KaHo SINT-LIEVEN
T.E.I. of KAVALA
DEPARTMENT GENT
GENERAL DEPARTMENT OF SCIENCE
Campus GUdestraat
Physics Laboratory
VISCOSITY MEASUREMENTS
Optimizing
several
and
comparing
viscometers
Third year Chemistry option Chemistry
1998
KristofT Pote
KaHo SINT-LIEVEN
T.E.I. of KAVALA
DEPARTMENT GENT
GENERAL DEPARTMENT OF SCIENCE
Campus Gildestraat
Physics Laboratory
l.E .I. K
Θ AΛ
TNi ’.-'’
A
H.
i
,
-.lOi.
,
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VISCOSITY MEASUREMENTS
Optimizing
several
and
comparing
viscometers
Third year Chemistry option Chemistry
1998
Kristoff Pole
TRAINING PERIOD DATA
Period :
10th of February 1998 until 12th of June 1998
Place:
T.E.I. of Kavala
General Department of Science
Physics Laboratory
Agios Loukas PO box 1194, 65404 Kavala
Tel. +30 51 24 43 48 internal 82
Fax +30 51 24 60 30
E-mail [email protected] g
Training supervisor : Professor Fotini Kogia, T E.I Kavala
Training mentor :
Doctor N. A. Maes, KaHo Sint-Lieven
First of all I would like to say thanks to the directors of T.E.I. Kava'a, KaHo
Sint-Lieven Department Gent and the European Community who allowed me to make my final
project in Greece and took care of all the practical arrangements to make my stay here possible
Than, I want to express my gratitude to professor Kogia and doctor Maes for their valuable help
and assistance in realizing this final project.
Some words of appreciation for Mrs Kogia’s family for their hospitality and support
They introduced me to the Greec customs and babbits.
Thanks to them I felt almost at home !
Not to forget my parents, my two sisters Isabelle and Krista and my fiiends who all gave me a lot
of support during these four months. I could always relie on them and they made my stay a lot
Finally I want to place all my Erasmus friends and many Greek students in the spotlight.
Together with them I benifited by the Greek wealth. They made my stay here in Kavala a real
pleasure. Thank you all very much !
Catchwords : falling-ball / Cannon-Fenske / open-tube /
optimizing and comparing viscometers / dynamic viscosity
The main aim of this project was to find viscosity as a function of concentration for several
liquids, in order to make it easier to assess the students work performed in the physics lab.
During these tests we tried to accomplish a further optimization of the falling-ball viscometer,
for example by choosing the right type of balls, and the optimal dropping interval. The whole
experiment was performed under ambient conditions what temperature and pressure concerns
For one of the liquids we investigated the viscosity as a function of concentration (and this at
several temperatures) and tried to find a logical explanation for this relationship
To check the accuracy of the falling-ball viscometer we compared it with two capillary
viscometers, namely the Cannon-Fenske and open-tube type
Generally we can say that the results fiom the open-tube and Cannon-Fenske viscometer
agree whereas the results found for the open-tube are different By investigating this
instrument we try to explain the main reasons for this large difference
As expected the open-tube is least precise. Small temperature variations, and accordingly
small viscosity changes were hard to detect
Alongside several experiments with the falling-ball viscometer are performed in order to
know the influence of all the possible variables on the resulting viscosity, and the way to
control them to come to a better result. Especially the viscosity from the intercept (found with
the least square method) gets our full attention in order to explain and control the large
variations of this value when compared with the average viscosity value.
Another main part was how to link the results found by using the big tube (1000 ml) we
applied and the small tube (100 ml) used by the students in the practical physics lesson. We
found a formula that takes into account the diameter of the tube to come to a good match
between the two results. As we saw that the results found with this formula did not match
well we corrected this formula to come to an optimal match between the results found with
the two cylinders.
TABLE OF CONTENTS
Page number
1
T.E.I. OF KAVALA
.1
1.1
INTRODUCTION................................................................................................... 1
1.2
STUDENT SERVICES AND FACILILITIES.......................................................1
1.3
OBJECTIVE AND ORGANISATONAL STRUCTURE..................
2
DESCRIPTION OF THE PROJECT
2.1
INTRODUCTION...
2.1.1
Main aim................
2.12
2.1,21
2.1.2.2
2.1.2.3
2.1.2.4
Other aims.......................................
Viscosity as a function of concentration
Comparison between lead and glass balls
Taking into account the diameter of the tube
Comparing the falling-ball viscometer with other viscometers
2.1.3
Final Result........................................................................................................... 5
.3
.3
,3
.4
,4
2.2
HISTORICAL BACKGROUND.............
6
2.2.1
History of rheology
6
2.2.2
History of viscosity measurements ...................................................................6
2.2.3
U n its ,......... ..............................
7
3
T H E O R E T IC A L PA R T
3.1
INTRODUCTION
32
DENSITY.............................
3.3.2
3.3.2.1
3.3.2 2
3.3.2.3
Falling-ball viscometer ............................................................ ........................9
Not taking into account the diameter of the tube..................................................9
Taking into account the diameter of the tube........................................................ 11
Velocity of the falling ball..................................................................................... 11
3.3.3
Capillary viscometers........................................................................
13
3.3.4
Coefficient of internal friction and kinematic viscosity...................
14
34
VISCOSITY AS A FUNCTION OF TEMPERATURE.................
15
EXPERIMENTAL PART
411
Density of the tested liquids...................................................................................17
4 111 Hydrometers..................
17
4 1.1.2 Weighing a known volume of liquid........................................................................17
4.1.2
Density of the balls................................................................................................ 17
4.2
FALLNG-BALL VISCOMETER...........................................................................18
4 2.1
Viscosity as a function of concentration for several liquids.............................. 18
4 2.2
Comparison between lead and glass balls
4 2.3
Viscosity as a function of water-concentration for glycerol.............................. 19
4 2.4
Measurements by using a small and a big cylinder ......................................... 19
.................................................19
4.3
OPEN-TUBE VISCOMETER....................................................
44
CANNON-FENSKE VISCOMETER.................................................................... 21
20
4.5
SAMPLE DESCRIPTION..
4.5.1
Detergent 1.........................
...22
4.5.2
Detergent 2.........................
...22
4.5.3
Motor oil.............................
...22
4.5.4
Olive oil...............................
...22
4.5.5
Frying oil.............................
4.5.6
Vacuum pump oil..................................................................................................23
4.5.7
Lamp oil......................
23
4.5.8
Glycerol.................................................................................................
23
5
RESULTS AND DISCUSSION
5.1
DENSITY OF THE TESTED LIQUIDS AND OF THE BALLS...
5.1.1
Density of the tested liquids..........................................................
...25
5.1.2
Density of the balls.........................................................................
...25
5.2
FALLING-BALL VISCOMETER.................................................
...27
Practical dropping speed investigation........................................
5.2.1
5.2.1.1 Practical dropping speed investigation for detergent 1.............................
5.2.1.2 Practical dropping speed investigation for detergent 2 and for glycerol...
...27
27
...29
5.2.2
Theoretical dropping speed investigation..............
.29
5.2.3
5.2.3.1
52.3.2
5.23.3
5.2.34
5.2.3.5
5.2.36
5.2.3.7
5.2.3.8
Viscosity as a function of temperature for several liquids
Detergent 1.............................................................
Detergent 2 .............................................................
Motor oil.....................................................................
Olive oil......................................................................
Vacuum pump oil with lead balls...............................
Vacuum pump oil with glass balls.............................
Glycerol............ ..........................................................
Discussion of the viscous behaviour of the tested liquids
.30
5.2.4
Explanation for the poor match between
the average viscosity and the viscosity from the intercept.................
.......
5.2.4.1 Causes.................................................................................................................... 51
5.2.4.2 Indications for the poor match.............................. . .......................................... 51
5.2.4.3 Possible solutions...................................................................................................53
5.2.5
Viscosity as a function of concentration for glycerol.
...57
5.2.6
Comparison between lead and glass balls....................
...59
5.2.7
Measurements by using a small and a big cylinder.............................................. 61
5.3
C.\NNON-FENSKE VISCOMETER...................................................................65
5.3.1
Investigated liquids............................................................................................. 65
5.3.2
5.3.2.1
5.3.2 2
5.3.2 3
Results
65
Motor oil................................................................................................................66
Vacuum pump oil
67
Glycerol................................................................................................................. 68
5.3.3
Conclusion.............................................................................................................. 68
5.4
OPEN-TUBE VISCOMETER............................................................................... 69
5.4 1
General comments............................................................................................... 69
5.4.2
Test results..............................................................................
5.4.3
Conclusion............................................................................................................. 72
69
6
FINAL RESULT................................................................................................... 73
61
FALLING-BALL VISCOMETER..........................................................................73
6.1.1
Viscosity as a function of tem perature
73
6.1.2
Viscosity as a function of concentration
73
6.1.3
Comparison between lead and glass balls..........................................................74
6.1 4
Measuiements by using a small and a big tube.................................................. 74
6.2
CANNON-FENSKE VISCOMETER....................................................................75
63
OPEN-TUBE VISCOMETER................................................................................ 75
6.4
FINAL CONCLUSION .ABOUT
ALL THREE VISCOMETERS.....
..75
BIBLIOGRAPHY
APPENDIX I: FURTHER INVESTIGATION OF THE A AND B CONSTANT
FROM THE ANDRADE EQUATION.
APPENDIX 2: NOMOGRAPH FOR VISCOSITIES OF LIQUIDS
Τ.Ε.Ι. OF KAVALA
INTRODUCTION
The T.E I , which stands for Technological Educational Institute of Kavala, is grouped
alongside the Universities and Polytechnic schools of Greece who provide Tertiary (higher)
Education.
The T E.I. is divided in three main parts, two schools in Kavala and one in Drama (36 km
away from Kavala). It contains :
• a School of Applied Technology, with departments of Electronic and Mechanical
Engineering, Petroleum Technology and the General Department of Science
• a School of Business Administration and Economics, with departments of Accountc...cy
and Business Management. Foreign Languages and Physical Education.
• the Department of Forestry in Drama.
The academic year starts on September 1st and ends on July 5th. It consists of a winter and a
summer semester Each semester exists of fifteen lesson weeks and is followed by an exam of
two weeks. A total study consists of six semesters of course, followed by 6-8 months
placement in industries, organisations and enterprises.
12
STUDENT SERVICES AND FACILITIES
The students receive the following benefits :
• free textbooks and teaching notes
• free medical care
• discounts on all travel by public transport (up to 30 %)
• free use of school library
Students can live in one of the 230 rooms (for two persons each). In the school restaurant all
the meals are provided by T.E.I
These accommodations are also offered to the foreign Erasmus students for a reasonable
price. Those students whose family income is below a stated minimum are offered free
accommodation and meals.
When registered, every T.E.I. student automatically becomes member of the student
associations of their school, who provide a wide range of sport and cultural activities An
elected representative boards in all the administrative committees of the institute.
The school takes part in several European exchange programs like Erasmus, Lingua,
Euroform, Eurashe, TEXT (Trans-European Exchange and Transfer consortium)..
Also exchanges between the academic staff of T.E. I. Kavala and other European universities
for teaching , participation and formation of joint co-operation have been organised
Recently, study proposals were accepted for activities under the ‘’Linking Higher Education
and Industry” program
I3
OBJECTIVE AND ORGANISATIONAL STRUCTURE
"The aim of the institute is to offer education at the highest level of appliea scientific
knowledge, while promoting modem technological skills.
It aims at creating responsible citizens who are able to make positive contribution to the
economic, social and cultural development of their country. It maintains close co-operation
with its employers, the professions and other public organisations.
It works in close co-operation with its counterpart Higher Education Institutes in the fields of
technology and research, both at home and abroad.
It serves the continuing needs of its graduates with a view to the development of the Greek
people as a whole”
(Tech. Ed. Inst, of Kavala, 1993)
Fig. 1: The top-down hierarchical organis-iional structure of the T.E.I. of Kavala
DESCRIPTION OF ^HE PROJECT
The basic goal of the project is to get the viscosity in function of temperature for several
liquids, such as : two detergents, olive oil, Esso motor oil, a lubricating oil for a vacuum
pump and glycerol.
Therefore the saTi“ set-up as foreseen for the students of the practical physics lesson, is used,
namely a falling-ball viscometer with a glass tube of 1000 ml.
The viscosity in function of concentration is also measured for one of the liquids to see if
there is a logical explanation for the found relation.
Afterwards, the falling-ball viscometer will be further optimized and compared with other
viscometeis of the capillary type.
2.1
INTRODUCTION
2.1.1
Main aim
By using the falling-ball viscometer (Fig. 2) we try to obtain dynamic viscosity η in function
of temperature. The measurements are done fully manual.
The first thing to know was at which height the dropping speed reached maximum (viimted)
Therefore a students t-test (95 % interval) is used to compare the different areas of the tube.
Also theoretically we calculated where and when the falling ball reaches vumiied
Fig. 2 : Falling-ball viscometer (the set-up we used)
2.1.2
Other aims
2.1.2.1 Viscosity as a function of concentration
For one of the tested liquids, the viscosity as a function of concentration is determined by
using the falling-ball viscometer. This experiment is performed at several temperatures, to
check the influence of it on the resulting graph, and to compare the resulting graphs with each
other.
We find an explanation for this relation in order to come to a general conclusion about
viscosity as a function of concentration.
2.1.2.2 Comparison between lead and glass balls
For one of the liquids we check if the measurements with lead and glass balls (Fig. 3) are an
estimation for the same viscosity. For this liquid we do the testing at the different room
temperatures with two kind of balls.
Fig. 3 : Lead and glass
By using a students t-test the average viscosities are compared with each other
This test is an indication for the importance of the smoothness of the ball surface on the
resulting viscosity.
2.1.1.3
Taking into account the diameter of the tube
We make a comparison between a small tube of 100 ml and a big tube of 1000 ml by using
another formula that takes into account the diameter R of the tube.
This formula is used to calculate the viscosities from measurements in both tubes and we
compare these results with each other by using a students t-test (95 % interval).
This can be an indication for the influence of the tube diameter on the resulting viscosity,
and, at the same time, a verification o f this formula.
2.1.1
Comparing the falling-ball viscometer with other viscometers
By using capillary viscometers (open tube (Fig. 4) and Cannon-Fenske (Fig. 5) ) we tested the
accuracy o f the falling-ball viscometer Important is that these capillary viscometers are not
absolute as the glass undergoes small deformations (expansion and shrinkage) as the
temperature changes
The big advantage of these capillary viscometers - especially the Cannon-Fenske - is that they
are small and can be placed in a constant temperature bath. In this way the measurements are
done in a much larger temperature interval than for the falling-ball viscometer where no
temperature controlling is possible and consequently we work at room temperature
V0
Fig. 4 : Simple open tube
Fig. 5 : Cannon-Fenske viscometer
2.1.2
Final Result
The final aim is to bring together all the results from the three methods and come to a general
conclusion about the quality of the falling-ball and the other viscometers, we will have
investigated alongside
Coming to *his conclusion is most certainly the hardest thing to do as the real viscosities of
the testing liquids are not known. In this way it is dangerous to draw conclusions about the
accuracy o f the testing results. This makes a questioning (or evenly a rejection) of one of the
testing methods almost impossible
fflSTORICAL BACKGROUND
2.2.1
History of rheology (1)
Everything began with Archimedes (287-312 BC) and his principles o f buoyancy (his
experiment with the bath-tub and the scene afterwards are very famous).
Only little of the Ancients knowledge appears in modem fluid mechanics. After the fall of the
Roman Empire ( 476 AD) we have to wait until the time of Leonardo da Vinci (1425-1519) to
see some progress in fluid mechanics.
After da Vinci the accumulation of hydrauhc knowledge rapidly gained momentum with the
contributions of Galileo, Torricelli, Mariotte, Pascal, Newton, Pirot, Bernoulli, Euler and
d’Alambert. It was this last scientist who observed in 1744, th a t: «The theory o f fluids must
necessarily be based upon experiment ».
Near the middle of the last century, Navier and Stokes were succeeded in modifying the
general equations for ideal motion to fit those of a viscous fluid.
Towards the end of the last century many significant advances in our knowledge were
realized One o f the most important contributions was made by Prandtl (2) in 1904 when he
introduced the concept of the boundary layer (Fig. 6). In his short descriptive paper, Prandtl
provided an essential link between ideal and real fluid motion for fluids with a small viscosity
(e g. water) and provided the basis for much of modem fluid mechanics.
Fig. 6 : Liquid flow with speed v = vo that comes on a flat plate sorting in a boundary layer of
liquid, on the plate surface. This boundary layer is caused by the fact that the fluid particles at
the body walls remain at rest (v = 0).
2.2.2
History of viscosity measurements
In viscosity measurements there is also an impro..„..icr.t demonstrable ; the very first one used
an open tube (3) and simply note the time to drain a standard amount of liquid. This method
is daily used in petroleum and other industries in the form o f Shell - or Zahn cups. Afterwards
this was perfected, leading to Cannon-Fenske type viscometers
The open tube needs to be calibrated (with fluids of quite similar properties to the fluid under
investigation), which is not longer necessary for the Cannon-Fenske viscometers, as they are
calibrated once by the producer.
Later the falling-ball viscometer was invented, based on Stokes Law. The sample viscosity is
correlated to the time a ball requires to traverse a definite distance. This instrument measures
accurately the viscosity of Newtonian liquids and gases. Its measuring accuracy when backed
up by a precise temperature control is not surpassed by any other type of viscometer
More recently a whole range of viscometers (most of them computer controlled) have been
introduced. One very popular is the rotating-disc type viscometer with two concentric
cylinders and the investigated liquid in between. Mostly the outer cylinder rotates at constant
speed, whereas the internal one (side of the cup) is static Sometimes it is the other way
around.
Of course there is a large number of other viscometers available at this moment, which are not
mentioned here as they were not used in this project.
223
Units
The first dynamic viscosity unit was given the name “’poise” (after Poiseuille, who did some
of the first work on viscosity). In 1960 the SI committee (Systeme International d’Unites)
decided that the standard dynamic viscosity unit is Pa s. To go fiOm Pa s to poise the
following relation is used :
1 Pa.s
10 poises
Here, in the physics lab of T.E.I. poise is used as unity o f dynamic viscosity. To meet with
the other results we also use poise, and not Pa s.
T H E O R E T IC A L PA R T
INTRODUCTION
The falling-ball viscometer is based on Stokes law, which will be discussed further on To get
the viscosity value out of the radius of the ball and the dropping time the density of the liquid
and balls is needed
3.2
DENSITY
Density is the mass (= the amount of matter) contained in a unit volume.
This term fundamentally depends on the number "f molecules per unit of volume.
As molecular activity and spacing increase with temperature, fewer molecules exist in a given
volume of fluid as temperature rises, thus density decreases with increasing temperature
Notwithstanding this we measured the density only at one temperature.
3.3
VISCOSITY
3.3.1
Definition (4)
Viscosity is fundamentally a consequence of the intermolecular interactions in the fluid It is
the transfer of momentum from one part of a fluid to an adjacent part.
The common way to represent this physical property is by a viscous liquid between two plates
A and B, with surface S (Fig. 7). Plate A is being moved with a constant speed vo, while plate
B is at a standstill. A laminar flow is created where the bottom layer is at a standstill, and the
upper layer moves with a speed vo. In between the speed increases linearly from 0 till vo for
values of y from 0 till d.
Microscopically the molecules in a liquid are surrounded by a ’cage’ of other molecules
Momentum transfer in the liquid will involve the movement of these cages around one
another Increasing the temperature causes the cages to jiggle a bit more, allowing them to
slip more easily past one another, thereby reducing the momentum transfer between adjacent
bits of the fluid, and thereby reducing the viscosity of the liquid.
Y
Fig. 7 : Viscous fluid between
2 plates, A and B
Fig. 8 Speed in function of y (the distance
between a layer and the plate B)
The second graph (Fig. 8) gives the speed of every layer in function of y, the distance between
a layer and the plate B
3.3.2
3.3.2.1
Falling-baJI viscometer
Not taking into account the diameter of the tube
This method is based on Stokes law that says that for a falling ball (with radius r) in a liquid
with viscosity η experiences a resistance F«, from which the magnitude for not too large
velocities is given by :
When a ball is dropped in a viscous liquid a stationary state is obtained after a certain time as
the ball falls with a constant dropping speed vumited At that moment (5) the sum of all the
forces on the ball is zero (therefore it is very important to do the measurements in that part of
the tube where vumtaj is obtained.
When the resulting force on the ball is zero we may say :
weight + upward pressure + resistance force = 0
Where pb,u is the density of the ball and puquid is the density of the liquid in the tube
After estimating vumitid (out of the dropping time and the length of the dropping area) the
viscosity can be calculated:
-P ,u ^ ,) g r^
This is the basic principle of the falling-ball viscometer: after measuring the diameter r of a
ball (lead or glass) we drop it in a tube that contains the liquid and measure the time t to run
the distance s. The speed viimied is equal to s/t.
There is also a second way: by taking the log of the formula linear relationship between
log vumited and log r can be obtained. The relation between viunied and r is of an exponential
kind (Fig. 9), but to facilitate the calculations we take the log of this formula and find:
2
logt'ta
Equation of the
f 2-logr
(linear) form (Fig. 10).
Rg 9 E)qxnential relatia
betvveen rand
Fig. 9 and Fig. 10: Illustration of the exponential and li..car relationship
(Experimental /alues for olive oil)
3.3.2.2
Taking into account th , diameter of the tube
There is another viscosity formula (6)(7) that also takes into account the diameter of the tube
next to the ball-radius and the dropping time:
_ ^'
ipball
~
Plkpud\S ' ^
With r = radius of the ball and R = radius of the tube
Also here there is a second way to derive the viscosity: by taking the log of the formula a
linear relation between log vumiied and log
r^
can be obtained. The viscosity is
part of the intercept.
(1 + 2,4(r/R))
Equation in logarithmic form.
3.3.2.3
Velocity of the falling ball
By taking into account all the forces that work on the falling ball we want to calculate
theoretically (8) how much time is needed to gain vun^ed
The speed v of the falling ball is caused by the following forces:
V = weight - Friction (Stokes law) - upward pressure (Archimedes force)
or
4
3
t g - l S -π-η
dr
df=
- Α π -r
we integrate between i, = 0 s and t-^=ts
J
J
f=-
J
β π - η -r
3-mg-18-^--r7-rv^
J
3m g-18-«··
- ini^mg-nK-nr-v^
- A- K- r
p g
'■ p g )+ c
(1)
fVe want to find c ;when t = 0 than v == 0
=
m g -4 -;t
6·π ·η r
^
’•rig)
*
<2),>,(1>:
/ = --— ----- ln(3 m g-18
6·π ·η·Γ
r - v ^ . a - 4 - Γ- ri g ) - ^ - f ^ m ^ -
g
A n r^ p g
^
In
β π η -r
3 ■m ■g - IS ■π ■η ■r ’ ^lunlUd “ 4 ■Λ"■Γ ’ p ‘8
3 m g -Λ π -r^ p g
3 m g - \S n η
^■p g
3 m g - \S π ·η ·Γ ·ι> ^^,„^-4 ·π r
\S η η -r v ^ ^ ^ = ^ m g - 4 -π .r’ rig)|l-«" ■
3 - t r^ '
j
g -A t
■Ρϊιφαά ■8 (
**J*^ ^
\S■t■η■t
[
J
2 jp i^ - P b ^ ) g
The relahonship between v and t is of an exponential type:
y^A .i^- β ^ή
This relation is described by the following curve:
Fig. 11: Speed of the falling ball v as a function of dropping time t.
Knowing that the falling ball gains the constant droppmg speed v , , ^ when t = 5/-B
m
6 ·π·η ·Γ
We want to calculate where the falling ball gains vum««i in order to know in which interval of the cylinder
measurements have to be taken:
dTint egration gives :
h ~ l·
■d7+ —
tVe want to calculate c :when .r = 0 than ( =0 -+c = ---- ---b n η -r
(A)in{3)gtves :x = A t * ------- «
6 tt „ r [
knowing 'hatl = —
5 m
π η-Γ
■'
”
(4)
' - li t h e distance necessarylo gain
j
2(pi^-p,^^)gr^'
9 η
5 m
^
m
/.s
(, η η f 6·π η -r
Now we can calculate theoretically after which distance x the falling ball gains its maximum
dropping speed vu™ted.
3.3.3
Capillary viscometers
By using the stream method whereby an amount of liquid streams through the narrow opening
of a tube, or passes through the capillary of a Cannon-Fenske viscometer (Fig. 12), the
kinematic viscosity v can be determined fi-om the time necessary for a fixed volume of liquid
to pass through a small tube under standard head (pressure on the liquid) condition.
Fig. 13: Tube-type viscometer
The relation between time and viscosity for the tube-type viscometer (Fig. 13) may be
indicated approximately by applying the Hagen-Poiseuille law (9)(10) for laminar flow in a
circular tube:
S-η· L
Φ is the flow rate
The difference in pressure (pi - P2) is here the hydrostatic pressure of the liquid with height
h+L(seeFig. 13).
The dynamic viscosity is than:
7
= -
■jh + L)
8-Ζ, Φ
kinematic viscosity is
^
77 π -R* g {h + L)
p
8 - Ι Φ
We can find φ = V/t by measuring the drained volume of liquid and time
When the drained volume and the height of the tube are constant, than:
V = — = constant
So the kinematic viscosity is in a linear relationship with the time to drain. For the different
liquids the times to drain are in proportion to the kinematic viscosities at the same
temperature
Pi ■
By choosing an appropriate standard with a known viscosity to calibrate the open tube the
kinematic viscosity of another liquid can be estimated. If the density of this liquid is known,
the dynamic viscosity can be found.
With a constant the deformations of the glass caused by the changing temperature, is taken
into account. Therefore this constant is measured twice; once at 40 °C and once at 100 °C, by
the manufacturer. With these two measurements a line can be constructed, and we can find
the apparatus constant at other temperatures.
Example for a 100 type Carmon-Fenske with serial number E84:
For the Cannon-Fenske viscometer the apparatus constant c was measured once (by the
manufacturer) with a standard viscosity liquid at two or sometimes three different
temperatures. We can find this constant c with: c = v/t
In this way the viscosity can be immediately estimated fiOm the draining time for another
liquid by multiplying the time with the apparatus constant c at its according temperature.
3.3
.4
Coefficient of internal friction and kinematic viscosity
η (dynamic or absolute viscosity) is defined as
coefficient of internal friction
Due to the appearance of the ratio η/ρ in many of the equations of fluid flow, this term has
been defined by :
P
In which v is called the kinematic viscosity
The dimension of η is Pa s. Before 1960 the dimension of η was poi'“ (P)
(1 poise = 0,1 Pas).
Considering ν=η/ρ shows the dimension of v to be m^/s, a combination o f kinematic terms,
which explains the name kinematic viscosity.
An old dimension that is still used (mostly in America) is the Stokes (St), named after the
English physician George Stokes.
One Stokes equals one cm^/s, so the following relationship between both can be found :
I St = 1 cm /s =
0"* m^/s
Although η and v are widely used, they may prove both surprising and troublesome to the
beginner in the field. For example, water is more viscous than air in terms of η, but air is
more viscous than water in terms of v because air is relatively much less dense than water.
3.4
VISCOSITY AS A FUNCTION OF TEMPERATURE
The viscosity as a fimction of temperature can be described by the following equation (11):
η = A
This relation is of an exponential type. It is a good approximation to assume that
In η is in a linear relationship with T ‘.
In Π = In
A
+
R
■\
|
)
This simple form was apperently first proposed by de Guzman (in 1913), but is more
commonly refered as the Andrade equation (12).
Parameter B corresponds with the energy of flow activation (13). This was found after new
research.
The A constant modulates the viscosity η at several temperatures.
By using the equation we can find the units of these two constants A and B :
By using the ideal gas law we will calculate the unit of R:
PV
P V = n R T ----------------------------► R = - -----n T
We fill in the units:
mol K
mol K
J
mol
A = poise
Many variations for the Andrade equation have been proposed to improve upon its correlation
accuracy , many include some function of the liquid molar volume in either the A or B
parameter.
Another variaton on this Andrade equation involves the use of a third constant C to obtain the
Vogel equation :
\ηη = A' +
B'
The three constants A’, B’ (we use A’ and B’ as these constants ars not the same as the ones
in the Andrade equation) and C are three constau.a for a fluid. These constants can be used to
derive information about the viscous behavior of a liquid.
EXPERIMENTAL PART
4.1.1
Density of the tested liquids
Two basic methods are used :
• Hydrometers
• Weighing a known volume of liquid
4.1.1.1
Hydrometers
The used Nakamura hydrometers have a precision of ±0,001 g/ml.
To create great variation of immersion for small density variation, and, thus, to provide a
sensitive instrument, changes in the immersion of the hydrometer occur alone a slender tube,
which is graduated to read the specific gravity of the liquid at the point where the liquid
surface intersects the tube (Fig. 14)
To be able to determine the whole range of densities, hydrometers with several weights are
needed
Fig. 14 ; Nakamura hydrometer
4 1.1.2 Weighing a known volume of liquid
Normally a picnometer is being used, but we worked with a glass cylinder of 50 ml.
A standard amount of liquid with volume V (eg 25,0 ml) is taken, and the mass m of the
liquid is determined with a balance
Here the precision is ±0,1 g/ml
4 1.2
Density of the balls
By measuring the radius of 10 balls with a screw micrometer (Fig 14) and weighing them all
together the density can be determined.
This needs to be done for the lead and both kinds of glass balls (big dull ones, and transparent
small ones).
FALLING-BALL VISCOMETER
4.2.1
Viscosity as a function of temperature for several liquids
All the experiments were done under ambient conditions what temperature and pressure
concerns.
The testing is done by using different kind of balls (different diameter, and different material).
For the lower viscosity liquids (olive oil, and a lubricating oil for a vacuum pump) the glass
balls, with lower density and accordingly lower weight were used.
For the high viscosity liquids lead balls with diameter between 0,1500 cm to 0,3000 cm were
used.
The te s t:
• First of all the diameter of the ball is measured with a screw-micrometer (Fig. 15)
(precision ±0,0001 cm).
• The ball is being released when it touches the surface o f the liquid (Fig. 16)
• The digital chronometer is started by hand when the ball passes the 800 ml mark (Fig 17).
• It is stopped when the ball passes the 100 ml mark (Fig. 18).
• The dropping time is being noted.
• Twelve measurements for each liquid at each temperature were carried out
Fig. 15 : Measuring the diameter of the ball with a screw-micrometer
Fig. 16 ;Release the ball in
Fig. 17 :Start the chronometer Fig. 18 :Stop the chronometer
the middle of the tube
when the ball
when the ball
passes the 800 ml mark
passes the 100 ml mark
4 2.2
Comparison betweet. glass and lead balls
The measuring is similar to the method explained under 4 2.1.
The dropping time is being measured for one of the liquids at a constant temperature with
glass and lead balls (Fig. 19).
Again we take twelve measurements with each kind of balls in the above-mentioned way
Mso here the ball ^'ameter and the dropping time are being noted.
Fig. 19: glass and lead balls of different diameter
4.2.3
Viscosity as a function of water-concentration for glycerol
By using small amounts of water into 99 % pure glycerol the viscosity/water-concentration
graph can be derived.
Now the testing is done in a 100 ml glass cylinder (the mixing of the two liquids would be
very hard when a cylinder of 1000 ml is being used).
The water is added with a pipette of 10,00 ml, by counting the number of added drops.
We start with extra pure glycerol and take twelve measurements, using lead balls with
diameter of approximately 0,2200 cm.
-\fter every series of measurements 10 droplets of water are added and mixed very v. cll.
Again we take twelve measurements.
The water is added until the dropping time gets shorter than 3 seconds as smaller dropping
times are hard to be measured
This whole experiment is performed at several ambient temperatures.
4.2.4
Measurements by using a small and a big cylinder
The large vessel has a content of 1000 ml while the small one a content of 100 ml.
We work at a constant (room) temperature.
By doing twelve measurements with both tubes (with lead balls) we find the according
dropping times.
This experiment is performed at several temperatures in order to get a series of results.
4.3
OPEN-TUBE VISCOMETER
The kinematic viscosity v is measured at several temperatures.
The tube is being calibrated with standard viscosity liquids (a known viscosity at a certain
temperature).
The test:
• The glass tube (Fig. 20) is, after plugging the outlet, being filled till the brim.
• Than the plug is removed, and at the same time the chronometer is started (Fig. 21).
• When all the liquid in the tube is drained, the chronometer is stopped (Fig. 22).
• The draining time is being noted
• The measurement is done twice for every liquid -t one temperature
alter Stepper
Fig. 20; Filling the
tube
Fig. 21: Remove the plug,
and start the chronometer
Fig. 22: When the liquid
is drained, stop
the chronometer
4 4 CANNON-FENSI'vE VISCOMETER
By using a constant temperature bath (Fig. 23) a much larger temperature interval is possible
The test:
• First the two bowls [1] and [2 ] are being filled by placing the tube upside down in a
recipient containing the liquid, and filled by removing the air with a pipette bulb (Fig. 24).
• Than the instrument is turned again (into normal position), and the pipette bulb is
removed
• The chronometer is started «'hen the meniscus passes line A (Fig. 25).
• It is being stopped when the meniscus passes line B (Fig. 26).
• The time is noted.
pipette bulb
Fig. 23: Constant temperature bath.
Fig. 25: Starting the chronometer when the
meniscus passes line A
Fig. 24: Filling bowl [1] and [2] by
removing the air with a pipette bulb
Fig 26: Stopping the chronometer when
the meniscus passes line B
4.5
SAMPLE DESCRIPTION
4,5.1
Detergent 1
Product name ; Svelto extra concentrated
Type : detergent to wash the dishes
Contents mentioned on the label:
• Anionic tensio-active substances...................................... more than 5 but less than 15 %
• Non-ionic tensio-active substances....................................less than 5 %
• Amphoteric tensio-active substances
• Preservatives
• Bio degradable substances................................................ more than 90 %
Producer : LEVER HELLAS AEBE
Address : Marinou Antipa 92, 14121 Neo Iraklio
Tel.
: +30 1 271 99 01
4.5.2
Detergent 2
Product name : Sweep
Type : liquid detergent detergent for the dishes
Contents mentioned on the label:
• Anionic tensio-active substances.....................................................................15%
• Non-ionic tensio-active substances.................................................................. than 30%
• Amphoteric tensio-active substances.............................................................. less than 5 %
. ..less than 5 %
• Preservatives..
Distributor K. Stamoulis and sia (unlimited company)
57500 Trilofos of Thessaloniki
Address
+ 30 31 43 33 31
Tel.
+ 30 31 44 85 98
Fax
4.5.3
Motor oil
Product name : Esso Super Oil
PREMIUM MOTOR OIL
Type : High grade greasing
SAE 15W-40
Contents mentioned on the label: Premium motor oil, produced m Greece.
Producer : EKO ABEE
Address ; Mesogion 2, Athens
4.5.4
Olive oil
Product name : Olive Oil
Type : acidity 0 - 1 %
Contents mentioned on the label; none
Produce*· : ELAIS (ΕΑΑΙΣ)
Address : Neo Faliro 18547, Athens
Tel.
; + 30 1 489 65 99
4 5.5
Frying oil
Product name : KORE soya oil
Type : oil for frying
Contents mentioned on the label:
• Multi-unsaturated fats............................................................................................... 57 %
• Other mono-unsaturated fats..................................................................................... 24 %
• Cholesterol (mg/10 g)............................................................................................... 0
• Sodium (mg/10 g)..................................................................................................... 0
• Energy value (kJ/10 g).............................................................................................. 376 kJ
Producer : KORE A.E. (limited company)
Address : Orizomilon 16, 12244 Egaleo
Tel.
: +30 5 39 45 12
4 5.6
Vacuum pump oil
Product nam e: unknown
Type : lubricating oil for a vacuum pump
Contents mentioned on the label: none
provided by the producer of the vacuum pump: OGAWA SEIKI CO., LTD
Address : Tokyo Central 1618, Tokyo - Japan
Tel.
: + 03 367 82 11
4.5.7
Lamp oil
Product name : MAMIKADIS lamp and cooking oil
Type : Petroleum based oil for small heating units and lamps
Contents mentioned on the label: none
Producer : AEEP G. MAMIKADIS and sia
Address : Panepistimiov 56, 10678 Athens
4.5.8
Glycerol
Product name : Glycerin 99 %
Reinst, DAB, Ph Eur., B P , Ph. Fran?., U.S.P , FCC, E 422
Glycerol 99 % extra pure
Type: Laboratory product
Contents mentioned on the label
• Assay............................................................................................................ 9 8 -1 0 1 %
• Water (Karl Fischer)....................................................................................max. 2 %
• Sulphated ash................................................................................................
• Free acid (as CHjCOOH)..........................................................................max 0,003 %
,
.......................................... max. 0 ,0001 %
.
..............................................................................
, pjj
.............................................max. 0,001 %
.
..............................................................................max. 0,001%
• Heavy metals (as Pb)
0,0005 %
. Chloride (Cl)...................................................................................................max. 0,001 %
• Halogen compounds (as C l)......................................................................... max. 0,003 %
• Sulphate ^S0 4 ) ............................................................................................. max. 0,001 %
• Aldehydes, red matter (asHCHO).................................................................max 0,0005 %
• 1-Butanol (G C )............................................................................................. max 0,2 %
Producer : Riedel-de Haen AG
Address : D - 30926 Seelze, Germany
Tel.
: +31 51 37 99 90
RESULTS AND DISCUSSION
5.1
DENSITY OF THE TESTED LIQUIDS AND OF THE BALLS
We used hydrometers, and weighing a known volume of liquid for the liquids.
To be able to determine the whole range of densities, hydrometers with several weights were
needed
For the balls we measured the radius and the weight.
5.1 1
Density of the tested liquids
able 1: Density estimated by weighing a certain amount of liquid .
The density can be fo und with : p = m/v
liquid
detergent 1
detergent 2
'acuum pump
oil
motor oil
olive oil
frying oil
glycerol
volume
ml
25,0
24,0
25,5
weight
g
26,22
25,00
22,56
density
g/ml
1,05
1,04
0,89
29,5
27,0
30,5
40,1
25,96
25,14
28,13
50,92
0,88
0,93
0,92
1.27
Table 2: Density estimated with
a hydrometer
liquid
detergent 1
detergent 2
vacuum pump
oil
motor oil
olive oil
frying oil
glycerol
density
g/ml
1,050
1,060
0,875
0,885
0,930
0,922
1,270
Table 3: Average density of the
liquids
density
Q/ml
1,05
1,05
0,88
liquid
detergent 1
detergent 2
yacuum pump
oil
motor oil
olive oil
frying oil
glycerol
5.1.2
0,88
0,93
0,92
1,27
Density of the balls
As we had b’dls of two different materials (glass and lead) it was necessary to estimate their
density separately. From the glass balls we also had two different sorts : big dull-glass ones, and
small transparent ones.
Out of the radius (η) of 10 balls, and their total weight m,aui, the density can be found with :
p =
m
knowing
that
4
2
= —- λ^-Σ γ,
Table 4 Test results for lead balls Big Pb balls where used, as they have a larger weight and
a larger radius
diameter
cm
0,8450
0,8300
0,8220
radius
cm
0,4225
0,4150
0,4110
0,8230
0,8430
0,4115
0,4215
Table5^_Test_resultsJbrbig
diameter
cm
radius
cm
0,3743
0,4538
0,4201
0,3657
0,3636
0,1872
0,2269
0,2100
0,1828
0,1818
0,3728
0,1864
0,3687
0,3665
0,3720
0,4149
0,1844
0,1832
0,1860
0,2074
Vtotai= 1,512
density = 11,41 g/cm
mtaai = 17,25
balls
'9 cmv.
0^
density = 2,551 g/cm
Table 6: test results for small transparent-glass balls : in order to find a good measurable
diameter
cm
radius
cm
0,2721
0,2968
0,2593
0,2517
0,2670
0,2588
0,2513
0,1361
0,1484
0,1297
0,1259
0,1335
0,1294
0,1257
0,2578
0,2930
0,2708
0,2607
0,3020
0,2824
0,2628
0,2550
0,2929
0,2918
0,1289
0,1465
0,1354
0,1304
0,1510
0,1412
0,1314
0,1275
0,1465
0,1459
4 density = 3,088 g/cm
2
FALLING-BALL VISCO' lETER
2.1
Practical dropping speed investigation
tie first parameter to know is at which height the dropping speed reached maximum (vumitoj)
herefore a students t-test (95 % level) was used to compare the different areas of the tube The
ost ideal would ha\ e been to compare the maximum dropping speed for the different areas
imediately, but than balls with the same diameter are needed We tried to do this test but the
:sult was very doubtful as none of the balls had a perfectly equal diameter
was better to do the same test with randomly picked balls and this time compare the viscosity
id not the maximum dropping speed.
his testing was only possible for the two detergents and for glycerol, as the dropping time of the
ther liquids (motor oil, olive oil and lubricating oil for a vacuum pump) was already very short
id a reduction of the measuring area would result in a too short test time. For these liquids we
jsumed that the dropping speed is maximum, what seems acceptable as the ball immediately
ained a large speed when it was being dropped in the liquid
•nly the test results for one of the detergents are included because all ihe tests were done in the
ime way and therefore it would be excessive to give all the data.
.2.1.1 Practical dropping speed investigation for detergent 1
he investigated intervals are:
Standard dropping area : between the 800 and 100 ml mark
between the 800 and 200 ml mark
between the 700 and 100 ml mark
■ between the 700 and 200 ml mark
• between the 900 and 100 ml mark
• between the 900 and 200 ml mark
*Ve took 10 measurements for each of these intervals and first of all compared them with the
stand v d zone (between the 800 and 100 ml mark) using a double-sided test, to see if the resulting
viscosities are estimations of the same value
If the difference between the viscosities would be significant (Ho untrue. Hi true) a right one-sided
I-test would be carried out to see if the viscosity was really larger for the investigated area.
Table 7: Test results for the dropping speed investigation of detergent 1
dropping area
length of the measunng
900-100
700 - 200
700-100
600 - 200
300-100
d
V
y
■
s
c
0
s
i
t
y
(poise)
n
a
m
i
c
900 - 200
19,26
19,25
16,05
25,75
22,50
6.600
6,621
6,700
6706
6,673
6.666
6,606
6,732
6,627
6,621
6,662
6,612
6,561
6,670
6,672
6,546
6,449
6,489
6,510
6,584
6,600
6,466
6,462
6,656
6,451
6,526
6,626
6,517
6,570
6,560
6,661
6,596
6,545
6,643
6,543
6,582
6,5β£
6ΤΪ8
6,541
6,512
6,610
7,673
6,534
6,727
6,645
6,578
6,843
6,476
22,50
cm
6,666
6,596
6,621
6 .^
6,503
6,433
6,498
6,672
6,406
6.4X
6,448
6,50e
C^omparison between
lOolml
800 ml and
ml and
200 ml on the tube
measurements tx
This means that we can say (with 95 % certainty) tha· rt is not an
estimation for zero, or that the difference between the two viscosities
significant
8. The two measuring areas are not an estimation for
the same viscosity.
-----►This is only important as the constant dropping speed is higher than in the investigated area
the viscosity must be tower -> right or>e-stoed test to see the constant dropping speed is really larger
----- ►Thus the viscosity needs to be significantly smaller to reject the used measunng area as the viscosity,
and the constant dropping speed are Inversely proportional
2.
Right one-sided t-test
1. Ho:diO or
(xi - vi) = 0
H, d^O
2. Alpha = 0,05
3. Presumed is that the viscosities are normal distributed and that they are equal.
d=
0,1398
■ξ,=
0,0748
4.
Testmethod under Ho :
[+to.oo,
[+1,83;i
We can say (with 95 % certainty) that d is not significantly bigger than ze
So the difference between the two viscosities is not significant
8. The constant dropping-speed is not bigger than in the
standard area, so we are doing the measurements in the
reliable area
The following table (Table 9) gives all the results of the t-tests for detergent 1 in order to make the
derived conclusion seem logical.
standard area to compare the
viscosities of the several areas
with, and which, we used to test.
dropping area
length of the measuring
area (cm)
average viscosity (poise)
two sided t-test between the 10
viscosity measurements
(95% level)
right one-sided t-test between
the 10 viscosity measurements
(95% level)
800 - 100 800 - 200 700 - 100
700 - 200 900 - 100 900 - 200
22,50
16,05
25,75
19,25
19,25
22,50
6,659
6,626
6,714
6,519
6,584
6,493
significant significant significant
significant significant
significant significant significant
As all the tests are non significant (the dropping speed in the investigated area is not bigger as in
the standard area) we can be sure that the used measuring interval (between the 800 and 100 ml
mark of the tube) is reliable, and this with 95 % certainty.
5.2.1.2 Practical dropping speed investigation for detergent 2 and for glycerol
We carried out the same experiment as above also for two other liquids: another detergent with a
larger viscosity and glycerol. Ideal would have been if we had performed this for the other liquids
too: olive oil, motor oil and a lubricating oil for the vacuum pump.
The problem was that the dropping time was already very short (2 to 3 seconds, depending on the
temperature) for those three liquids, and making the measuring interval shorter would sort in a
shorter dropping time which is almost impossible to measure precisely by the human eye, as the
dropping speed is so large that it is hard to follow the ball on its way down.
5.2.2
Theoretical dropping speed investigation
The point x were the falling ball gains its maximal dropping speed, and the time t necessary to
gain this speed can be calculated theoretically by investigating the forces that cause the ball to fall
with the speed vumhed
In 3.3.2 3 we extracted the following formula to find x and t
().η
6·π·η
6■π■η■r
6·π·η·τ
As m = 4.π.r’.pball we find th at:
^
81
9
η
9·;;
>r all the tested liquids we take the average viscosity (from ten measurements) at 20,0 °C and the
erage ball radius from the ten balls we dropped to find this average viscosity value.
/hen considering Table 10 we see that the distance x and the time t to gain viunied is small for all
le liquids. When we start the measurement at the 800 ml mark the falling ball has already
aversed a distance of 15 cm so a much longer distance than teoreticaly necessary.
IS all the results in Table 10 are so small we can conclude that other forces must act on the ball
arcing it to fall with a speed vv„Mcd· This is the reason that a longer distance and time is necessary
Dr the ball to gain vuniit*d when this experiment is done in practice
>2.3
Viscosity as a function of temperature for several liquids
The graph is based on the average viscosity, resulting from twelve measurements at one
emperature, but the smallest and largest viscosity value are removed in order to get a larger
iorrelation (r) (closer to 1).
This is necessary because the correlation r plays a very important role in the exactness of the
/iscosity value out of the intercept, which we found from the equation of the best-fitting line.
In theory the correlation should be one as all the measurements are an estimation for the same
viscosity value, but due to small variations (eg imperfections of the ball, small changes in human
reaction time, unstable temperature,...) we find a lower r.
For some of the liquids (olive o il, and lubricating oil for a vacuum pump) we had to do fifteen
measurements, in order to find a reasonable correlation. Also here the selection of the
measurements was done by checking the influence of a measurement on the correlation by
removing it. When the removal of one of the measurements caused a big enough rise of r, it was
removed, otherwise the measurement was kept. This way of working can be questioned, because
the correct viscosity is not known but it is the most evident (and easiest) way to get a better
correlation.
It is hard to prove the influence of r on the intercept which will provide us a second viscosity
value A more thorough discussion will be given in chapter 5.2.4
Table 11 : Calculating the viscosity the correlation froml2 measurements for glycerol at 17,1 °C.
The correlation is 0,9386.
n.
1
2
3
4
5
6
7
8
9
10
11
12
ball diameter
cm
0,2287
0,2410
0,2210
0,2158
0,2452
0,2159
0,2380
0,2362
0,2270
0,2333
0,2270
0,2273
radius
cm
0,1144
0,1205
0,1105
0,1079
0,1226
0,1080
0,1190
0,1181
0,1135
0,1167
0,1135
0,1137
S
14,262
12,988
15,132
15,847
12,616
14,644
13,132
13,349
14,615
13,786
14,932
14,381
cm/s
1,578
1,732
1,487
1,420
1,783
1,536
1,713
1,686
1,540
1,632
1,507
1,565
viscosity
poise
18,320
18,526
18,151
18,124
18,628
16,764
18,268
18,290
18,495
18,428
18,896
18,247
log (r (cm)]
log(Vtonted (cm/s)j
-0,9418
-0,9190
-0,9566
-0,9670
-0,9115
-0 9668
-0,9245
-0,9278
-0,9450
-0,9331
-0,9450
-0,9444
0,1980
0,2386
0,1723
0,1522
0,2513
0,1865
0,2339
0,2267
0,1874
0,2127
0,1781
0,1944
Average 18,261 poise
viscosity
[correlation r
=
0 ,9 3 8 6 [
Table 12 : After removing measurement n. 6 (smallest one), and n. 11 (biggest one) from Table 11
we get a much better correlation of 0,9967.
n.
1
2
3
4
5
7
8
9
10
12
ball diameter
cm
0,2287
0,2410
0,2210
0,2158
0,2452
0,2380
0,2362
0,2270
0,2333
0,2273
radius
0,1144
0,1205
0,1105
0,1079
0,1226
0,1190
0,1181
0,1135
0,1167
0,1137
droDDina time
s
14,262
12,988
15,132
15,847
12,616
13,132
13,349
14,615
13,786
14,381
Vjirnited
cm/s
1,578
1,732
1,487
1,420
1,783
1,713
1,686
1,540
1,632
1,565
viscosity
poise
18,320
18,526
18,151
18,124
18,628
18,268
18,290
18,495
18,428
18,247
log [r(cm)l
log [yiimiea (cm/s)]
-0,9418
-0,9190
-0,9566
-0,9670
-0,9115
-0,9245
-0,9278
-0,9450
-0,9331
-0,9444
0,1980
0,2386
0,1723
0,1522
0,2513
0,2339
0,2267
0,1874
0,2127
0,1944
0,99671
Afterwards all the viscosities at their respective temperature are visualised by putting them in a
graph, and the best fitting line is given (exponential type) to create a more fluent course
We can estimate viscosity in two different ways: one out of the average viscosity , and the other
out of the intercept of the best fitting line found with the least-square method In the example
below these estimations were made for the motor oil
For some o f the temperatures we had several measurements
Table 13: Calculation of the viscosity from the intercept (experimental values for motor oil).
n.
1
2
3
4
5
6
7
8
9
10
diameter radius droDoing time
cm
s
0,1780 0,0890
3,710
0,1807 0,0904
3,565
0,1791 0,0896
3,665
0,1850 0,0925
3,456
0,1769 0,0885
3,694
0,1915 0,0958
3,221
0,1901 0,0951
3,253
0,1730 0,0865
3,865
0,1812 0,0906
3,595
0,1835 0,0918
3,529
cm/s
6,065
6,311
6,139
6,510
6,091
6,985
6,917
5,821
6,259
6,376
viscosity
poise
2,997
2,968
2,998
3,016
2,948
3,012
2,998
2,950
3,010
3,030
log [r (cm)] log (Vtantej (cm/s)]
-1,0506
-1,0441
-1,0479
-1,0339
-1,0533
-1,0189
-1,0220
-1,0630
-1,0429
-1,0374
average viscosity
poise
0,7828
0,8001
0,7881
0,8136
0,7847
0,8442
0,8399
0,7650
0,7965
0,8045
0,9923
2,681
intercept
F ig .
27 :
log
r/logvnmu.d
g r a p h
Note: Only for detergent 1 a full investigation of the average viscosity from ten measurements and
the viscosity from the intercept will be performed. The reason is that for all the liquids large
variations were found in the viscosity from the intercept, and never a match with the average
viscosity is found, evenly not after sorting the results to create a more fluent graph. Therefore it is
useless to pay too much attention to the viscosity from the intercept.
More important are the reasons for this poor match and the possible ways to get a better result.
They will be discussed in chapter 5.2.4
5,2,3.1 Detergent 1
n.
1
?
3
4
5
R
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
temoerature viscosity
poise
•c
20,017
12,0
16,541
13,8
15,057
14,3
14,237
14,9
12,825
16,0
11,946
16,1
11,461
17,0
11,607
17,0
10,606
17,1
10,440
17,3
10,014
17,7
9,845
18,1
9,472
18,6
9,420
18,6
8,460
19,1
8,817
19,1
7,640
19,3
8,435
19,4
8,474
19,7
7,933
19,8
7,916
19,8
7,602
19,9
8,195
19,9
7,868
20,0
7,975
20,0
7,673
20,3
7,704
20,3
6,761
20,9
7,019
21,1
6,956
21,1
6,311
21,3
6,294
21,4
6,649
21,7
6,374
22,0
5,974
22,6
5,496
23,1
viscositv correlation
poise
0,9981
38,029
0,9960
18,261
0,9876
26,780
0,9975
17,989
0,9949
18,244
0,9872
11,979
0,9953
13,640
0,9922
14,877
0,9947
12,939
0,9942
10,701
0,9935
16,570
0,9700
24,206
0,9896
17,845
0,9906
10,895
0,9920
13,964
0,9919
12,120
0,9766
20,583
0,9837
6,825
0,9965
10,467
0,9882
8,797
0,9895
7,907
0,9889
9,863
0,9819
14,925
0,9885
11,208
0,9941
7,218
0,9962
10,440
0,9942
9,264
0,9815
16,230
0,9942
10,905
0,9828
10,149
0,9972
7,070
0,9883
12,874
0,9956
6,984
0,9946
9,026
0,8116
5,056
0,9931
6,645
laverage 7
n.
1
3
5
8
11
14
15
16
19
22
25
26
27
29
30
31
33
34
36
temperature viscositv viscosity· correlation
T
poise
poise
°C
0,9981
38,029
20,017
12,0
0,9876
26,780
15,057
14,3
0,9949
18,244
12,825
16,0
0,9922
14,877
11,607
17,0
0,9935
; 6,570
10,014
17,7
0,9906
10,895
9,420
18,6
0,9920
13,964
8,460
19,1
0,9919
12,120
8,817
19,1
0,9965
10,467
8,474
19,7
0,9889
9,863
7,602
19,9
0,9885
11,208
7,868
20,0
0,9962
10,440
7,673
20,3
0,9942
9,264
7,704
20,3
0,9942
10,905
7,019
21,1
0,9828
10,149
6,956
21,1
0,9972
7,070
6,311
21,3
0,9956
6,984
6,649
21,7
0,9946
9,026
6,374
22,0
0,9931
6,645
5,496
23,1
laverage r
0,9928j
Fig.28;
R g. 28: viscosity/temperature graph
average viscosity fromten
fTEasurerrETts
viscosrty fromthe irteicept
“ Bicnertieel (average
viscosity fromten
measuiefTEnts)
Bponentieel (viscosity from
Fig, 29:
Fig. 29: viscosity/temperature graph using the viscosity
from the intercept for detergent 1
temperature / “C
First of all we take a look at Table 14 with all the test results
We worked in a temperature interval between 12,0 and 23,1 °C, and this causes a viscosity
drop from 20,017 to 5,496 poise.
That means that viscosity η and temperature influence each other inversely, like we expected.
Always the best fitting curve (exponential type) is given, to create a more fluent line.
In Fig, 28 the average viscosi. <graph and the viscosity graph out of the a value, after the
results were sorted, are given
We tried to do the same for Fig. 29, but it is much more difBcult This graph shows the
viscosity fiOm the intercept before sorting and the best fitting curve, and after sorting.
When one looks clear the form of the average viscosity graph can be found in these wide
varying values, but this is much less obvious, and some imagination and a lot of good will is
needed.
Also here the best fitting curve is given, only to show that its form is similar to the average
viscosity graph
After removing the worst results, a more fluent graph can be found, but, when we put it next
to the average viscosity graph (like wc did in Fig. 28) it is laying higher than the other one ,
and it rises faster. When we place the correlation next to the viscosity values (see Table 14
and 15) we see that after sorting the results the values with the better correlation are left.
Immediately we have an indication for the influence r has on the accuracy of the viscosity out
of the a value. When the average correlation’s are compared (before and after sorting the
results), we can find one of the reasons for the big variation in the results based on the
intercept. The correlation, and the ways to increase it will be discussed in 5.3.
The viscosity in function o f temperature relation can be subscribed by the following equation;
By taking the log of thi; formula we can find a relation of a linear form between In η
(average viscosity values) and (1/T). Out of the A and B value of this linear equation we can
get information about the viscous behaviour of this liquid.
After some calculations we found:
Fig. 30: In η/(1/Τ) graph for detergent 1
0,06
0,07
(1/T) / (1/s)
The correlation r between In η and (1/T) is 0,9778
In A = 0,3391-------- ►A = 1,4037 poise
3/R = 34,19______ ►B = 284,12 (J/mol)
5,2,3 2
Detergent 2
average viscosity from
ten measurements
the viscosity from
the intercept
—
r -----------
Table 16; All the results
n. temoerature
-c
1
12,0
13,7
2
14,3
3
4
14,9
16,0
5
6
16,1
17,0
7
8
17,0
9
17,1
17,3
10
17,7
11
18,3
12
18,7
13
18,8
14
15
19.1
19,2
16
19,3
17
19,6
18
19,8
19
19,8
20
19,8
21
19,9
22
20,0
23
20,1
24
20,1
25
20,4
26
20,5
27
20,9
28
21,1
29
21,1
30
21,2
31
21,4
32
21,8
33
22,0
34
22,4
35
23,2
36
viscositv viscositv
poise
poise
60,010
81,853
49,612
255,2'“':
82,553
44,669
216,039
40,623
63,655
37,689
62,220
34,396
17,117
32,173
35,903
36,754
46,498
30,726
55,954
30,003
41,613
28,608
42,957
30,325
10,298
27,535
78,946
27,057
33,391
24,428
127,565
25,153
33,468
21,862
26,831
24,219
10,298
23,080
56,667
21,313
47,988
24,007
36,311
21,329
97,304
22,802
60,177
22,687
32,979
23,337
49,617
21,442
94,354
21,723
30,650
18,759
67,676
19,596
152,452
18,816
24,184
18,003
7,685
18,114
21,068
19,151
20,693
17,969
25,051
16,658
28,763
15,237
The temperature interval lays between 12,0 and 23,2 “C causing a viscosity drop (average
viscosity from ten measurements) from 60,010 to 15,23 7 poise.
If we look to the viscosity from the intercept and compare it with the average viscosity we see
that they don’t match togheter. No further investigation of these results is made here as the
conclusion is the same as for the other detergent.
In Fig, 31 the two courses (average viscosity and viscosity from the intercept) are shown. The
variations in the viscosity from the intercept are very large, and when the results would be
sorted in order to find a more fluent line, the course would lay higher than the average
viscosity course as most of the results are to big in comparison with the average viscosity.
Fig.
31:
viscosity/temperature
f o r d e te rg e n t 2
graph
o
a.
1 5,0
20 .0
t e m p e ra tu re / "C
The average viscosity graph can be subscribed by the following equation :
η = y4
As explained in chapter 3.4 the natural logarithm of this equation can provide us a linear
relation between In η and (1/T). Out of the equation of the best fitting line (found with the
least square method) The A and B term - two fluid constants - can be calculated.
Fig. 32:ln η/(1/Τ) graph for detergent
\ ηη = .\ ο .Λ +^ - -I
Correlation between In η and (1/T) = 0,9700
In A = 1,3022------------►A = 3,677 poise
B/R = 35,923------------ ►B = 298,52 (J/mol)
5.2.3 3 M otor oil
the average viscosity viscosity from
from
the intercept
ten values ^
n.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
temnerature
”C
11,8
13,8
14,4
15,0
16,0
16,1
16,8
16,9
17,2
17,2
17,7
17,9
18,2
18,3
19,0
19,1
19,2
19,3
19,3
19.7
19,8
19,9
20,0
20,0
20,0
20,2
20,2
20,8
21,0
21,0
21,2
21,6
21.7
22,0
22,9
23.0
viscosity viscosity
poise
poise
4,799
4,123
5,742
4,352
4,873
4,015
11,672
4,024
1,947
3,703
5,457
3,600
4,245
3,476
4,683
3,458
3,930
3,303
5,110
3,371
6,015
3,264
2,997
3,293
5,885
3,202
6,007
3,169
4,019
3,011
6,187
2,933
3,066
2,975
5,557
2,840
4,786
2,993
5,795
2,874
2,074
2,737
3,064
2,776
4,664
2,831
5,600
2,908
7,394
2,879
7,952
2,737
5,553
2,782
0,866
2,645
4,781
2,717
1,463
2,694
7,814
2,629
3,969
2,574
1,367
2,521
3,795
2,524
8,481
2,433
6,999
2,388
We worked in a temperature interval between 11,8 and 23,0 °C causing a viscosity drop from
4 799 to 2 388 poise What we notice immediately is that the viscosity d^rease is rather
small This is logic as motor oils are supposed to have a stable viscosity (certainly at those
temperatures the car engine is operating in) for the well functioning of the car.
F ig . 3 3 :v is c o s ity /te m p e ra tu re gra p h
average viscosity fr
10,0
15,0
20,0
tem perature / °C
Fig. 33 shows the average viscosity and the viscosity from the intercept course. Again the
difference between the two courses is striking. If the results would be sorted to find a more
fluent course for the viscosity from the intercept, it would lay higher than the one from the
average viscosity.
By calculating the fluid constants A and B we will discuss the viscous behaviour of this liquid
in 5 2.3.8
They can be extracted from the formula that subscribes the viscosity in function of
temperature relation best.
By taking the natural logarithm we will estimate A and B by using the equation of the best
fitting line.
Fig. 34: In η/(1/Τ) graph
for motor oil
0 05
0,06
0,07
(1/T) / (1/s)
Equation:
ln7 = ln A + -
-
Correlation r between In η and (1/T) = 0,9798
In A = 0,1008---------- ^ A = 1,106 poise
B/R = 18,72________ ^ B = 155,56 (J/mol)
5,2.3 4 Olive oil
the average viscosity viscosity from
from
the intercept
ten measurements
n.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
temoerature
•c
11,8
13,7
14,3
15,0
16,1
16,1
16,8
16,8
17,2
17,2
17,8
17,9
18,1
18,2
19,0
19,1
19,1
19,1
19,3
19,4
19,9
19,9
20,0
20,0
20,1
20,2
20,7
20,9
21,0
21,1
21,6
21,8
22,0
22,9
23,0
viscosity
poise
1,690
1,613
1,513
1,577
1,407
1,452
1,397
1,522
1,390
1,382
1,319
1,378
1,334
1,331
1,288
1,333
1,365
1,320
1,251
1,283
1,183
1,263
1,321
1,257
1,312
1,322
1,229
1,227
1,233
1,207
1,180
1,159
1,213
1,166
1,136
viscosity
poise
6,922
5,591
5,308
12,368
2,175
4,668
1,436
24,066
1,448
1,473
1,811
4,002
2,366
4,228
3,818
19,020
6,417
3,072
8,608
3,321
33,143
5,100
2,638
4,758
7,142
36,275
4,207
7,781
6,248
2,860
15,202
6,062
5,194
8,172
4,206
The used temperature interval lays bemeen 11,8 and 23,0 °C causing a viscosity drop from
1,690 to 1 136 poise The decrease in viscosity IS small
The most im p o L l remark that » e have to make here is that all the
performed with glass balls, because they are more light and because
dropping time Doing measurements with lead balls was almost impossible for this liquid due
to the very short dropping time (2 seconds and less) evenly for the very small lead balls. In
chapter 5,2.6 we will discus if glass and lead balls estimate the same viscosity.
Fig. 35 shows the average viscosity from ten measurements and the viscosity from the
intercept course
F ig . 3 5: v is c o s ity /te m p e r a tu r e g r a p h
fo r o liv e o il
;
ZZ
35.0
g
O
a
30,0
25,0
"T 20,0
w 15,0
O
w
>
10,0
5.0
0,0
10,0
average viscosity
15,0
20,0
te m p e ra tu re / °C
The difference between the two courses is very big. For the average viscosity values we need
a much smaller viscosity scale (eg between 0 and 2 poise) to get a clear look on the form of
this course The average viscosity measurements seem to lay almost on a line (linear relation)
whereas a curve (exponential relation) is expected.
This is indicated by the low correlation (0,9374) of the exponential relationship between
In η aid (1/T) and the higher correlation (0,9532) of the linear relationship between η and
temperature.
It seems that this liquid has a very stable viscosity that hardly changes in the investigated
temperature interval
We will calculate the fluid constants A and B from the intercept and slope of the equation of
the best fitting line found for the relation between In η and (1/T).
Fig. 36: In η/(1/Τ) graph
for olive oil
Equation of the best fitting line;
Equation :
l n7=In/l+ — —
Correlation between In η and (1/T) = 0,9374
In A = -0,2758--------^ A = 0,7589 poise
B/R = 10,225______ ^ B = 84,97 (J/mol)
5.2.3.5
Vacuum pump oil with lead balls
The average viscosity
fiom
ten measurements
viscosity from
the intercept
TabI e 19: All the results
for Vac. pump oil (Pb)
n.
temperature
°C
1
12,0
2
13,8
14,4
3
4
15,0
5
16,0
6
16,1
17,0
7
17,0
8
9
17,1
17,2
10
17,8
11
18,0
12
18,4
13
18,4
14
19,1
15
16
19,2
19,3
17
19,3
18
■'9,7
19
19,8
20
19,8
21
19,9
22
20,0
23
20,0
24
20,2
25
20,2
26
20,2
27
20,8
28
21,0
29
21,1
30
21,-*
31
21,5
32
21,5
33
22,0
34
22,7
35
23,1
36
\
\
viscositv viscositv
poise
poise
3,470
1,742
3,156
5,295
2,787
2,862
2,898
2,069
2,624
4,126
2,556
2,316
3,6C3
2,422
2,489
6,989
3,692
2,405
2,375
3,352
5,384
2,295
9,855
2,328
2,224
9,138
2,239
10,369
6,364
2,144
2,117
4,695
2,017
0,969
2,^33
2,110
4,851
2,087
1,900
1,985
8,520
2,068
3,503
1,965
7,274
2,042
3,156
2,062
5,816
1,973
3,956
2,024
3,621
2,054
1,359
1,879
1,672
1,888
r,391
1,884
3,830
1,838
4,493
1,831
3,365
1,816
3,166
1,797
7,277
1,761
0,965
1,682
The investigated area lays be ,veen 12,0 and 23,1 °C causing a (average) viscosity drop from
3,470 to 1,682 poise The smallest glass balls were used as they have the longest dropping
time (still short due to the low viscosity of this liquid)
Fig. 37 shows the viscosity as a function of temperature relation for both the average viscosity
and viscosity from the intercept.
the viscosity from the intercept is demonstrable, and hardly no measurements overlap
The fluid constants A and B are found from the equation that subscribes the following
course:
Fig. 38: In η /(1 /Τ ) graph
for vacuum pump oil (pb balls)
_
.-
I
^ 0 ,5
=*
Eauation of the best Itting line:
y = 19,33x - 0 , 2 6 8 5 -------%
J
0 0, 04
0,05
0,06
0,07
(1/η /
(1/s)
"’’he correlation r is 0,9778
In A = -0,2685--------►A = 0,7645 poise
B/R =
19^33 ----------- ►B =
160,63 (J/mol)
0,08
0,09
5.2.3.6 Vacuum pump oil with glass balls
The average viscosity
from
ten measurements
viscosity from
the intercept
Table 20; AllI the
t h e 'r ^ l
for vac. pump oil (glass)
n.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
temperature
»c
12,0
13,8
14,4
15,0
16,0
16,1
17,0
17,0
17,1
17,2
17,8
18,0
18,4
18,4
19,1
19,2
19,3
19,3
19,7
19,9
19,9
20,0
20,0
20,2
20,2
20,2
20,8
21,0
21,1
21,4
21,5
21,5
22,0
22,7
23.1
viscositv viscositv
poise
poise
4,383
3,“35
5,223
3,289
4,108
3,023
3,936
3,116
3,173
2,788
2,725
2,765
3,720
2,551
2,886
2,593
1,977
2,453
4,217
2,485
4,170
2,476
6,068
2,370
33,268
2,138
3,501
2,353
3,591
2,287
4,924
2,238
5,530
2,006
17,220
2,077
3,778
2,214
5,412
2,007
11,509
1,982
6,827
1,976
2,439
2,022
4,775
2,051
4,286
2,140
2,630
2,093
2,483
1,955
1,931
1,999
4,608
1,990
7,263
1,864
2,621
1,804
10,520
1,891
6,386
1,936
3,786
1,865
1,927
1,776
We worked in the temperature interval between I2,0and23,l "C cauaing a (average)
le o s i t * drop from 3,765 ro 1,776 poise Here all the mea^rements rvhere perfomied wrth
Ξ g U s balk They have a smaller mass than the lead balls and so a Ό γ ; <I™PP™8 «">0
The t a g e r l e dropplg time the easier it I, for the human eye to spot the ball when rl passes
the start and stop mark.
Fig. 39 shows the average viscosity and the viscosity from the intercept course
Fig. 39:temperature/viscosity graph
for vacuum pump oil (glass balls)^
viscosity from
36.0
intercept
31.0
26.0
average viscosity from
21,0
ten measurements
16,0
Logaritmisch (viscosity
11.0
from the intercept)
6,0
10 ,C
15,0
20,0
25,0
“ Exponentieel (average
viscosity from ten
t e m p e r a tu r e
/ “C
ments)
Looking at the graph we see that almost all the viscosity values from the intercept are larger
than the average viscosity value at the same temperature, like we saw for all the other
investigated liquids.
Here it seems that the variations in the viscosity from the intercept value are not that large as
most of the measurements lay below 6 poise Notwithstanding this there are several values
who are significantly larger than the average viscosity.
We will estimate the fluid constants A and B by using the intercept and slope of the equation
that subscribes the linear relation between In η and (1/T):
Fig. 40: In η /(1/Τ ) graph
pum p oil (glass balls)
Correlation = 0,9751
In A = -0,2986--------►A = 0,7418 poise
B/R = 20 548----------^ B = 170,75 (J/mol)
5 2.3 7 Glycerol
average viscosity
from
ten measurements
n. temperature viscosity
°C
poise
1
12,0
31,959
2
13,8
27,021
3
14,2
25,179
4
14,8
24,605
5
20,942
16,1
6
19,935
16,2
7
17,0
19,837
8
18,740
17,1
9
18,305
17,1
17,4
18,168
10
17,8
17,212
11
18,0
16,718
12
18,9
16,058
13
15,392
14
19,2
13,611
15
20,0
16
20,1
13,631
20,9
12,333
17
11,861
18
21,1
12,256
19
21,3
11,677
21,8
20
11,410
22,2
21
10,409
23,2
22
viscosity from
the intercept
viscosity
poise
26,143
30,245
26,379
30,448
31,293
22,665
26,137
16,487
26,318
22,149
22,405
20,867
20,843
19,340
16,682
21,880
23,065
15,858
20,703
11,050
11,961
11,268
For glycerol we worked in a temperature interval between 12,0 and 23,2 °C causing a
(average) viscosity decrease from 31,959 to 10,409 poise. Due to the fact that the glycerol
was available later less measurements were taken than for the other tested liquid, but the same
temperature interval was obtained A very important remark we want to make is that glycerol
is one of the easiest measurable liquids with this falling-ball viscometer as it is completely
colorless and transparent what results in a perfect visibility of the falling ball.
As the visibility of the ball improves the chrononipter can be started and stopped more
precisely when the ball passes the start and stop mark
Fig. 41 shows the viscosity as a function of temperature courses found by using the average
viscosity (from ten measurements) and the viscosity from the intercept
What we see immediately when looking to this graph is that although the viscosity from the
intercept course lays higher than the average viscosity course, the two graphs are almost
parallel This means that the difference between the two best fiting curves is almost the same
for all the temperatures In fact this is the only fluid for which we find this result.
Notwithstanding this there are still large variations in the viscosity from the intercept.
To be able to discuss the viscous behavior of glycerol we will calculate the fluid constants A
and B out of the equation that subscribes Fig. 41 best.
By taking the natural logarithm of this exponential equation we can get a linear relation
between In η and (1/T).
From the equation of the best fitting line we will calculate A and B
Correlation r = 0,9816
In A = 1,1301---------- ►A = 3,096 poise
B/R = 29,921------------ ►B = 248,64 (J/mol)
5.2.3 8 Discussion of the viscous behaviour of the tested liquids
As mentioned before the relation between temperature and (average) viscosity is subscribed
best by the following equation
77
= ^.
By taking the natural logarithm of this exponential equation we can get a linear one. By using
the equation found with the least square method we will estimate the A and B value.
Out o f this A and B value we can get information about the viscous behaviour of a liquid. We
will do this by comparing the A and B values and their according graphs with each other in
order to find the meaning of this A ^nd B value.
Table 22 : Test results : The A and B value fiom all the tested liquids
liquid
In [A (poise)]
detergent 1
detergent 2
Motor oil
Olive oil
vac pump oil
4,0715
39.5276
3,0222
2,1361
2,1468
vac pump oil
I glass pans
II glycerol
2,1001
0,742
20,548
170,754
1,776
3,765
22,1093
3,096
29,921
248,644
10,409
31,959
potse
1,404
3,677
1,106
0,759
0,764
B/R
(J/(mol.°C))
34,190
35,923
18,720
10,225
19,330
B
minimal n
(J/mol)
284,119
5,496
298,520 15,237
155,563
2,388
84,970
1,136
160,632
1,682
poise
20,017
60,010
4,799
1,690
3,470
The biggest and smallest (average) viscosity value is given to explain the variation of
bintercept (A) and slope (B). Fact is that the temperature of this minimal and maximum
viscosity is not perfectly the same for all the liquids, but we only give these (average)
viscosity values to have an idea how viscosity varies for each of the liquids, in order to find
an explanation for the intercept and slope.
The intercept seems to be directly related to the maximum viscosity as the liquid with the
largest maximum viscosity (detergent 2) has the largest intercept value.
For the slope we find something different: The differences between the B values are not so
large notwithstanding that the viscosities of the liquids are totally different. We found that B
corresponds with the energy of flow activation, but due to a lack of time we could not
investigate what is meant with this name
The only thing we can conclude is that A and B are influenced by the extent of the viscosity
change
In Appendix 1 we will discuss if the A and B constant we find are really the slope and
intercept from the Andrade equation
Another variation on this Andrade equation involves the use of a third constant C to obtain the
Vogel equation:
It is not possible to calculate the A’, B’ (we use A’ and B’ as these constants are not the same
as the A and B constants from the Andrade equation) and C constants by using all the
measurements (all the average viscosity values). Therefore we will calculate the Vogel
equation for all the tested liquids by using three measurements: the largest and the smallest
viscosity value at their respective temperature and the viscosity at 20,0 °C.
This way of working is not ideal but these calculations will only be added to see if theoretic
(although based on measurements we took) viscosity as a function of temperature course
meets the one we found experimentally. Better would be to take several times three viscosity
measurements and than estimate the average A’, B’ and C value. As we do not precisely
know which is the function of the constants (in the literature about viscosity they are indeed
mentioned as fluid constants, but nowhere is explained what the real meaning of these three
factors is), it is not very useful to pay to much attention to these constants
Table 23 : Three average viscosity values (from ten measurements) at their according
temperature for each of the tested liquids
largest τι
liquid
20,017
60,010
4,799
1,690
3,470
detergent 1
detergent 2
motor oil
olive oil
yac pump oil
ead balls
vac.pump oil
glass balls
glycerol
ftemoeraturel
“C
(12,0)
(12,0)
(11,8)
(11,8)
(12,0)
poise
5,496
15,237
2,388
1,136
1,682
ftemoeraturel u at 20,0 X
poise
"C
7,868
(23,1)
22,80?
(23,2)
(23,0)
2,831
1,321
(23,0)
2,042
(23,1)
3,765
(12,0)
1,776
31,959
(12,0)
10,409 ___ ________
1,976
(23,1)
13,611
We give an example of the calculations needed to find A’, B’ and C for detergent 1
By using two of the three viscosity values we will calculate B’. We do this twice
By using the largest and the smallest viscosity value we will calculate B’ the first time :
In 20 ,017
=
B'
^2 0 +
>“ 2 0 ,0 1 7
f
12 ,0
(In 20 ,017 - In
(12
Or :
-
In 5 ,4 %
. ^ = >° ^■'*96 + C
5 ,4 % ) ■((12 ,0 +
,0 + C ) - (23 ,1 +
=A
,
^’
23 ,1 + C
-
23 ,1 + C
C ) ■(23 ,1 + C ))
C )
Now we will use the largest viscosity and the one at 20,0 °C to give us a second B' value:
/
In 7,8
1 2 ,0 + C
In 2 0 ,0 1 7
® ~
= In 7,868 - 1 2 ,0 + C ~ “
2 0 ,0 + C
fin 2 0 .0 1 7 - In 7,868 ) ((1 2 ,0 + C ) (2 0 ,0 + C))
(1 2 ,0 + C ) - ( 2 0 , 0 + C )
, v
'
As 1 and 2 are equal we find an equation with one unknown variable C :
iln20.017-ln7,868) (a2,0+C) (20.0+C))
(In20,017-In5,496) (0 2 ,0 + 0 (23,1+0)
(1 2 ,0 + Q -(2 0 ,0 + 0
(12,0+0-(23,1+C)
Afier somecalculatims we can find that
C = 129\33
By using this C value we can calculate B’ from 1 or 2 By using the B and the C value A’ can be calculated out of the Vogel equation for one of the
three measurements __________ _______________________ ^ A’ = 156 06
Table 24 The A’,B’ and C values for all the investigated liquids.
II
liquid
1 deteroent 1
1 deteroent 2
II mo!or oil
1 olive oil
Svac.pump oil
D lead balls
Uvac pump oil
1 glass balls
Mfllycerol
A·
-150,48
-28,95
7,45
-0,07
14,16
B'
200575,44
9292,13
489,11
16,40
2415,31
c
11
1291,33 1
-293,19
71,37
1
-39,62 1
174,94
2,64
10,86
-3,72
-1,77
214,55
29,02
I
As you can see all three these fluid constants have a lot of spread, and there is not
immediately an explanation why one liquid has for example a big A’ constant, and the other
one not.
What we also notice is the big differerence between the fluid constants of vacuum pump oil
measured with lead and with glass balls. These causes some doubt about the fact if glass and
lead balls estimate the same viscosity. A more thorough investigation of this matter is given
in 5.2.6.
For glycerol we will estimate the viscosity as a function of temperature course from this
Vogel equation and compare it with the course we found experimentally with the falling-ball
method.
As shown in Fig. 43 the two courses seem to meet each other more or less, although the
theoretical curve seems to lay lower than the other one.
Anyway a discussion of this graph is ary dangerous, because due to the choice of the three
viscosity values used to calculate the Vogel equation the two courses begin and end in the
ThTs^Ses a further investigation of all the tested liquids useless as a similar result would be
5.2 4
Eiplanation for th ' poor match between
the average viscosity and the viscosity from the intercept
5.2.4 1 Causes
Immediately we have to say that the main reason for this difference is not known.
All we can do is check the inf uence of the different factors on the intercept
•
The human reaction time sorts in small changes in the time measurement If all these
small changes are put together more spread will result.
•
None of the balls is perfectly round. This can be proved by measuring the diameter at
several sides of the ball This irregulanty is bigger for the glass than for the lead balls
As an example we take one glass, and one lead ball - that seem perfectly round at first
sight - and measure the diameter at five different sides
side
1
2
3
4
5
diameter / cm
0.4402
0.4470
0.4361
biggest difference = 0 ,0119 cm
0.4413
0.4351
side
1
2
3
4
5
diameter / cm
0.2830
0.2790
0.2811
biggest difference = 0,0040 cm
0.2779
0.2823
5.242 Indications for the poor match
As we look at the following equation (which gave us a second viscosity, based on the a
value), the b value should be 2 :
logv,
'^'^Pbail Ph<juid^ S
* --------- ^ r , ----------bx
form
It is easy to check if the b value is really an estimation for 2 by using a students t-test (95 %
intt.^al). This can be an indication (not a prooO that it is not illogical that the a value is not a
good estimation for the viscosity
There is not a direct relation between the a and the b values This makes the result doubtful
In this way it is dangerous to draw any conclusion, and therefore we just provide this test as
an account for the poor agreement between the two viscosity values.
Table 25 Investigation o f the slope for ail the tested liquids
n.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
18
19
20
21
22
23
24
25
26
27
28
29
OLIVE
OIL
b
0,375
1,047
0,314
1,433
1,530
1,303
1,086
1,578
0,669
1,714
1,228
1,657
1,163
1,580
1,339
1,194
0,737
1,182
1,389
1,987
0,985
1,980
1,782
1,843
1,968
1,413
1,300
1,379
1,380
n(#)
Average X
std. dev. S
29
1,329
0,433
tw
tw
-8,353
X - 2
S
MOTOR 01 VAC.PUMF> VAC.PUMP' DETERGENT■ DETERGENT GLYCEROL
(Pb balls) (glass balls)1
1
2
h
b
b
b
b
b
2,115
2,018
1,957
2,414
1,959
1,758
1,403
1,891
1,729
1,718
2,308
1,862
1,591
1,783
1,555
1,547
1,497
2,000
1,495
1,731
1,410
0,431
1,734
2,414
1,710
1,415
1,105
1,748
1,254
1,791
1,470
1,295
1,851
1,500
1,766
2,050
2,020
1,815
1,373
1,547
1,697
1,217
1,979
1,951
1,691
1,671
1,533
1,791
1,840
1,746
1,364
1,763
1,939
1,449
1,804
1,651
1,681
1.912
1,645
1,726
1,823
1,891
2,045
1,823
1,584
1,715
1,721
1,870
1,575
0,785
2,089
1,947
1,987
1,973
1,765
0,187
1,923
1,531
1,608
1,842
0,943
1,184
1,506
2,251
1,785
1,700
2,439
1,631
1,769
1,822
1,953
1,850
1,746
0,998
1,867
2,253
1,634
1,857
1,759
1,714
2,133
2,463
1,927
1,770
2,313
2,059
1,872
1,832
1,859
1,902
1,157
i,eo i
2,139
1,559
1,990
1,689
1,679
1,909
1,928
1,858
1,853
1,732
1,814
1,815
1,922
2,264
1,788
1,813
1,648
1,688
1,879
1,747
1,917
2,130
1,788
1,832
1,825
1,830
1,999
1,703
2,009
1,942
2,041
1,828
1,841
1,907
1,730
2,093
2,283
2,063
1,958
1,163
1,948
1,721
1,787
1,886
1,689
1,978
1,755
1,813
2,011
1,920
30
1,862
0,227
-3,334
30
1,786
0,270
-4,345
29
1,548
0,468
30
1,869
0,121
30
1,720
0,363
13
1,900
0,107
-5,197
-5,919
-4,228
-3,343
~ t„-i
Limits of significance are ]to,o25 ni ; to.975 n i[
1-2,09 ; 2, 09(
Limits of
significance
The difference between every of the average b-values and 2 is
Result
statistically significant.
The b-value is not an estimation for 2, and this for all the liquids.
]-2,18;2,18|
5.2.4.3 Possible solutions
The correlation r seems to play a mayor role in the accuracy of the estimation of η from the
intercept (= a value). In our discussion of viscosity in function of temperature for detergent 1
f 5.2.3.1) we ^dded the correlation r for every measurement to show that the viscosity from the
intercept of the best fitting line, matches better with the average viscosity when r is larger
Mostly r is smaller than 0,98. As the correlation gets better the viscosity from the intercept is
closer to the average viscosity
We will try to improve r and check the influence on the viscosity from the intercept.
Table 26: Example for the lubricating oil for a vacuum pump, using lead balls
average η
poise
low correlation, very poor match
.higher correlation, much better match
although a low correlation, a good match
although a high correlation, a not so good match
As shown in Table 24, the relation between correlation and viscosity from the a value is not
always valid. Sometimes this rule is not followed, and this can be the main reason for the
large difference between the two viscosity values and their accompanying graphs.
We want to enlarge the r value to check its influence on the viscosity from the intercept. We
tried this out by taking more measurements - and see if this gives a better correlation - for the
two detergents, glycerol and for motor oil by taking once 10 measurements and the second
time 20 measurements, and this at one temperature (20,1 °C).
Table 27: Results for detergent 2 :
number of
measurements
10
20
average_n
poise
22,154
22,100
Ti from the a value
poise
52,123
59,571
correlation r
n from the a value
poise
18,580
16,415
correlation r
0,9498
0,9169
Table 28: Results for glycerol:
number of
“
10
20
averaae n
poise
13,411
13>88
0,9828
0,9920
Table 29: Results for detergent 1
number of
measurements
10
20
^
average π
poise
8,267
8,251
Ti from the a value
poise
13,839
69,521
correlation r
0,9446
0,7908
Table 30: Results for motor oil.
number of
measurements
10
20
correlation r
η from the a value
poise
0,6897
16,523
'
4,722
0,8796
average τι
poise
2,874
2,850
These tests show different results : for detergent 1 and 2 we can say that an increase in the
number of measurements thus not result in a better match between the viscosities; the
opposite is true. For glycerol and motor oil a rise in the number of measurements involves a
better correlation, and a better match between the two viscosities
Due to these different results drawing a conclusion is hard, not to say impossible as the
influence of the number of measurements on r seems to depend on the tested liquid, and
probably on other (not known) factors
Also here a larger r involves a better match between the two viscosities, but we already
noticed (see above) that this in not always true.
Another factor of big influence is the human reaction time. This causes all the measurements
to be larger than the real dropping time. With an example we can prove this:
Tile 31: test resJtsfoundfa detergent 1d 19,7°C
"
1^ u
vigmsrty |log[r(an1]|lcg[vMKj(cmis)]
dcpprqtirTE
cttYs
s
1 Q1912 0,0055
d oiTdooBBi
3 0 1 9 « OOETO
4 01922 00061
g 01901 00051
a 0178H ΟΟΘ03
η 01064^ 0.0832
d O18ldoO0D0
d 01738 00866
id 01731 00666
9200
1083E
9075
9,136
9447
10503
9,666
10060
11,197
11,310
pose
1
0S2d -1,0198
2421
8449 -1,0660
2076
857ll -1,0132
2479
84711 -1,0173|
2462
8957^ -1.Q22a
2362
840τ| -1,049l|
2142
8430| -1,0aB
2327
836o| -1,0414
2232
8459 -1,06ΐη
2000
85W| -1,062t|
1,060
areragyn=0474 !r=
pose
ia=
b=
03841
0317:
03040
03915
02TOi
O330E
0366C
034S
03031
0298?
Ο9Θ6Β0Ο1ΘΘ
2,334
1,8116
Rg 44: logrrtog
graph
Tabe 32 Ted resJtscf TiJe 31 ^
lasirpei theciOpargtries\Λ#ι 0,500seoortl
n
d
|r
dqganalime
viacQsrtv |kg[r(ai1]|lcg[\v*d(cnYs)]
am |om s
loTfe pose I
I
011&dcioged
279^ 229E
69831 -1,0198
0361·
2 Q1/iSQ0881 1
11.338' 1,984 88341 -Ι,ΟβθΟ
02EW
Z Q19<dqogTd
2575^ 2390
9043 -i.oiq
037K
* Q19CsjqoQBil
2636^ 2336 8934 -1,0173
0368!
£ Q1901T0109^
0354i
91947^ 2252
8020 -1,0220
e Q17EqQ089d
11,003 2045
03107
080^1 -1,04^
7 Q18B4^Q09Gd
8666^ -1,0303
iQi6a 2213
0344£
£ Q181aQOGOa
1Q5Bq 2127
03277
0775^ -1,0414
£ Q173gqoeed
11,ΘΘ7 1,9«
0284'
8836^ -1,0617|
1C Q1731|Q08BE|
11,81o| 1,906 8880( -1,062t|
0279E
221S2
1,8213
R9«:lcgrtog>4rt«igrw*'
d ItcM Mrsline
y=1,a20<+2219B
-1.0B -1,06 -1,M -1,02
loBtr(atfl
^
η=131634poise
Tatie33 TestingnesJtsof Idle 31 cfterrasingdl thedt^ig tinesvvlti 1,OCX)second
jlog[r(ai1]jlog[A*b(crri^]
dcnirplimB VW)
cm 1s
arts pose
03397
94421
10292 2186
01912 ooged
0278
11,839 1,900 9224 -Ι,ΟΘΒα
017B2 00881
0348E
9,515| -1,0120
10075
01940 oogTd
939d -1,0173|
0346:
01922 00961
1013E 221£
03337
10447 2154
01901 00961
947^ -1,022α
9203 -1,04M
029V
11,502 1,966
0178E ooegd
0324'
9,301 -1,0303
10Θ6Ε 210E
01864 00933
0307Ϊ
11,08C 2031
9,190| -1,04141
01818 OOGod
0266E
12197 1,845 92141 -1,06171
0173E 00863
0261£
-1,06271
1231C 1,826
01731 OO806|
0
2
4
£
£
7
£
£
1C
ayeragen=SC322
pdse
Rg46c logrtogi^gratfii
Ec^^tTid thebed ttrg ire
21138
1,7392
As shown, the match between the two viscosity values gets worse with larger human reaction
time (systematic fault) although the correlation r stays almost the same. How larger the
systematic fault, how more the viscosity from the intercept changes
Ideal would be to start and stop the chronometer with an automatic detection system, such as
coils or a fibreoptic sensor system) with a much smaller reaction time. Than it would be
possible to calculate the fault caused by the human reaction time, and to take this under
account in every measurement.
By assuming that the diameter of each ball is measured absolute it is possible to calculate the
theoretic dropping time by lowering all the dropping times with the same value m order to
find a perfect match between the two average viscosity and the viscosity from the intercept.
For the measurements in Table 29 we tried to find the human reaction time:
T iie 34 ^ kMflnng dl »ie (icppng timescf T iite 31 ν# ι Q446 SBOonfea perfect rrA h
befc^eena«agB η and η firin the rteraept is fom l
So when all the dropping times are lowered with 0,446 seconds we find a perfect match
between the two viscosities, but only for this specific example The human reaction time for
this measurement is 0,223 seconds (0,446 divided by two, because human reaction needed to
start and stop the chronometer).
Would we calculate this for another measurement than we would find another result
For example: we did the same calculation for glycerol at 21,4 °C and than we found that the
human reaction time was 0,116 seconds
This can make us conclude that other (not known) factors must have on influence on the
viscosity estimation from the intercept
The only advice we can give is to take some more measurements than asked and than sort
them in order to get a higher correlation Although a high correlation is not a guarantee for a
good match between the two viscosities (systematic faults can cause a bad result, despite a
high correlation), it enlarges the chance for a good match and, it is the only variable that can
be controlled easily.
Tracing a systematic fault is very hard due to the fact that all the measurements are influenced
on the same way, and nothing is known about the real viscosity of the tested liquids. Best is
to use an automatic detection system to start and stop the chronometer in order to minimise
changes of the dropping time by human reaction time.
5.2
5
Viscosity as a function of concentration for glycerol
For this experiment glycerol was used as tested liquid, and this for the following reasons :
• Pure glycerol has a rather large viscosity so when mixed with another, low viscosity,
liquid dropping time can still be measured easily.
• The other liquids, such as motor oil or olive oil can be mixed with other organic liquids such as methanol - but the dropping time is already so short that a decrease of viscosity
would sort in an immeasurable short dropping time.
• Glycerol can be mixed easily with water The water is added with a pipette of 10,00 ml.
By counting the amount of water drops the added volume can be calculated
• Water is added until the dropping time gets shorter than three seconds in order to maintain
a reasonable precision Shorter dropping times are hard to measure as the ball falls to fast
to follow it on its way down
This experiment has been performed at several temperatures, to find the influence of
temperature on the viscosity/water-concentration relation
Out of the twelve results found for every water concentration the best then were used to
calculate the average viscosity
Here the viscosity from the intercept is not used because the variations are to big to find a
clear course, and comparing the results found at the several temperatures would be
impossible
Fig . 48; G L Y C E R O L
a v erag e v is c o sity (from ten va lu e s)
as a fu n c tio n o f w a te r-c o n c e n tra tio n
,
As we look at the 3 courses (average viscosity values from ten measurements) the difference
between them is small. It is logical that the viscosity of a liquid (here glycerol) drops as it is
mixed with a low viscosity liquid. Until 2 vol % HjO the relation is of a linear kind As the
%
gets bigger the relation is parabolic
So lar it has not been possible to derive any general laws for the variation of viscosity which
explain the experimental findings
The three graphs come closer to each other when the water concentration gets larger and
probably they would come together or very near to each other at very large water
concentrations These higher concentrations can not be measured with the *^illing-b?'’
viscometer as the dropping time gets too short which causes a lack of precision.
By using the viscosity values found for two temperatures it is possible to calculate viscosity
as a function of concentration for other temperatures by linear interpolation for each water
concentration.
Table 35; Estimating the viscosity as a function of temperature course at 21,3 °C
by using those of 20,0 and 23,0 °C for linear interpolation.
at 20,0 "C
HjOconc.
Vol.%
0,00
0,50
0,99
1,46
1,96
2,44
1
1
3,38
I
i
II
4,76
viscositvix)
poise
14,03
12,16
11,28
9,974
9,267
7,934
7,852
7,121
6,423
5,601
5,351
23,0 “C
viscositv (Vi)
poise
9,856
8,891
7,78
7,055
6,563
5,901
5,284
4,977
4,707
4,366
4,133
d. = tx-v,)
poise
4,174
3,269
3,500
2,919
2,704
2,033
2,568
2,144
1,716
1,235
1,218
i= (d /(2 3 - 20)).1,3
poise
-1,809
-1,417
-1,517
-1,265
-1,172
-0,881
-1,113
-0,929
-0,744
-0,535
-0,528
at21,3°C
viscositv = X - i
poise
12,221
10,743
9,763
8.709
8,095
7,053
6,739
6,192
5,679
5,066
4,823
Now we will compare the viscosity values found by linear interpolation (last row of table 35)
with those we found experimentally :
As shown in this graph the two lines lay very close together, but do not overlap perfectly.
By using linear interpolation it is possible to calculate viscosity as a function of concentration
at other temperatures roughly. For precise results, measurements need to be taken as
predicting the viscosity of a liquid in another temperature area is risky (certainly for very high
or very low temperatures). When we would compare the -xperimental and theoretical values
at temperatures much larger or smaller than the area used for linear interpolation we would
find a significant difference between the two graphs.
Due to intermolecular deformations (or sometimes destruction) the viscosity of a liquid can
change in an unpredictable way at a certain temperature.
5.2 6
C om p ariso n betv ■'en lead and g
s balls
This test was done to see if both the type of balls estimate the same viscosity, and if the
imperfections of the glass balls have a big influence on the viscosity we estimate
At each temperature the viscosity of the lubricating oil for a vacuum pump was measured both
with glass and lead balls
The comparison between these two viscosities was done with a students t-test (95 % interval)
for the average viscosity
Table 36: comparison between average viscosities found
for lead and giass balls at one temperature.
n.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
viscosity / poise viscosity / poise
using Pb balls using glass balls
X)
1,682
1,761
1,797
1,816
1,831
1,838
1,879
1,884
1,888
1,965
1,973
2,017
2,024
2,042
2,054
2,062
2,068
2,087
2,110
2,117
2,144
2,224
2,239
2,295
2,328
2,375
2,405
2,422
2,489
2,556
2,624
2,862
2,898
3,156
3,470
y.
1,776
1,865
1,936
1,891
1,804
1,864
1,955
1,990
1,999
2,007
2,051
2,006
2,140
1,976
2,093
2,022
1,982
2,214
2,077
2,238
2,287
2,138
2,353
2,476
2,370
2,485
2,453
2,551
2,593
2,765
2,788
3,023
3,116
3,289
3,765
d,
x,-y,
-0,094
-0,104
-0,139
-0,075
0,027
-0,026
-0,076
-0,106
-0,111
-0,042
-0,078
0,011
-0,116
0,066
-0,039
0,040
0,086
-0,127
0,033
-0,121
-0,143
0,086
-0,114
-0,181
-0,042
-0,110
-0,048
-0,129
-0,104
-0,209
-0,164
-0,161
-0,218
-0,133
-0,295 H
1 :3= 0(or x = y)
t-test on d,: ) Ho
Hi 3 0 (or X^ y)
2) a = 0,05
3) Presumed is that the viscosities are normal distributed, and they are equal.
n = 35
-0,84
= 0,0874
3 ·=
4) Test method under Ho : T = D . n°-^ ~ to-i
Sd
5) t„ = -5,72
6) a = 0,05 and the test is two sided.
[-to.025ji-I , to,025ji-l] = [-2,01 ; 2^01]
7) Result: t„ is not in this interval, so d (or the difference between the
viscosities) is statistically significant from zero and Ho can’t be accepted.
We hove proved (with 95 % certainty) that the viscosity’s are not the same.
We can conclude that the imperfections of the glass balls have an influence on the dropping
time and so on the viscosity.
This can show us that the Stokes law only works for perfectly round, and smooth balls (more
or less like the lead balls).
The reason is that the flattened surface of the glass balls causes extra movement in the liquid,
which sorts in a bigger friction between the ball and the liquid, and so in a longer dropping
time and a higher viscosity.
y
Fig 50: A perfectly round ball falling
Fig. 51: An irregular (flattened) ball falling
While they do not estimate the same viscosity, all ti.^ ..-.ulis found with the glass balls (used
for olive oil and for vacuum pump oil) are doubtful, as these glass balls cause extra fluid
movement and have to cope with an attendant friction.
Therefore all the measured dropping times are to long, and the respective viscosities are to
large (indicated by the fact that most of the d, in Table 36 are negative), and the viscosity in
function of temperature graph lays higher for the glass than for the lead balls.
5,2.7
Measurements Dy using a small and a big cylinder
By using
the diameter of the tube (R) can be taken under account in the viscosity calculation.
This test was performed for glycerol only as it has a rather large viscosity and accordingly
longer dropping time. Another advantage is that this liquid is completely colourless so the
falling bail can be followed easily on its way down (important for the small tube)
We examined if the given viscosities found with this formula meet each other by using a
students t-test (95 % interval) and if there is a (statistically) significant difference between the
two results to get an optimal comparison between them.
Table 37. Comparing the average (by using a two sided t-test on 3) viscosities for both the
tubes, found with the formula that takes under account the tube diameter
temperature viscosity / poise viscosity / poise
di
X
using a big tube using a small tube poise
20,9
20,1
20,0
20,0
18,0
X.
y.
Xi-Yi
12,047
12,641
12,528
12,725
15,358
10,826
10,862
10,702
10,974
14,005
1,221
1,779
1,826
1,751
1,353
Ho : a = 0
H, ; a # 0
. a = 0,05
Presumed is that the viscosities a ! normal distributed
and that they are equal.
15
1,779733
0,314268
A method under Ho:
T=
18,9
14,764
12,366
2,398
17,0
21,3
18,111
11,778
16,422
9,639
1,689
2,139
21,2
20,6
11,514
12,507
9,543
10,923
1,971
1,584
: = 0,05 and the test is two sided
[-to,o25.n; to,975.n]
=
21,1
11,948
9,851
2,097
Hi is true as t* does not lay in the interval. This
20,9
12,095
10,05
2,045
means that 3 is not an estimation for zero.
21,0
20,8
21,1
11,838
11,885
11,542
10,066
10,332
10,024
1,772
1,553
1,518
The two tubes do not estimate the same viscosity as
the difference between them is statistically
significant bigger than zero.
Sd
,=
21,93312
[-2,14;2,14]
The difference between the two viscosities is significant, meaning that they do not estimate
the same viscosity. This questions the used formula, and we tried to find a more reliable one
by changing the 2,4 value in this equation. In that way it is possible to find come to a better
comparison between the two viscosities.
Out of the average ball radius r and the average ν,™κ«ι for both the tubes we can find which
constant (other than 2,4) makes the two viscosities match perfectly together for each
measurement.
Example
Table 38 Correcting the formula that takes under account the diameter of the cylinder by
using the average radius and the average dropping speed found for a measurement
(at the same temperature) with both size of tube..
small tube
big tube
average radius r average
cm
cm/s
0,0883
1,360
0,1107
1,997
When we use the new formula, but replace the 2,4 factor by an unknown factor x we find :
,
J
9 -v .
·( 1+ λ: - 1
After filling in all the values :
2 ■(l 1.409 -1.270) ■981 ·0.1107^
9.1.997.il.r.M 12Zl
I
3.070
J
2 ■(l 1.409 - 1.270) ■981 ·0.0883^
^
9.1.360·ίΐ.χ.Μ ?^1
[
1.315 J
After some calculations we can find : x = -1,9649
Thus, when x is -1,9649 the viscosities of this experiment found w th this formula are equal
By estimating x for all the measurements and than taking the average, we can obtain the most
reliable x value, in order to find an as good as possible match between the viscosities
measurements with both size of tube.
Table 39; Calculation of the new x value for each of the measurements
n.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
temnerature
°C
20,9
20,1
20,0
20,0
18,0
18,9
17,0
21,3
21,2
20,6
21,1
20,9
21,0
20,8
21,1
*
-1,0422
-2,2992
-2,5415
-2,5862
-0,6977
-0,8701
-3,6813
-3,5107
-1,9649
-3,5270
-3,3401
-2,6686
-2,1170
-2,1153
When we take the average x value we find : x = -2,3823
This value lays very close to -2,4. This makes us conclude that x in the formula has to be
-2,4 and not +2,4 as found in some literature (6X7). Again a students t-test can give some
more reliability to this conclusion. We will test if dj, found with the new form of the formula,
is statistically significant bigger or smaller than zero (95 % interval)
Table 40: Comparison between the average viscosities found for both the tubes
by using the corrected formula with -2,4 as x-factor
temperature viscosity / poise viscosity / poise
using a big tube using a small tube poise
•c
20,9
20,1
20,0
20,0
18,0
18,9
K
14,245
15,039
14,900
15,263
18,342
17,589
y.
14,946
15,073
14,816
15,160
19,516
17,312
x.-y.
-0,701
-0,034
0,084
0,103
-1,174
0,277
17,0
21,3
21,2
20,8
21,1
20,9
21,0
20,8
21,1
21,662
14,056
13,720
14,878
14,288
14,396
14,074
14,178
13,695
22,992
13,306
13,108
15,123
13.595
13,846
13,885
14,308
13,856
-1,330
-0,2212
0,750
0,612
a = 0,05 and the test is two sided
-0,245
0.671 7
0,550
for zero.
0,189 8 The two tubes estimate the same viscosity as the
difference between them is an estimation for zero.
-0,130
-0,161
and that they are equal.
-0,036
0,629
With the following test (Table 41 on the next page) we want to find out if it is necessary to
use this corrected formula (thus with -2,4 and not 2,4 as constant) that takes under account
the tube diameter, or if the normal formula (not taking under account the tube diameter) gives
an evenly good match between the viscosities found for both size of cylinder
By using a students t-test we can prove (with 95 % certainty) if the two tubes estimate the
same viscosity when we do not take under account the cylinder diameter
Table 41 Comparison between the average viscosities found for both the tubes
when the tube diameter is not taken under account
temperature viscosity / poise viscosity / poise
°C
using a big tube using a small tube
X,
20,9
20,1
20,0
20,0
18,0
18,9
13,054
13,736
13,611
13,854
16,718
16,058
y.
12,557
12,625
12,427
12,757
16,308
14,426
17,0
21,3
21,2
20,6
21,1
20,9
21,0
20,8
21,1
19,728
12,817
12,52
13,59
13,005
13,145
12,86
12,931
12,527
19,159
11,179
11,045
12,684
11,424
11,646
11,671
11,999
11,632
d,
poise
. Ho:d=0
Hi :d?tO
x -y ,
0,497
1,1i1
1,184
1,097
0,41
1,632
. a = 0,05
0,569
1,638
1,475
0,906
1,581
1,499
1,189
0,932
0,895
Presumed is that the viscosities are normal distributed
and that they are equal.
=
15
1,107667
0,40948
St method under HO :
P*n°^ ~ tn-1
Sd
t* =
10,47664
a = 0,05 and the test is two sided
[-to, ,n ; to,975,n]
=
[-2,14:2,14]
7 Hi is tme as t« does not lay in the interval. This
means that d is not an estimation for zero.
ε The two tubes do not estimate the same viscosity a;
the difference between them is statistically
significant bigger than zero.
025
The difference between d and zero is statistically significant when the formula that does not
take under account the tube diameter is used, and this means that the two tubes do not
estimate the same viscosity.
As final result we can conclude that a reliable link between the results from both size of
cylinder can be found when the following formula is used :
9 v ,
-2.4·'
5.3
CANNON-FENSKE VISCOMETER
5.3.1
Investigated liquids
This experiment has been performed for all the petroleum based liquids ; Esso motor oil,
lubricating oil for a vacuum pump and glycerol.
The reason is that this equipment is developed for petroleum testing. For non-petroleum
products OstwaJd viscometers are used, but as they were not available no testing with
capillary viscometers could be done for these liquids.
This apparatus estimates the kinematic viscosity v of a liquid To find the dynamic
viscosity η, v has to be multiplied with the liquids density
The test was done in the 20 °C - 100 °C temperature interval
Between 20 and 35 °C we measured the viscosity per degree increment, because this interval
is near to (and partly overlapping) that one applied with the falling-ball viscometer.
From 35 °C until 100 °C viscosity was measured per 2,5 degree increment.
The time was measured twice for every liquid at every temperature, and afterwards the
average value was used to estimate v and so η.
5.3.2
Results
Some general comments :
• Several types of Cannon-Fenske were used, with different diameter of the internal
capillary. To do a precise measurement the time to drain the lower bowl must be minimal
200 s, but nothing is said about the maximum time. This rule most be followed as the
meniscus otherwise passes the start and stop mark to fast, and no precise testing can be
done.
All Cannon-Fenske have a number ranging from 100 till 450. Number 100 stands for a
very narrow capillary (used for low viscosity liquids at high temperatures), number for
450 a wide one (for large viscosity liquids at low temperatures).
• It takes quite some time before glycerol adopts the constant temperature of the bath
We noticed this because the measured time varied considerably when the test was made to
short after changing the bath temperature Ten minutes is the minimal time for this liquid
tf> get bath temperature.
This is an indication for the small warmth conduction coefficient of glycerol. This means
that the liquid cools and heats slowly.
• The opposite can be said for the motor oil. When the bath has reached a stabile
temperature, the draining time can be measured for the motor oil.
This is important in a car engine: the oil reaches the optimal motor temperature
(about 300 °C) very fast, and no long pre-heating is needed before driving the car.
• When measurements need to be done in a larger temperature interval it is better to start at
the lowest temperature and than increase temperature gradient in stead of the other way
round.
The reason is that these constant temperature baths don’t have a cooling other
than a spiral with water flowing through it. It takes a long time before the bath
is cooled to the right temperature by this spiral (the temperature of the water is mostly
around 20 °C, depending on the season). On the other hand the heating of the cold
bath by the heating unit goes very fast.
5.3.2 1 M otor oil
As shown in the graph below, the viscosity of the oil is almost constant at higher
temperatures This is necessary for the well functioning of the engine
The viscosity as a function of temperature graph measured with the falling-ball viscometer
is also added to compare both the graphs with ea''^ '^ther
Fig. 52.
F ig . 52: v is c o s ity as a fu n c tio n o f
te m p e r a tu r e fo r m o to r oil w ith C a n n o n ·
F e n s k e a nd fa llin g -b a ll.
> Cannon-Fenske
results
• falling-ball
viscometer
10
20
30
40
50
60
70
80
t e m p e r a t u r e / “C
Discussion;
• The form of the two courses is very similar, and they coincide in the overlapping
temperature interval. We can conclude that both the viscometers estimate the same
viscosity
5.3 2.2
Vacuum pump oil
F i g . 5 3: v i s c o s i t y a s a f u n c t i o n o f
t e r n p e r a t u r e f o r v a c u u m p u m p oi l
with C a n n o n - F e n s k e and falling-ball
■CannonFenske
re su Its
> fa llin g -b a II
v is c o m e fe r
30
40
so
so
70
80
90
100
tern p e ra tu re / ”C
Discussion :
• Also here the two courses overlap very well. Again the same conclusion can be drawn :
the two viscometeis estimate the same viscosity.
5.3.2
3 Glycerol
Here a perfect overlap of the two graphs is found and there are evenly test results who match
together perfectly
Fig. 54: v i s c o s i t y as a f u n c t i o n of
t e m p e r a t u r e fo r g l y c e r o l by u s in g
C a n n o n - F e n s k e and fa lling-ball
■ Ca nnon-Fenske results
• falling-ball results
10
20
30
40
50
60
70
80
90
100
tern pe r a t u r e / “C__________
As you can see in Fig. 54 there are ome measurements (between 20,0 and 35,0 °C) who lay
lower than the other ones, meaning that the viscosity is too low for that temperature. These
measurements were taken after doing those between 90 and 100 °C.
What we can suppose (but not verify) is that the glycerol was overheated (due to the long
expose - three to four hours - at these high temperatures) and that the glycerol chains were
broken into shorter pieces resulting in a lower viscosity TTiis conclusions gains value when
we see that al these incorrect results lay on one line.
On the other hand glycerol is thermally rather stable what makes the assumption of a thermal
destruction doubtful
Would this drop in viscosity be caused by a pollution of one of the Cannon-Fenske (rests of
previous investigated liquids) than the chance is very small that the glycerol and the pollution
would mix perfectly, and that all our measurements would be lowered with the same value. If
not mixed properly we would never find this kind of fault (all the results on one line), but the
viscosities would vary wildly depending on the speed used to fill the glass bowl (with a
pipette bulb the liquid is sucked into the lowest bowl, what causes mixing of the liquids).
And, if one of the Cannon-Fenske would have been polluted, it would most probably have
been with a petroleum product (such as petrol, an oil product ) and glycerol does not mix
with most of these petroleum based products.
The measurements between 20 and 35 °C were done again but now with new glycerol, and, as
shown in the graph, these results fit perfectly with the other ones.
5.3.3
Conclusion
The Cannon-Fenske viscometer can be seen as a standard test method for kinematic viscosity
of liquid petroleum products.
Some advantages:
• This instrument is very easy to handle; filling and cleaning it goes fast when done on the
appropriate way (see chapter 4 4 p.20)
• It can be used in large temperature intervals (-20 till 300 °C, or evenly larger temperature
intervals depending on the construction material of the instrument) when placed in a
constant temperature bath.
• Taking measurements is very easy. Notwithstanding this the viscosity is measured
precisely.
As the results fi-om the Cannon-Fenske and those from the falling-ball viscometer meet each
other well, and this for all three the tested liquids we can conclude that both the instruments
measure the same viscosity.
As the Cannon-Fenske is a high precision instrument (it can be seen as a standard viscosity
measurement) this test is a sort of accuracy verification for our falling-ball viscometer
54
OPEN-TUBE VISCOMETER
54 1
General comments :
•
The investigated liquids are motor oil, lubricating oil for a vacuum pump, fiying oil,
olive oil and lamp oil. An investigation of the two detergents was not possible as they
would foam too much when the tube is being filled or drained.
• The calibration liquids are water and glycerol. Water was used to calibrate the tube for
lamp oil, glycerol to calibrate the tube for the other oils.
This immediately limits the precision of the measurements, as the calibration of this
viscometer needs to be done with liquids of the same viscosity range and the same
properties to take precise measurements
• When the tube is being filled small air bubbles are formed that can influence the
draining time as they swirl around in the liquid when the tube is being drained
• Working with this open-tube viscometer is not that easy : The big length of this
instrument makes filling it hard, and as the tube needs to be filled to the brim small
amounts of liquid have to stream down the outside of the tube to be sure that tube is
totally filled ( so that the volume of tested liquid is the same for all the measurements)
As all the tested liquids were oils, this causes a difficult handling of the instrument as
the outside of the tube is very slippery
• A lot of liquid is spilled because the tube needs to be cleaned after measuring a liquid
and than filled with small amount from the next liquid that needs to be tested to remove
stains of cleaning liquid.
5.4.2
Test results:
First the tube is calibrated by measuring the draining time for water and glycerol twice.
By using the average draining time from these two measurements and the kinematic
viscosity value found in the nomograph (Appendix 2). We can calculate the kinematic
viscosity for another liquid from its draining time.
Only eight measurements were taken. We worked in the 17-23 °C temperature interval.
Measuring lower temperatures was not possible as we only started with this experiment in
March and no lower ambient temperatures were obtained.
Together with the results found for the open-tube, we provide the results from the fallingball viscometer, at least for those liquids that were investigated with both the viscometers :
motor oil, vacuum pump oil and olive oil.
Fig. 58: MOTOR OIL
10,0
15,0_ 20,0 25,C“
temperature / *C
tefnperature/vtscostty graph
15.0 temperSifl. / -C
25.0
Discussion ;
When we look at the graphs we see that the general form of the viscosity as a function of
temperature relation can be found in the results from the open-tube viscometer.
We look especially to Fig. 55, 56 and 58, that compare the results from the open-tube with
those from the falling-ball viscometer, to see that for all tree the liquids there is no match
between the two courses. As the course found with the Cannon-Fenske viscometer meets
the one found with the falling-ball viscometer there is also no match between the results
from the Cannon-Fenske and open-tube viscometer.
For olive oil and vacuum pump oil we can say that the two courses are (roughly) parallel,
meaning that the viscosity found with the open-tube at every temperature is an equal value
larger than the viscosity found with the falling-ball viscometer. Assumed is that the large
height of the tube causes this increase in viscosity. Due to the large amount of liquid above
the opening, a large pressure is caused. This large pressure results in extra fluid motion
(turbulence), just before the opening (Fig. 60 and 61), causing an attendant friction between
the fluid molecules and so a larger draining time and a larger viscosity For some liquids eg for glycerol - this turbulence can be seen when looking carefully to the fluid just above
the drain.
A possible solution would be to use smaller (less high) tubes with a wider bore (more or
less like Zahn-or Shell cup viscometers)
Fig ΘΟ: When the p(ug isjust rentved the
pressire on the liquidjust above the dan
is maximal causing strong turbulent flews.
Fig 61: When the tite is almost totally daned
the pressure on the liqdd just above the dan
is decreasing and so the tabulent flews
are not visible any more.
The insufficient calibration also has its influence on the difference between the results from
the two viscometers. For motor oil, vacuum pump oil, frying oil and olive oil the tube was
calibrated with glycerol, a liquid with a much larger viscosity and different structure. For
the lamp oil we should expect better result as the calibration of the tube was done with
water which has a similar viscosity, but a different structure as the lamp oil is a petroleum
based product and water not.
The problem is that no comparison can be made to check the results for lamp oil as the
viscosity measurements were only taken with the open-tube and not with the falling-ball
and Cannon-Fenske viscometer. Reason is that the viscosity of this liquid is too small:
when this liquid is tested with the falling-ball viscometer the velocity of the falling ball is
that large that it can not be followed by the human eye. Measurements with
Cannon-Fenske were not possible as instruments with a too narrow capillary are needed to
measure a long enough draining time.
Another remark to make is that the precision of this instrument is poor. As shown in the
graphs we performed for every liquid one measurement at 21.1, 21.2 and 21.3 ®C to see if it
is possible to measure this small viscosity changes with this instrument. For none of the
liquids a good result is found: the separation between the three measurements is poor,
meaning that the highest temperature of the three (21.3 °C) is not measured as the lowest
viscosity value and vice versa.
5.4 3
Conclusion
The reliability of these measurements is low, first of all caused by the large height of the
tube, which leads to an attendant fiiction, and so results in a longer draining time and larger
viscosity
Secondary we name the insufficient calibration as the precision if this instrument is directly
related to calibration fluid that is used
And finally there is the poor precision of this viscometer so only rather large viscosity
changes can be measured
Due to the several disadvantages of this viscc. -eter and the not precise result that is found,
further use of this specific instrument can be questioned
FINAL RESULT
FALLING-BALL VISCOMETER
6 . 1,1
Viscosity as a function of temperature
The main aim of this project was to find viscosity as a function of temperature for several
liquids
This experiment was done for six fluids.
Two ways were used to estimate the viscosity : first of all the average viscosity from ten
measurements, and second the viscosity from the intercept (fi-om the equation of the best
fitting line found for the linear relation between log r and log vunaed)
For all the tested liquids we can conclude that the average viscosity value is by far the most
reliable, as the viscosity fi-om the intercept copes with a large spread.
We tried to find out which variables cause these large variations of the intercept, and the ways
to control them
• We discovered that the correlation (for the relation between log r and log vunmtd) has an
influence on the intercept value A high correlation (close to 1) involves a better match
between the two viscosities But with some examples we proved that this relation
between the correlation and the intercept is not always valid
• Other influence is the human reaction time. This causes the measured dropping time to be
larger than the real dropping time Again some examples were used to show the influence
of a long human reaction time on the intercept. We tried to calculate the human reaction
time by distracting all the measured dropping times with x seconds so that average
viscosity and viscosity fi-om the intercept were equal.
We also found out that the human reaction time is not constant, but depends on the
measurement
Out of the equation that subscribes the relation between viscosity and temperature best
(Andrade equation) we tried to extract information about the viscous behaviour of the
investigated liquids but we came to the conclusion that the real meaning of these constants is
hard to find
We aiso investigated a modified version of the Andrade equation, namely the Vogel equation
with three fluid constants Also here we came to the conclusion that the real meaning is not
known
6.1.2
Viscosity as a function of concentration
For glycerol this relation was investigated at three different temperatures.
As we expected the viscosity of glycerol decreased when it was being mixed with small
amounts of low viscosity liquid like water
’ Intil 2 Vol. % H :0 this relation is of a linear form; above this concentration the relation ■" of
a parabolic type
Why we find this specific course for the viscosity as a function of concentration relation is not
known
By performing this experiment at three temperatures we check the influence of temperature on
the viscosity/water-concentration relation. The three curves are lying next to each other, and
their form is very similar. For larger water concentrations the three courses come closer to
each other, meaning that the difference in viscosity is getting smaller.
By using linear interpolation we tried to calculate the viscosity as a function of temperature
course for other temperatures. By using the results found for 20,0 °C and 23,0 °C we
calculated these for 21,3 °C and compared them with the practical results for this temperature.
In this way it is possible to predict the viscosity/concentration course for another temperature
roughly. We advise to do this only for temperatures near to the ones used for linear
interpolation because intermolecular deformations (due to a change in temperature) from the
mixed liquids can cause unpredicted viscosity shifts, which will not fit with the theoretically
found results.
6.1.3
Comparison between lead and glass balls
For the lubricating oil for a vacuum pump we investigated if lead and glass balls estimate the
same viscosity. Therefore we used a students t-test (95 % interval) to compare the viscosities
found at the different temperatures. We found out that the difference between the two
viscosities is significant, and this means that the different type of balls do not estimate the
same viscosity.
The reason for this difference is that the flattened surface of the glass balls causes extra fluid
movements, which results in an attendant friction between the falling ball and the fluid. This
friction causes the ball to fall slower, and so the dropping time to be longer and the viscosity
larger than expected.
This proves that Stokes law can only be used for perfectly round balls (more or less like the
lead ones) as irregular balls cope with a larger friction than found with Stokes law.
6.1.4
Measurements by using a small and a big tube
With this investigation we tried to link the results found with a big tube (like we used) and
those found with a small tube (used by the students in the practical physics lessons).
We found a formula that takes under account the diameter of the tube:
_ ^ *ipbalt ~ Pbquid)' S ' r*
+ 2-44
By using a t-test we checked if the two tubes really estimate the same viscosity when this
formula is being used.
We found out that the difference between the two viscosities is significantly larger than zero,
so they do not estimate the same viscosity.
By changing the +2,4 value into -2,4 (this was found experimentally) the match between the
two results is much better.
Again a students t-test was used to compare the results found with this corrected formula.
Now the viscosities found with the two tubes are the same, so, to find an optimal match
between the results found with the two tubes the following equation can be used:
9-v,
1- 2 . 4 ·
6,2
CANNON-FENSKE VISCOMETER
This instrument is very useful: in a simple way we can take a precise and accurate viscosity
measurement.
As this method is almost an absolute method to measure the kinematic viscosity, this test can
be seen as an accuracy verification for our falling-ball viscometer.
We found that the results for the two viscometers meet very well, and that they evenly overlap
in the temperature interval where we have measurements for both the viscometers.
This makes us conclude that the accuracy of our falling-ball viscometer is good.
Only glycerol caused some problems: Between 20 and 35 °C we found results that didn’t
match with the other ones. All the viscosities in that temperature interval were much to low.
We tried to find an explanation for these unexpected results:
• Overheating due to the long disposal (three to four hours) at high temperatures
(90 to 100 °C) the day before.
• Contamination of the Cannon-Fenske viscometer with low viscosity liquids
But, the real reason for this incorrect results is not known as it is very hard (let’s say
impossible) to check these theories in practice.
Afterwards the same measurements were done again with new glycerol and than the results
fitted with the good results, and not with the unexpected ones.
6.3
OPEN-TUBE VISCOMETER
We tested if it is possible to measure the viscosity of a liquid with a minimal set-up like the
open-tube (only a tube and a chronometer are needed).
We found that the results don’t meet with those found for the falling-ball viscometer; all the
viscosity measurements found with the open-tube are larger.
We found an explanation for the difference between the results from the two viscometers:
• Due to the length of the tube a large amount of liquid presses on the drain.
This large pressure acts on the fluid layers near the drain, and causes turbulent flows just
above the drain. These turbulent flows cause an attendant friction between the fluid
molecules resulting in a longer draining time and a larger viscosity.
• Also the poor calibration has its influence on the too high viscosity result.
Best is to calibrate this instrument with fluids of quite similar properties to the fluid being
measured. And as we only calibrated with two liquids, with other properties than the
investigated liquids it is not that such a surprise to find these unexpected results.
6.4
FINAL CONCLUSION ABOUT ALL THREE THE VISCOMETERS
The best instalment that we used was (like expected) the Cannon-Fenske viscometer, but we
found out that also the falling-ball viscometer can provide us accurate viscosity
measurements. The big advantage is that no special equipment needs to be bought (like the
Cannon-Fenske which are expensive and fragile), only some basic lab equipment is needed.
The open-tube we used is not a real good viscometer. First of all the handling of this long
tube causes a lot of problems and the results we found didn’t meet those we found for the
other two viscometers.
But, when a smaller tube would be used, and a better calibration it is possible to take accurate
measurements with this type of viscometer.
APPENDIX 1: Further investigation of the A and B constant from ihe And; .de
equation
We will try to prove that the A and B value we estimate are those from the Andrade
equation.
Therefore we used the A and B value we found in Ref 15 for water:
A = 1,026.10'^cp and
B = 4010 cal mol ‘
We want to find these values experimentally by using the falling-ball viscometer
Therefore we need at least two viscosity measurements at their specific temperature to
be able to calculate the Andrade equation for water and so to find A and B
But this causes some problems The viscosity of water is much too low to be
measured in the tube of 1000 ml. The ball falls way tov. fast to perform a precise time
measurement
To solve this we will use the open-tube viscometer as cylinder. Due to its large height
it must be possible to measure the dropping time. Problem is that the diameter of this
instrument is small so the bail needs to be dropped precisely in the middle of the tube
otherwise it would touch the side of the cylinder causing an attendant friction. Due to
this extra friction we would measure a longer dropping time and so a larger viscosity
We take measurements and see that the ball falls so fast that we can not start and stop
the chronometer when the start and stop mark is passed. Even the ver>' light glass
balls cope with this problem. A remark we want to make is that the velocity of the
falling ball so large that it bounces up when it hits the bottom of the cylinder.
The conclusion is obvious: we can not verify if the A and B we find experimentally
are really the A and B constant from the Andrade equation.
a p p e n d ix
2: NOMOGRAPH FOR YISCOSITIES OF LIQUIDS
iv>-;
BIBLIOGRAPHY
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