )494 C52 1.'78 1664 487
349 4.0 x 2.0 137 LI51 4.17 81'7 :;;'Oi:; 1.9,8 '594 636
350 4.0 x 2.0 175 ')71+ I~,.EA 1413 262 1.86 ;:'86 5':)9
351 4.0 x 2.0 2'50 7')1 5.48 2707 210 1.f,6 1333 425
352 4.0 x 2.0 2')3 965 5.59 3149 229 1.61 1511 47B
357 6.0 x 1.0 83 277 1 . I. IA- 521 525 2.98 2:;;'

PADDLES -
CALCULATED
RESULTS
CEl'lT'SR HEIGHT = 7.0 inches
0.15 Percent CAITBOPOL
2S1
Run Diameter h iii N.;:>o H' N' K/K Nil Nil
x Height
Nu Re Pr \V
(Btu__ )
Re Pr
(inches x OF hr ft. 2
inches)
Cooling
345 4.0 x 1.0 "-R 190 2.54 853 304 0.58 411 532
345 4.0 x 1.0 85 278 1.48 1322 285 0.53 532 595
347 4.0 x 1.0 135 445 2.22 2670 234 0.57 1285 487
348 4.0 x 1.0 154 507 2.32 3 1 +70 c:34 0.72 1650 1+91
349 4.0 x 2.0 74 2l~5 4.16 723 349 0.66 342 739
350 4.0 x 2.0 119 391 4.6:' 1283 290 0.69 512 608
351 4.0 x 2.0 173 570 5.44 2247 256 0.73 1071 537
352 4.0 x 2.0 210 ()95 5.58 3011 241 0.75 1433 50.6
357 6.0 x 1.0 57 188 1.45 653 La3 0.59 311 368
358 6.0 x 1.0 144 471 1.45 2570. 275 0.66 1246 56B
359 6.0 x l.0 195 6 L "2 1. 55 l~D16 271 0..74 1912 570
360. 6.0. x 1.0 274 90.0 1.61 6212· 220 0.74 3027 451
361 6.0 x 2.0 64 212 3.67 597 4·07 0..58 286 ()i+9
362 6.0 x 2.0 114 375 5.12 1230 356 0.66 586 746
363 6.0. x 2.0 194 640 3. ~)1 2485 308 0.74 1179 650
364 6.0 x 2.0 267 879 3.55 3632 282 0.78 1724 593
365 8.0 x 1.0 77 255 1.2) 9(~4 44·6 0.6L~ 465 944
366 B.O " 1.0 111 367 0.91 1762 378 0.66 838
"'
796
307 8.0 x 1.0 20.3 670 1.04 1+0.65 322 0.75 1920 581
358 8.0 x 1.0 267 6['.0 1.09 5630 293 0.78 2557 519
359 8.0 x 2.0 89 294 2.13 730 L~45 0.62 350 929
370 8.0 x 2.0 139 458 2.24 lLI-I+3 390 0.69 688 d18
371 8.0 x 2.0 273 895 2.51 3127 305 0.74 1512 631
372 8.0 x 2.0 286 9 1 +7 2.64 3313 360 0.82 15 L I-4 '773

PADDLES -
CALCULATED RE6ULTS
CENTSH HEIGHT = 7.0 inches
0.20 Percent CARBOFOL
2Sl
Run Diameter h N Npo N' N' K/K N" Nil
.\U Re
x !1eight
Pr . w . He Pr
( Btu
(inches x ;:»
01" hr
inches)
ft.-
Hee.tinf5
395 4.0 x 1.0 83 274 2.16 682 952 1 ;8') 173 3762
394 4.0 x 1.0 86 287 2.07 689 1076 2.07 173 4295
397 4.0 x 1.0 106 350 2.18 1017 81) 1.75 257 3236
392 4.0 x 2.0 59 196 '7.56 287 1396 1.93 72 5')49
393 /1-.0 x 2.0 95 ')13 5.54 447 1072 1.65 113 4226
391 4.0 x 2.0 125 lHO b.?'> 599 963 1.66 152 3'799
390 4.0 x 2.0 153 S05 5.74- 757 958 1.68 191 3801
402 6.0 x 1.0 77 256 1.l1-6 470 1566 1.98 118 6222
403 6.0 x 1.0 124 408 1.46 B40 1176 1.70 212 4646
'-1-04 6.0 x 1.0 150 ll-95 " 1.50 1073 1054- 1.00 272 4159
405 6.0 x 1.0 190 624 1.57 1611 858 1.46 410 ~~73
399 6.0 x 2.0 12l~ 410 3.82 429 1467 1.69 109 5787
398 6.0 x 2.0 149 493 3.73 502 1532 1.80 126 6088
400 6.0 x 2.0 184 G04 3.80 795 1120 1.l~3 202 4404
401 6.0 x 2.0 215 707 3.86 884 1091 1.47 225 4293
411 8.0 x 1.0 79 260 1.03 416 1825 1.78 105 7203
410 8.0 x 1.0 112 '»71 "1.06 565 1837 1.92 142 7308
412 6.0 x 1.0 111-3 4?l 1.09 948 1333 1.62 241 5253
413 8.0 x 1.0 188 61'1 1.08 1424 1171 1.50 361 4619
407 8.0 x 2.0 74 245 2.36 271 2251 1.93" 68 8916
406 8.0 x 2.0 lll·8 489 2.26 483 1756 1.63 122 " 6938
408-2 8.0 x 2.0 179 585 2.34 727 1367 1. ;9 186 5361
409 8.0 x 2.0 2"2;7 773 2.48 1035 1174 1.37 26') 4597

25.]
CALCULATED RESULTS
PADDLES - CENTER HEIGHT = 7.0 inches
0.20 ?ercent CARBOPOL
Run Dial:1eter h lIiNu N N' N' K/Kw 1'1" Nil
Po Re Pr Re Pr
x Height ( Btu )
(inches x OF hr ft.2
inches)
Cooling
395 4.0 x 1.0 48 1;:'9 2.16 667 976 0;72 168 3862
394 4.0 x 1.0 50 164 2..07 753 978 0.76 190 3886
397 4.0 x l.0 60 197 2.18 1000 834 0.73 253 3298
392 4.0 x 2.0 42 1"39 7.57 ':,,)4 1308 O.TL 77 5182
393 4·.0 x 2.0 56 184 5.52 412 1178 . 0.74 104 4644
391 4.0 x 2.0 77 253 6.72 586 986 0.75 148 3892
390 4.0 x 2.0 100 329 5.75 791 913 0.78 200 3613
402 6.0 x 1.0 46 152 1.47 503 11+55 0.72 127 5764
403 6.0 x 1.0 82 269 1.46 874 1126 0.74 222 4439
40L~ 6.0 :ic 1.0 105 7,47 1. 50 1065 1063 0.77 270 4194
405 6.0 x 1.0 149· I~Bd 1.57 1064 863 0.78 408 3390
399 6.0 x 2.0 81 2Gf} 3.82 421 1495 0.75 107 5904
398 6.0 x 2.0 112 370 3.75 574 1')22 0.79 146 5218
400 6.v -:-: 2.0 143 471 3.79 731 1227 0.81 185 4848
401 6.0 x 2.0 164 5'59 3.85 866 lll5 0.80 220 L~394
411 8.0 x 1.0 48 159 l.03 401 1897 0.71 102 7500
410 8.0 x 1.0 69 227 1.07 612 1685 0.76 155 6676
412 8.0 :x 1.0 87 288 1.09 861 1481 0.77 217 5864
413 8.0 x 1.0 147 475 1.07 l'i34 1256 0.82 337 4973
407 8.0 x 2.0 46 152 2 .?-'7
I 289 2096 0.68 73 E3275
lj·06 d.O x 2.0 99 327 2.26 481 176') 0.78 122 . 6973
408 8.0 x 2.0 140 451 2.3'5 655 15">3 0.79 166 60L.4
'+09 8.0 x 2.0 175 5'76 2.47 905 13'':''1 0.82 230 5365

255
CALCULATED !tESULTS
PROPELLERS - CLEARANCE
10 inches
\AJAT~R
Run Diameter h i'\lU N po N N K/K
(inches)
Re Pr w
(~!~- ?)
of hr ft.~
geating
155 5.2 417 1?29 0.12 105,811 2.22 1.18
159 5.2 745 2215 0.65 240,406 2.3:5 1.14
156 5.2 807 2348 0.50 279,594 2.03 1.09
157 5.2 936 2'163 0.63 426,654 2.22 1.11
158 5.2 1203 3472 0.68 669,367 1.93 1.06·
Cooling
155 5.2 340 1067 0.12 73,003 :3. L~7 0.85
159 5.2 68L~ 20,)3 0.64 200,81.J-4 2.90 0.88
156 5.2 663- d2U 0.49 158,165 L~. 03 0.91
157 5.2 859 2755 0.62 254,897 1+ .11 0.93
158 5.2 1065 3 L !-l6 0.66 358,108 4.11 0.94

2.56
CALCTjLATED .l.E8UIJTS
PROPELLERS - CLEARANCE == 10 inches
93.7 Percent GLYCElHHE
Run Diameter h r; ,.
!'ju
(inches) (Btu_ )
Npo If
Re
N pr KIT{
w
of hr ft.2
Heating
278 4.1 57 385 1.04 854 575 7.43
277 4.1 102 590 0.80 2960 '130 3.92
276 4.1 139 941 0.73 4106 400 4.09
275 L~ .1 11l-6 988 0.75 3958 509 4.67
274 6.0 61 L~12 0.80 888 564 7.06
273 6.0 98 665 0.h5 2136 460 5.22
272 6.0 117 1062 0.66 5485 325 3.38
271 6.0 224 1517 0.68 11651 230 2.36
Cooling
278 4.1 18 119 1.04 13lj·O 372 0.10 .
277 4.1 37 251 0.80 2851 343 . 0.14
276 4.1 60 L~04 0.73 5725 290 0.20
275 4.1 67 453 0.75 613/+ 334 0.23
274 6.0 25 171 0.80 1537 331 0.10
273 6.0 38 260 0.55 2802 353 0.15
272 6.0 57 389 0.55 4633 382 0.22
271 6.0 85 573 0.68 5597 399 0.28

CALCULA'rED RELmL'l'S
PROPELLr~RS - CL2ARANCE = 10.0 inches
257
0.15 Percent CARBGPOL
Run Diameter h N'l Npo N' lIT' K/Kw N:' Nil
- l\U fie "Pr ~"i.e
(inches)
Pr
( Btu
2)
of hr ft.
Heating
341 4.1 117 387 0.8l~ 15'+7 295 2.40 7~'O 625
342 4.1 138 451 0.62 2546 230 1.95 1237 473
'543 4.1 163 537 0.52 3184 228 1.98 1533 474
344 4.1 188 61.0, 0.64 4141 226 1.96 1970 476
353 6.0 90J 2)f-O O.P.~: 759 389 2.33 364 812
3 5L~ 6.0 194 ~)36 D.57 3062 268 l.81 1481 ',54
355 6.0 279 'j15 G.50 54 58 237 1.65 2634 491
355 6.0 '139 1111 0,63 ('676 213 1. 51 3726 440
Cooling
341 4.1 64 210 0.84 1650 . 275 0.60 788 '777-
342 4.1 86 283 0.62 2')27 253 0.63 1113 529
343 4.1 102 337 0.52 3032 240 0.66 1447 504
344 4.1 133 439 0.64 4058 231 0.70 1923 488
354 6.0 144 474 0.57 30L~0 270 0.69 1468 559
355 6.0 208 6$7 0.59 L~88'-I' 267 0.77 2311 564
356 6.0 278 '315 0.63 70')7 2')2 0.78 3396 485

2S8
CALGUL\'F2D TE&)LTS
PS:OPELLJ:;RS - CLE::ArlAIWE = 10 inches
CA:~IlO?OL
SOLU'rIOl,S
Run Diameter h ~'.:i'~u N Nlie IiPr K/Kw i'-J f1 Nil
- ?o
Cinches)
Re Pr
( Btl)
o}l'"l
hr 2)
ft.
0.20 I'ercent CARBOPOL
Heatint;;
381 6.0 68 :~24- 0.71 607 1412 1.85 153 5005
382 5.0 8'7 23) 0.57 790 1332 1.99 198 5:>05
383 6.0 163 537 0.,-,5 IG75 89L~ 1.55 425 '5524
Cooline;
'585-2 LI· .1 LI·4 147 0.64 959 997 0.82 270 3042
3Bl 6.0 41 1'56 0.71 555 1500 0.72 166 5142
382 6.0 58 190 0.57 896 1162 0.75 227 1,596
383 5.0 112 '569 0.69 1660 903 0.78 L~21 3562
0.24 Percent GJLR30FOL
Heatiw5
427 6.0 71 2% 0.5'l- 622 2122 1.39 131 10097
428 6.0 90 298 C).55 h05 1866 1.3L t 159 3910
429 6.0 124 407 0.65 990 1724 1.2':1 207 8231
eooline;
427 6.0 39 129 0.65 623 2078 0.85 133 9907
428 5.0 55 181 0.55 798 1885 0.87 Iv7 8994
429 6.0 72 237 0.54 950 1806 0.89 200 8587

CALCULATED HESULTS
DISK AND VANE ;rURBINE0 - CENT:~R HEIGL-IT 7.0 inches
2S9
vI-HER
Run Diameter h NNu N po
N n KjK
x Height
Re Pr
(_Btu _ )
(inches x oj{' __ h rit. " 2
inches)
Heatine;
'"
--------
173 4.0 x 0.75 411 1256 3.36 45,152 2.80 1.25
174 4.0 x 0.75 857 2521 1+.94 147,191 2.17 Lll
175 4.0 x 0.75 109 l l- 3261 5.~2 216,571 2.36 loll
176 4.0 x o. -;5 1316 3905 5.71 -")20,234 2.30 1.09
169 5.0 ""- 1.0 555 1632 .3 JI-8 75,276 2.17 1.15
170 5.0 x 1.0 1065 3171 4.73 185,358 2.35 loll
171 5.0 x 1.0 1250 3'715 "i.os 2eu,100 2.::S;z, LI0
172 5.0 x 1.0 1529 lI-4':!? 5.09 369,025 2.15 L07
128 5.0 x 1.25 524 1549 4.45 72,611 2.23 L15
129 6,0 x 1.25 '789 2360 4.76 133,592 2.58 1.15
130 6.0 x 1.25 1239 3694 5.05 250,161 2.38 1.10
131 6.0 x ;1-.25 1346 3911 5.21 390,960 2.01 1.07
165 7.0 x 1.375 681 2030 4.69 94,306 2.37 1.15
166 7.0 x 1. 3'15 957 2867 i/-.49 147,990 2.L1-5 1.13
16'1 7.0 x 1.375 1230 3673 5.08 268,931 2.40 1.10
168 7.0 x 1.375 1405 LI-166 5.26 377,867 2.29 1.09

260
Run
CALCULATED ilE0liLTS
DISK Al.lD VANE 'l'URBINE,~ - CENTEH HEIGHT
:i)iameter
x ;Iei ~;ht
(inc!les x
inches)
h
(Bt~___ )
of hr ft.2
7.0 inches
K/Kw
--------------------------------- ._---._._---------
':i:1 f1' ~~~R
Coo!.?:,!};E;.
173 L~. 0 x 0.75 389 llSf, 3.36 L~:s,;;;:S6 2.95 0.83
174 1+.0 x ().75 862 2556 Lj·.9:) 1 L I·1 ,183 2.29 0.88
1'75 I~ .• 0 ./-. 0.75 82E3 2631 '.).2'3 1Li·6,005 ;.i .79 0.92
176 1+.0 x 0.75 1296 4·098 5.6:» 218,257 3.6') 0.94
169 5.0 x 1.0 451 1 £.J.2~i "3.42 49,13(:) 3.63 0.88
170 5.0 1.0 8L~7 2715 f+. h6 116,297 '+.10 0.9'5
171 5.0 x 1.0 1028 ~265 067 ::>.00 194,925 3.22 0.92
151 G.O x 1.25 1262 40b2 ').09 210,3"'0 4.23 0.95
165 7.0 x 1. 7 >75 622 1907 LI-.66 gO, "")20 2.88 0.88
166 7.0 x 1.375 702 22% 4.43 li l O,716 3.88 0.91
167 7.0 x 1.375 1193 3782 '),01 185,74-8 3.74 0.94
168 7.0 x 1.~75 1368 ~·368 5.18 .:::'39,388 3.95 o. ')5

DISK AND VAI'E .rU~1BINES
CALCULATED RB.:3ULTS
- CEWPER HEIGHT = 7.0 inches
Run Diameter h N N po
N Re
l'J K/K....,.
x ~~eisht ( Btu
(inches x of hr ft. 2)
inches)
Nu
'Pr
2. 6/
Heatin~
93.7 Percent GL~CElnNE
270 4.0 x 0.75 89 601 1~.05 1002 422 5. ?6
269 4.0 x 0.75 145 906 L~.20 2842 275 3.15
268 4.0 x 0.75 170 1154 4.62 3571 289 ).04
267 4.0 x 0.75 186 1261 1+.47 316B 430. 3.70
266 6.0 x 1.25 92 622 3.53 891 458 5.33
265 6.0 x 1.25 126 857 3.91 2037 329 3.71
264 6.0 x 1.25 116 7:-::'9 4.09 4293 274 2.95
263 6.0 x 1.25 126 852 4.34 3780 385 3.55
Coo1in[5
270 4.0 x 0.75 ;;;') 2~i8 4.07 1407 303 0.12
269 4.0 x 0.75 ,)4 36'1 4.1B 2273 341 0.19
268 4.0 x 0.75 70 lj.'75 4.61 ':)062 344 0.23
267 4.0 x 0.75 81 546 4.47 3 1 +25 39.9 . 0.27
266 6.0 x 1.25 29 19') 3.53 982 399 0.11
265 6.0 x 1.25 52 353 3.92 2391 282 0.16
264 6.0 x 1.25 66 l~45 4.07 3045 382 0.21
263 6.0 x 1.25 89 ~~,01 4. )l~ 3815 382 0.26

)::1
t:. 0,-.
CALCUL~_T !':D I~EBU- i 1 8
DISK AND VANE TU!1IlIN"ES .- c;':r':T:R !L~'I:; ;{'r
7_0 inches
0.15 Pc:;:'cent GAR](;l'OL
Run Diameter h i\l')u Hpo Ni~e N' K/K 1~ " [";"
Hei:J;ht '3tu
Pr \\1 ~{e 'Pr
x (----_. ~)
(inches x
0]" hr ft" c'
inches)
Heating
._----------------------";'-.....
33'? L~. 0 x 0.'?5 152 L~;S6 3,W) 71') 354 2.27 -:>36 752
338 ll-.O ., 0.7') 169 ';i,)7 4.17 1 :')1 285 1.97 656 595
)39 l~ .• 0 ". 0.75 2 1 ,3 794 L~. ()5 270li 212 1,611- 1:';;;0 430
340 4-.0 z 0.75 319 1041 5.211 ~-~l!-l 180 1. L/') 2160 362
333 6.0 x 1 ')r::
• "'7 11+0 1;62 7jil)l 662 1+11 2.16 ;16 3D")
331, 5.0 ;( 1.25 175 577 ;:, • ') 2. ,)0 ';;30 7,)0
335 6.0 ;-.: 1.25 310 1017 LJ-.6e 2')83 ~67 1. 56 1260 548
336 6.0 x 1.25 1~13 1 ;5')t) I'. ,35 3513 2,:,g 1.'_1-;;; ::.;~~
1702 ,/ ,.....
Cooli!]£;
337 I; .0 x 0.75 77 .>5 1 1 :0.'50 /92 317 0.61 --";0 (~60
338 4.0 .'. 0.,?5 121 !.ou I~
.17 b"O 2t)S a.t'7 ~:~6 596
339 1'>.0 }: o.,?') 1'3 L I (-,7)3 j~ . • C)~, 2LJ.',:1 2-;;1 0.70 1207 4'(7
340 4.0 b 0.75 25'S 8;2 5.20 ')';'1 ~l ;::'.:.:::£) 0.76 12,tl/~- 1·72
333 6.0 x 1.25 71.j· 21,/1
".31 bc'j L~ 3g O. b L " c:34 9')0
33LJ- 6.0 x 1.25 11::) ;)"74 '). dl. 976 £111 G,,?O 1i-'j7 ';'/7
335 :,.0 x 1.25 22'0 7':A il, .. bc ..) 247U .2SU ~; c 7:S l1')S '')79
336 -.0 :-:- I.e') ~iO:S 9C)f, II. nl! 2qC, 21n 0.79 ISS0 587

DISK AND VANE '.i.'UR13HiES -
CEl'iTER HEIGHT = 7.0 inches
Hun
Diameter
x Heie:ht
(inches x
inches)
F flU
N'
He
X/K w
0.20 Fercent CARBOPOL
Heating
389
387
386
419-2
418
420
421
[1·.0 x 0.75
'+.0 x 0.75
4.0 x 0.75
6.0 x 1.25
6.0 x 0.75
6.0 x 1.25
6.0 x 1.25
95
105
157
77
115
161
207
312
:;;46
519
259
3tH
530
seC)
lj·.46 515
4.83 616
4.BO B16
~.74 2g6
3.95 361
4.24-:'47
l.e,58 802
989
982
927
1717
L·8 L !
1313
1139
1.61
L73
1. 70
1.a3
1.86
1. 56
1.48
131 3892
156
206
3879
3674
72 . 6779
91 6681
139
20 L >
5172
4486
Cool~!lEl
309
387
3e8
386
419
418
420
421
4.0 x 0.75
4.0 x 0.75
4.0 x 0.75
4.0 x 0.75
6.0 x 1.25
6.0 x 1.25
6.0 x 1.25
6.0 x 1.25
58
6 l e
68
106
4·9
66
106
151
192
212
228
Y:il
162
219
::Ab
lj·g8
Lj·.45
le. LIB
lj·.2'::;
4.1..31
'5.74
3.95
LI· o 2LJ·
1+.58
490
608
6 l eO
871
2'7'7
357
532
764
1046
996
1095
863
1773
1703
1353
1200
0.73
0.75
0.82
0.80
0.72
0.77
0.78
0.82
124
151.1-
161
221
70
90
135
194
4128
3937
4565
3410
7012
6758
5338
4·738
Heating
459
458
Cooling
Lj·59
458
6.0 x 1.25
6.0 x 1.25
6.0 x 1.25
6.0 x 1.25
120
135
cl0
269
4.06 347 2587 1.31 73 12359
4.15 352 2}52 1.36 7413023
4.05 333 2715 0.87 70 12912
4.15 360 2682 0.90 76 12722

264
CALCULATED RESULTS
USED
IN REGRESSION ANALYSIS
USING TWO DATA POINTS
FOR EACH PADDLE HEIGHT

26S
RESULT,:; U:3ED FOR
REGRESSION ANALY,:;IS OF PJ\DTlIJE LOCATION t:~F]'F~CT
USING '~':\iO S:~'1':3 OF DATA A'}' EACH
n::?E'IJLER ]~OCA~;ION
FLUID "lATER
Run Center Dianeter I~ l' N N pr K/K
Height x Heigh~
(inches) Cinches C )
_~u Re \'{
60 4.5 8.0 x 1.0 1531
61 L~. 5 6.0 x 1.0 116L~
230,279
125,783
2.26
2.36
1.17
1.22·
28 5.0 L~. 0 Y.: 2.0 1114 4 L I',785 2.31
29 5.0 4.0 x 2.0 1100 38,852 2.75
1.21
1.30
38 6.0 5.0 x 2.0 1328 66,193 2.24
37 6.0 5.0 x 2.0 1986 13LI-,OSO 2.22
1.17
1.12
59 6~5 8.0 x 1.0 1970 2/1-9,573 2.02 loll
63 6.5 6.0 x 1.0 12L~9 124,[302 2.34- 1.20
116 6.63 5.0 x 0.75 1029 67,084 3.04 1. 37
117 6.63 5.0 x 0.75 Hi50 205,955 2.57 1.19
124 7.0 4-.0 x 1.0 1003 41,94 J + 2.82 1. 32
125 7.0 4.0 x 1.0 1775 146,OLj-6 .:'.44 1.18
112 7.63 5.0 x 0.75 880 56,355 3.01 1. ';8
113 7.63 5.0 x 0.75 1977 229 ,48L~ 2.20 1. H)
21 8.0 7.0 "'
v 2.0 1912 109,8(:'5 2 .2L~
22
1.13
8.0 7.0 )~ 2.0 2l~11 111-.:: ,090 2.69 1.17
58 8.5 :-:. ° -~ 1.0 2206 2')1,-030 2.00
64
1.10
8.5 6.0 -r 1.0 16Lj-0 129,818 2.23 1.13
4-6 9.0 3.0 .. -- 2.0 2001 104,619 2.54 1.18
45 9.0 8.0 x 2.0 2707 176,730 2.65 1.15
56 10.0 8.0 x 4-.0 1780 '/6,779 2.73 0.88
56 10.0 8.0 x 4.0 2-:"'71 80,469 2.58 1.18
57 10.5 8.0 x 1.0 172:;' 157,826 3.53 0.90
57 10.5 8.0 x 1.0 2112 ;.:'25,157 2.30 1.14

266
APPENDIX C
CORRELATION OF DATA
Regression Analysis
Various portions of the calculations required the
fitting of a straight line to a group of data points.
A
statistical method based on minimizing the s~un
of the
squares of the deviations of one of the variables from
the straight line (least squares method) is described
by Volk (198) and is a reliable and objective method for
finding a linear relationship bett\l'een tHO or more variables.
Complete descriptions of the methods may be fotmd in Levenspiel
et ale (105) and Volk (198).
One depende:nt and one independent variable..
r1any
physical situations can be described by
y=a+·bx
(C-l
Hhere y is a dependent variable and x is an independent
variable.
If several sets of data of Yi versus the corresponding
xi are taken and plotted, the 1l1east squares lt line
through the data can be expressed
(C-2
v-Jhere the 1\ over the y differentiates betl..reen the predicted
A
y, y, and the measured Y, Yi-
It has been established that the parameters ,_ a and b,

of a least squares line can be calculated from
a=y-bi
b =
~ (Xi -X) (Yi - fj)
~ (Xi - X)2
(0-3
(0-4
l"fhere x and y are the averages of the xi and Yi data values ..
A relationship such as
(c-5
can be rewritten as
log 'I = log K + n log if
(C-6
so that it is expressed in the form of equation 0-1, Hhere
y :: log I
x = log 1)
a = log I{
b = n
Thus it can be seen that the use of the above regression
analysis can be used for many simple relationships, provided
they can be l.vri tten in the form of equation C -1.
A computer progra~ for solving equation 0-3 and C-L~
described by Eisen (59), Has used as the basic prograrn. for
calculating the parameters of the pOHer law equation and
the temperature dependent forms of the p01.ver lay.J as described
in Appendix A.
The computer progrom is given in Appendix
A.

268
I-'Iultiple Variabl,es Regression Analysis.
Physical behavior
is often a function of l'l1ore tha....n. one independent
variable and may be exnressed as
(c-7
Using the method of least squares a set of simultaneous
equations can be Hritten (105, 198)
I z.

269
(0-9
where y ""
log NNu
xl = log NRe
x2 = log N pr
etc .. and 0,0

270
COIU'UTER EROGRAMS
t ... I -. t «
---
FOR
JeIDLTIPLE VARI'ABLE REGRESSION Al."i'ALYSIS
."' - " oi'mt d d··· -, r
1.. Ba.sic Erogram. ('fll.e :first part of' this pror;ram. wa:g
altered to evaluate the G0l'lSta.:ntS of' the variQus
correlatioRs. The modifications Which f01lew were
used to evaluate the paddle aP.J.d turbine data whick
included ~peller width in£ermation.
These programs
were further modified for the propeller and anchor
data li>y skiJlpb.g tB.e WalDa and Dt/Da and WalDa terms.,
respectively. )
2. Modificatioms 'for evaluating constants for 'theoretical
eorrelati0Vls.
3. Meditieati€>ns for evaluatiE.l!: constants for semi-emperieal
c0rrelatioJas.
4. Modif'ieation for evaluating paddle ~0sition etf'eet.
5. N0menelature.

-------------- -.Basi.c "Progr.a.rr:L __________________ _
c ~ I t".J G l_ ~ 1-":.. ,. ~\ . ; U L r I ~ J L ~_ L r : "-, L f\~'; t~ {- G h? : _ ~.} s r G ~ i\ i"'. /\ L Y ~ I ~ .) e
-- ------------___ C - --------.---------------. ---------______________________ . _____ . _______________ J
______ ~I tv'it;'~I'j /" ( 1':-;. 1;; ) • C.J..J v ) , •. ,,,Jf','X ( ;,). :-",,) 1..>",1 X ( J )
. __ q _,'LU-.JLl:1LLL , .J ) -----------------------_._-------
C
_--------""C~-----------'»C...Qj'-':PUTAI I Of'! OF I,li P':-'I-

[)O ~ L= 1 • ,(
~-4z/
------------------------------~~
~J~Q __ ::L..,j '="L_-"-!::,.. ____ ~ ______________________________ ~ _________ __'
k=A(L,J)/(:J.(L.Ll*M(.),J) )*li-,',,~J
5 __ 2UNCi::i __ L .. tu_L,,-..J_~~ _________________ _
C
C
_________ ~ __ ~ _____ .C
K 1 =1

-----------~---------- -~----------
PU:'\JCH 113.F
C
CO~~UTATION OF T~L ST~NU~~U E~~Ck GF
TH'- PARTIAL REGRt -ssru:" COU-~=-IClu'"T::'~
--------~----
C
_____ ~p~0~J~~;~C~H~~1~1~4~ ___
PU"-ICH 1 1 5
__ ~S~t~-~!~G~O~ ______________________________________
DO
16 L=l.K
-----__________ -.-l)D~~_LL _________________________ _
16 SU=~0+A(L.~)*~~MX(L)*~~MX(~)
__ ~J d ::: ,:;,~x: -JtJ.~1,)j[:- N ) * * 0 0 ;-) ____________________________ _
~='-.,
PUNCH _lC'2_._:d.~::o_t:L ________ _ ---------------- -- - -- ----- .--
D017')=1.K
S ::J = S Y X * ~; I Ohl (r) -~. 20 "ElLLL) ____
114 FORi,1AT (26H STl'd'\l!~P[) Eh'c":CR UF PI',~)Tlf--\L,24H 1

--------- ]\iio.d.i:fic.ations foT' eva 1 l1R+,j ng
---------------COJlSt.;:;mts for cOT'r"'J ai";l on A
C
c
_ c ____ _
C P~OGRA;'l I NIT! i'l.L I L~, T ! O~; $
C
f-.(EI\[).EK,~N.-.JX
K=Ei<
N==Er\l
_?UI'::J_c:.:t1 ___ U' 2._~ _________________________________
PUI'K.H 1 CJ3 • N
_____ ~~2'1::== C,--! ~~ ________________________________________________ _
S:"ilYS==(JeO
00 2 L == 1 .-'-K~ _______________________________ _
SU~.rlX (L) :=': .. C'
::""1X YLLL==-,'~C______ _______
00 L -.J=L. 1<
c
___ 2 _'':i CL ,,-Jl -_'='--'L""________________________________________________________
C V-X UATA R~AU IN.
C
DO 3 L~ == 1
f-.(i=-AD. 1'11. XN
DO ~ _L:::: 1.J'i ______________________________
REAO.RUN.XNN0.X~RE,XNP~.VCFl.VCF2.VCF~,UA.HI
t'-J-->-L::J .. '01 (1 "C+XN)
FAl =Xi'-JRE*"cEXl
F- ::::XNRE:.*XGlPf--;fU::::/\ 1 *F A 1'-'-______________________ _
i\2u
r C -A3=XNNU/FA 1
Y = " cU4_~-ltL_OG ( F--~~='_"--"'3'-'----) _______________________________
W(I )=L.4343*LO(,(FA2)
__--'"-'L~~) := C _. 4

--~--------------
------ ~~ -------
c
c
_________ c _____ _
l) I ! ~ c:: N::O I 0 f'\. A ( 1 ," 1 i ). C ( 1 ,~ ) • ,j,) 1'.1 ~ ( 1 C ) , '- t·; X '( C 1 C ) " (1 ~ )
c
C Pf.;_X Y (L) = 0_ (2_____ ~ __
00 ;:: .J=L.K
2 _ I~ ( L • ,))=L,_,,_'-'_____________.________________________
c
__________ C ___ -'f ~ X U t\ T-,-p-,-, -'-CRc::l-'C'-'-,c,::;:U_",-1 C-f\.),-" 0,--
C
[) 03 _IL: =_ L_. L>

~QllSIants
for correlation C
c
C
C
C
A ( 1 ~~ Ii 1 'J ) , \.- ( 1 '-, ) -(j ,-) ~j i:: X ( 1 \ J ) ~ _ ! 1\ j ;.,... 'y
--------------------
1 " ) • ' ( 1 ::
C
~LkU. cK, Ei'l, UX
K=E::K
---------~------------'---
N=LN
PUi'JCHLC)~,~__ __ ___ _
PU:"CH
1('3,,~
S U tv1 y ::: :) • ()
~- ~ ---,- --------
DO ;:' L = 1 • K
::,U1'IXCL)::::()0\)
c
C
----------~-----------
c
S~!JXY (L) :::\~
--- - - - - ----,._--
UO ;:' U=L,K
2 .LICL,U):::'_'sCJ
v-X UATA R~AU
IN.
R r-=- AD, ,'''1 • X N
_DO __ :::l ___ l_:-=
r':;:i=.A[). !:?UN. XNNU, XN~-

Modi fi cati onB-foT' ev:alnatj ng---------------~7-7_-
- ________________ --Con stan ts faT' carre J at j on D ____________ _
C
C
C
iJ I i'~~N::o 18"" ,.J. (1 U, 1;;). C (1 L), ~'u:\)A ( I, \) ,_".'}, Y ( 1,- ). (1,)
-----------
C
P0>-;CH
1 ~)2. K
£0 >"CtL L:-;: -,.'_,,_'-' ______________________ . _______________________________ -, __ _
::., U ,\1 Y ::: () @ (;
SJ"lY ~ __ ~D __,_Q~_~_"'._________
DO L L::: 1 ,K
::; ,,', x y e L ) ::: v • ,,;
uO _f,-".2_:::L.Lt::.-_
2 ;:l,(L,,)=OoO
C
~---------~-------
~)().:J 1=1,><
READ .1< U N ,_xr'~f'J .)_.>

con s tAn t s f' 0 T' C 0 T'T'e.l.a.:t...J.i-,o-,-n.L-I--_E.L;L. ___ ~ ___ _
C
c
A ( 1 O. 1 ~: ) • C ( 1 u ) • ---,,~ IV1 X ( 1 -. ) , ,c i-, A Y ( 1 ,- ) •
r
--- -------------->

constants forco~~~latjQn
F
------------_..
'--------
___ C ___ S_Li:::i.c,U:' AN;) i·'ULTI~

'-
-------~--~-~ ------
'----____________ --.---M-O-d.ification for eva] ll.c8utJ..J.L· .LD4g'S-------- ______ 2.E-J.O..L----
.'----------
_____ ..c..onstants foT' corT'eJ ation G
C
'---________ CL-___________________________________________ _
LJ r '
c
C ?~OGR!,', I~ITI,c\LjL.-\TI()"': ..
..-.__.. _____ C ...____ _
1
_______
RLAlJ.EK,cN.-JX
K '" F ,<
~~=( .. N
_PLLl::KH LC2. ......1<
PU~~CH 1 C' 3. i'-..i
1 " ) • _ d' A '( ( 1 -, ) , . ( 1 ~
___.. _.__ S...ui-j"{_=-(L) -"- .. -""c~,_______________________________
~ _________ ~D00~.~L~)~L~-~1~.uK~ __________________________________ _
SU[\:,X (L) =(. e (.
S:-1X Y.tL.J .==.". ".C
UO 2. .j=L.K
C
-~------
--------
C
. _L:2-Q_3 ___ 12 :::: .. L..J.L
R E /\ 0 • ;\1 • X N
D 0 3 ____...L=__ L._ ~"1
------------------------------------------------------
READ.RUN,XNN.j.XNRE,XNP~.VCFl ,VCF2.VCF5,LJA,HI
FAl=XNRE**(1.30/eXN+l.CI)
FA2=XNPR-li-*C: .,2l-)
E)

.------~.~~--
------------------------
C ;:..d1""0LL_,c\,.c,.6L-:'Lv.LULL-t:. ~lJ"li i-\ii h(!- '"1t~:'. ,) j ()~~,.::,_L-",________
C
- __ ~ ____ ------.S ___ ~ ____ . __________________ _
PROGRA
--,- ------~-- -------------
I~ITIALIZ~T!O~$
Rt..AD.EK.cN,JX
K::.:::t:K
N=t:N
PUNCH l02.'l1

282
. .
INl'UT NOMENCLATURE FOR
.
ANALYSIS PROGRAMS;
MULTIPLE VARIABLE,REGRESSION
The program solves s~ultaneous
equations for the
.\
eonstamts (J(O), J(l), J(2), S(3), etc.) ror a correlation
of the t:ype ..
y II1II
J(O) 1- J(l) \-l{l) + J(2) W(2) + J(3) W(3) eo.-t-
ORR
DA
• Paddle position ratio
l1li
DIAR ::
EK -
EN
II:
HI 8i
RITE -
RITR •
JX
Impeller diameter
_ CENTER HEIGHT OF IMPELLER
- LiQufD HEIGnT
Diameter ratio = Vessel diameter/impeller diameter
Number of independent variables
Total number or data points
Impeller width
Center Height o~
paddle
Impeller geometry ratio :: Impeller l.vidth/im.pedler
diameter
= Number or different values of flow behavior index
(or impeller height) to be read in
M • Number at data points having srune flow behavior index
(or impeller height)
RUN II: Run number (ror identi~ication on data card)
VCF2 = Viscosity ratio, K/Kw
XN II: Flow behavior index
X}mu II:
XNPR m
Nusselt number
Pr~dtl number
XNRE = Reynolds number

28.J
ENGLISH ALPHABET
. - ¢,'"'~-=--
a
= Constant in eq. C-l
b = Constant in eq6 C-l
b o
' b l , b 2 , bJ' etc. = Constants called regression coef'f'icients
in eq. c-l~_
C = Constant in eq. c-6
K
= Fluid consistency index of power law
K Q Total number of independent variables in eq. c-4
n
x
I: Flovl behavior index of pm-rer law
= Independent variables
Xi = Individual X data values
Xl' x 2 ' x J
= Independent variables in eq. c-4
-X = Average value of' x
L'XI x2 • Z(xl - Xl) (x2 - x2)
2:' Xl Y = l:;{x l
Xl) (y - y)
Y
= Dependent variables
1\
y - A predicted value for y
Yi
y
= Individual data values
= Average value of y

284
0

References
2.8S
1.
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L.
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107·
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109.
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115.
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120.
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1113.
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