Nordtest Technical Report 501

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					                                                                                            TR 501
                                                                                            Approved 2002-04

                           suspension wire                acrylic glass pipe
                                to balance

                          cover of                               temperature
                        acrylic glass                              sensors



                                                                                   375 mm
                               holder            TB



                                         290 mm
                                         370 mm

                Study to characterize thermal
                 convection effects in water

                                  Peter Lau

Published by Nordtest            Phone: + 358 9 455 4600                       Fax: + 358 9 455 4272
Tekniikantie 12                  E-mail:                 Internet:
FIN–02150 Espoo
                                                                          NT TECHN REPORT 501
                                                                          Approved 2002-04

Authors:                      NORDTEST project number: 1543-01
Peter Lau

                              SP Swedish National Testing and Research Institute
Title (English):
Title (Original):      Study to characterize thermal convection effects in water

 The careful hydrostatic weighing measurements with alternative preparations performed could
 not verify the working hypothesis of an existing very thin air layer on objects immersed into
 water, a problem that occurs whenever primary density determinations are carried out. Most
 probably, the disturbing buoyancy effects we thought were caused by not de-aerating are
 instead most probably due to small convection currents in the water bath. These can be
 induced in two ways. One reason is a slight temperature difference between the artefact and
 the water. The other is due to the fact of not having a perfectly stable and isotropic temperature
 distribution. Our results indicate that the experiments suffered of both especially an ongoing
 convection despite a very stable vertical temperature gradient in the water (1mK/cm). The
 driving force is believed coming from small temperature variations in the surrounding air
 producing both additive and subtractive overlaying friction forces as a function of time. This
 effect has so far not been reported as an important error contribution. The idea of stirring the
 bath in order to achieve temperature homogeneity is not an alternative, as this would not allow
 performing weighing at all.

 Due to these findings, the planned experiments studying the air layer effect in liquids differing in
 surface tension and on various materials and surface roughness are not meaningful to carry
 out. It seems that the mentioned effect is enlarged in hydrometer calibration. We suggest
 instead a different goal for the project, namely to carefully study the temperature field and its
 behaviour in time both in the active and buffering water bath as well as in the surrounding air to
 indirectly determine the dynamic forces on the artefact under weighing. It is further important to
 repeat the measurements with some of the earlier artefacts at some controlled higher and lower
 temperatures than the test water. This would produce experimental data for modelling the
 convection effect on the hydrostatic weighing result. The model then could be used both for
 correction and uncertainty estimation purposes, an important aspect in hydrostatic weighing as
 this effect is of the same order than the stated measurement uncertainty so far.

Technical Group: Expert Group Quality and Metrology
ISSN: 0283-7234                      Language: English                 Pages: 63
Class (UDC): 531.75; 536.25         Key words:     Convection, temperature, evaporation, driving
                                                   force, density, layer formation hydrostatic
Distributed by:                      Publication code:
 Tekniikantie 12
 FIN-02150 ESPOO                    Report Internet address:
1           Introduction                                       2
1.1         Convection as a potential source of disturbance
            in hydrostatic weighing                            2
1.1.1       Convection introduced by a temperature
            difference between object and the water            2
1.1.2       Convection induced by temperature variations in
            the surrounding air                                2
2           The experimental conditions                        3
2.1         The measurement bath                               3
2.2         Room conditions                                    4
2.3         How to observe natural convection                  4
2.3.1       Particle speed with LDV-technique                  4
2.3.2       Particle luminescence                              5
2.3.3       Mathematical modelling                             5
2.3.4       Temperature logging                                5
2.3.5       Coloured water injection                           5

3           The temperature logging resources                  5
3.1         Temperature instrument and scanner                 5
3.2         Sensors and calibration                            6
3.2         The measurement program                            6

4           Bath and measurement conditions                    6
4.1         Changes to the bath                                7

5           Experiments and result interpretation              9
5.1         Undisturbed situation after preparation            9
5.2         Continued undisturbed insulated bath               10
5.3         Continued undisturbed non-insulated bath           11
5.4         Undisturbed bath falling temperatures              12
5.5         Non-insulated forced cooled bath                   14
5.6         Effect of insulation to prevent evaporation        15
5.7         Insulation on top and no cooling                   17
5.8         Insulation on top - heating to roomtemperature     18

6           Conclusions                                        20

Appendix: Collection of interesting temperature logs            24-38
Appendix: Study of traceability to the density of water, SP Technical Notes : 2001:43

1            Introduction
1.1          Convection as a potential source of disturbance in
             hydrostatic weighing
Most density determination methods make use of a hydrostatic weighing technique. If one is
interested in the density of a solid, it is weighed in two media with different density. Most
commonly air and water are used. To explain observed small differences in an inter-
comparison measurement an air layer not visible to the eye was assumed to cause possible
systematic errors if not pre-treated by de-aerating. However, the additional buoyancy effect
was expected to be of the same size or smaller than the stated measurement uncertainty,
which made the assumption difficult to proof.

Within the current Nordtest-project the hypothesis of an air layer effect was rejected. The
corresponding experiments were described in the Nordtest-report [1] New experimental
results pointed instead to natural convection currents producing an overlaying force. Small
temperature variations in the surrounding air were assumed to cause small convection forces
of varying size that earlier were not included in the mathematical treatment of the
experimental situation.

1.1.1        Convection induced by a temperature difference between
             object and the water
Earlier work in mass calibration pointed out that weights having higher or lower surface
temperature than the air inside the balance could affect the balance reading in an erroneous
way [2], [3], [4]. A temperature difference induced air convection upwards or downwards
thus overlaying a friction force. Considering temperature differences of ± 1 °C this effect
however is much smaller than the measurement uncertainties occurring in hydrostatic
weighing. Furthermore after a temperature equalization taking less than an hour the effect
disappeared completely [5] [6].

In hydrostatic weighing the same kind of object induced convection is expected. In [x] it also
was shown that object induced convection worked both ways giving higher density values
with colder object and lower ones with warmer object. But standard procedure prescribes
several hours of temperature stabilization. Usually the experiment is prepared in the
afternoon and the measurement starts next morning. Therefore the analogy to air convection
disturbance was not regarded to be valid as an additional source of error.

1.1.2        Convection induced by temperature variations in the
             surrounding air
Repeated short weighing series at various occasions during the day exhibited a spread in
object density that could not reasonably be ascribed to changes in water temperature or
changing gradients. Whereas the water density during the experiment changed by 20 ppm the
correspondingly calculated density varied by 88 ppm without any observable correlation.
The water temperature was measured with a resolution of 1 mK in two positions every time
the weighing result was recorded. The measured values were stable within 3 mK during each
measurement series of roughly one hour and probably within 10 mK in the volume around
the object over the total period. And of course these differences were considered in
calculation work.

The question raised in the first report [x] having the traceability to water as major objective
was the following. Is it possible that inevitable room temperature changes of a few tenth of a
degree between day and night can induce convection currents in the centre of a buffered bath
of roughly 40 litres?

2            The experimental conditions

2.1          The measurement bath
For density determination of solids up to 5 kg the double bath shown in figure 1 below is
used. Both are made of glass for good visibility and contain very clean and de-aerated water
in order to avoid formation of air bubbles. The main reason for the size was ease of handling
the weights and the wish for a thermally slow and thus stable system. The purpose of the
acrylic glass cover serves as a protection for air borne organic material and for dust that
might obstruct the meniscus formation around the suspension wire at the air/water interface.
The cover holds two temperature sensors and must be simple and fast to remove. It also
serves as protection for air movement and thus reduces evaporation. The pipe of acrylic glass
shielding the suspension wire serves the same purpose.

         suspension wire                acrylic glass pipe
              to balance

        cover of                              temperature
      acrylic glass                             sensors


                                                                 375 mm

             holder            TB



                        290 mm
                       370 mm

Figure 1: The ordinary bath of two concentric glass containers. Total volume 40 l. The
          balance on a stand above is not shown.

The pneumatic lifting cylinder at the bottom lifts the weight from its holder when the
comparison is performed with reference weights placed directly at the balance pan. This is a
cheap and practical design and prevents to use the reference weights in water. It also
minimizes the number of object and materials needed in the measurement water, which were
necessary when exchanging object and reference weight in the water. To be able to use
various weight combination for reference is important when the object for density
determination has an odd mass value, which is the case most of the time. The holder in this
design is expected to act in a total neutral way. This means it is weighed either with the
object in place or with reference weights on the pan. Assuming no additional forces
influencing these two weighing situations the weight of the holder disappears in the cal-

The bath is not actively temperature controlled. The reason is twofold. Earlier experience has
shown difficulties to achieve good short term (1 to 2 hours) stability at preferably 20 °C.
Any stirring of the bath in order to minimize temperature gradients is not acceptable in
connection with accurate weighing. Due to vibrations this is valid for the outer bath as well.
Having room temperature conditions with small variation (<± 0,5 °C per day) the outer
buffer bath was expected to guarantee a rather stable gradient and temperature fluctuations
less than ±0,05 °C in the measurement volume at steady state conditions over an experiment
period of one to three hours. All measurement data like pressure, temperature and humidity
of the air, water temperature and balance indication are read manually.

The bath is normally not insulated. The major reason is that the operator needs to be able to
observe the object, holder, wire etc. in order to discover disturbances of different kind.

2.2          Room conditions
The laboratory is in the basement below the ground and has a relative stable temperature.
The daily variation is in the range of 0,5 to 1 °C. Fluctuation at day time with no activity in
the laboratory are typical ± 0,2 °C and at night ±0,07 °C. During laboratory hours a usual
temperature rise is 12 mK/h. The decrease at night is 8 mK/h. When working at the density
stand temporarily changes in air temperature of up to 2 °C have been registered, which
mainly are due to human activity. The stated figures above are valid for all equipment
housed in the laboratory and the illumination that is never switched off.

2.3          How to observe natural convection?
The task for this study is to directly or indirectly find evidence for natural convection, to
understand how it arises and how it affects the weighing conditions.

2.3.1        Particle speed with LDV-technique
The first approach was to use LDV-technique (Laser Doppler Velocimetry) to measure a
kind of “flow profile” in the inner bath. In practice this would mean to introduce suitable
particles that would follow the “convection flow”. Further during steady state conditions
(quite stable temperature fields) their moving speed needs to be measured with more than
1000 counts per measurement point at many locations.

There are several reasons why this approach would not work. It is very delicate to find
seeding particles for a given water density that would follow a convection stream that in first
approximation is assumed not to exist and in a second approximation is expected to move
extremely slowly due to tiny differences in density. But even if the particles gave a good
picture of the water movement the induced laser effect in the water spot ( < 1 mm3) during a

time long enough to count thousands of particles passing this volume would probably heat
this volume element so strongly that it would generate the convection it ought to measure.
Furthermore is seems rather difficult to determine the actual volume element behind two
cylindrical not necessarily concentric glass walls with varying refractive index.

Despite a high potential to measure speed in a non contact way this technique does not seem
able to produce a representative picture of the natural convection situation.

2.3.2        Particle luminescence
A different approach starting with seeding particles could be to illuminate the bath in
different planes (parallel or intersecting) and using video technique to film sequences of
moving highlighted particles. A particular interesting design would be to use particles that
could be charged with short wave light and that could be observed exhibiting this energy by
phosphorescence observable by eye or CCD-camera. Thinking of the amount of labour and
expectable problems to find suitable tracers and more over the risk of influencing the energy
balance by induced light power, it did not seem reasonable to follow this track either.

2.3.3        Mathematical modelling
Assuming the border conditions were well-defined and experimentally known mathematical
modelling could be a very powerful tool to study thermal convection in a cylinder
symmetrical coordinate system and how it would change depending on altered conditions.
The effort necessary for this task is however to large to be included in this project at this

2.3.4        Temperature logging
For a qualitative study based on existing equipment the accurate measurement of water
temperatures at a few relevant points in the water bath can indicate temperature differences
that in turn can give an image of a water flow.

2.3.5        Coloured water injection
The careful injection of coloured water like ink was suggested to use not only as an indicator
but also as a quantitative means of measuring the convection currents. This approach was
never tried. However, although this idea seems to offer a very reasonable technique it is
probably quite impossible to inject a liquid of perfectly right density. Most probably the pure
existence of a careful jet to introduce coloured water would produce a current stronger than
the one we wish to observe. Moreover a density difference corresponding to let’s say 10 mK
compared to the water would immediately induce a convection in upward or downward

3            The temperature logging resources
3.1          Temperature instrument and scanner
For the ordinary density work a digital thermometer Unisys U241 is used. It consists of a
high resolution instrument for Pt-100 sensors with a scanner for eight channels. The in-
strument was so far only used with three sensors in a manual way. One of the sensors is
taken for the air and two for the water temperature. For this continued study the system was

completed with another five sensors. Further, for being able to monitor over long periods it
was connected to a computer via an RS-232 serial interface.

3.2          Sensors and calibration
The sensors were all calibrated for their respective channel and this order was never
changed. The corrections gained for each sensor and corresponding channel were stored in
the monitoring program and the stored data was on-line corrected. The calibration range was
limited to a range from 18 to 26 °C and the best value for the midrange 20 to 22 °C were
selected. Whereas calibration is performed in a water bath at high revolutionary speed the
measurements were performed in a bath with ideally no motion at all. Despite the systematic
difference in the measurement application no trial was done to correct for possible self heat
effects in the sensors themselves. The expected error giving higher temperature registrations
is estimated to be in the region of 5 mK and not more than 10 mK. As all sensors have rather
similar behaviour this effect is not expected to significantly change the relative temperature
differences between measurement points. The dissipated effect during each scan period is
further considered to be so small as not to faulty influence the convection to study.

Regarding the effect of self-heating thermocouples was preferable to use in this study. On
the other hand an accurate measurement of differences in the mK range with such sensors is
also tricky and quite expensive.

3.3          The measurement program
A temperature-logging program in visual basic was developed that can store the meas-
urement data and the corresponding time for a scan in an Excel sheet for later data ma-
nipulation. Besides the possibility to choose any combination of channels used it also
allowed for reading of the balance that is used in density determination. In order to get stable
temperature readings a time of 20 seconds was allowed before the instrument output was
read off and the scanner switched to the next channel. Together with the balance registration
a complete scan takes 2 minutes and 40 seconds. The scan interval is selectable in whole
minutes. Thus the shortest time between repeated measurements at one point is 3 minutes
and 40 seconds. This was considered to be suitable for the expected slow movements
observation times of several hours.

Every scan containing up to 9 values has only one time mark for the last channel Ch-7 or the
balance value. If necessary it would be able to reconstruct the time mark for each registration
afterwards, but this was not assumed necessary. For the diagram generation the date was
stripped off but the actual day hour was kept when transferring to the plot program, which
was KaleidaGraph. The date was replaced by a running day number, which seemed to be the
simplest way of transferring the date format between the different programs.

4            Bath and measurement conditions
Considering an ideal measurement situation with a totally homogeneous temperature
distribution in the inner water bath there is no driving force to produce any convection. The
main effect of convection is to equalize existing temperature differences. Thus as long, as
there are any temperature differences within the bath or compared to the surrounding
convection can arise. An interesting question for the mathematical modelling would be to
find the temperature conditions for starting natural convection, i.e. without any action of the

Changing air temperature and heat transport through walls and the water/air surface (in-
cluding insulation) is expected to influence the strength and pattern of the convection.
Further the experimentally given cylinder symmetry of the bath suggest to expect a corre-
sponding symmetry in the convection currents. Thus the idea is to vary some of these
conditions and looking how the temperature behaves in the all-together 8 available meas-
urement points. The interesting questions are:

        Where are the warmest and coldest spots within the measurement volume of the
        holder occupying the solid object and the space around it, especially above?
        Does this temperature pattern change with time when no active temperature control
        is applied?
        How much does equilibrium condition change between day and night with normal
        air temperature variations?
        How much is the temperature pattern changed by additional insulation?
        How long is the time for establishing a new equilibrium after a disturbance (with and
        without insulation?
        How stable is the equilibrium in time depending on different insulation conditions?
        Can relative temperature changes between the measurement points indicate a major
        direction of convection?
        Is this convection direction changed when inside-outside temperature conditions are
        What are the main causes for convection to occur?
        Can temperature inversions be simulated by actively heating/cooling the outer bath?
        What roll does evaporation play as generator of convection?
        Can changing gradients in vertical or horizontal direction qualitatively indicate
        convection effects?

4.1         Changes to the bath
For the various temperatures logging experiments the way the bath looks like was changed.
As shown in figure 2 the bath was insulated with a black 2 cm thick rubber carpet, both at
the bottom and the outside wall. White paper was put between the glass and the insulation
material and two windows were opened to be able to observe the inside using a flashlight.
During measurements with insulation these windows were closed with the same insulation
material. In all experiments the water surface of the outer bath was insulated using a black
cellular insulation material of 5 cm thickness. For preventing energy losses in some of the
measurements the top of the inner bath was also insulated with the same cellular material
consisting of two halve circles.

                                               130 mm
                                            70 mm
                                                                 Acrylic glass pipe

                                                                     Suspension wire

                    30 mm
                                            7    6      0
                            80 mm

                               180 mm


                                                                                                420 mm
                                                                                       375 mm
                                        4   5           2
        (6)   (3)

   Control bath

     copper spiral
                                                            290 mm
                                                            370 mm

Figure 2: Changes to the bath – additional heating/cooling, additional insulation, addi-
          tional temperature sensors.

Assuming some kind of cylinder symmetry the 8 available sensors were all placed in one
plane. Figure 2 shows the basically chosen sensors placement. Sensor 0, 1 and 2 were
fastened on the central acrylic protection pipe and always kept in the same relative position.
In normal measurement the sensor 1 and 2 are somewhat above and below the measuring
object. Sensor 4 and 5 were placed at the same height as sensor 2 as close as possible to the
wall of the inner bath. Sensor 7 as well was attached near the inside wall. The so far
mentioned positions were never changed. The sensors 3 and 6 on the other hand were used
for different purposes and therefore shifted sometimes between different positions. Figure 2
indicates the alternative positions (numbers in brackets).

The placing served to study vertical and horizontal temperature gradients at such places
where convection initiation were expected to occur in the first place. Thus sensor 3 and 6
were alternated between the outer and inner bath and occasionally to measure the air tem-

Typically the sensors were inserted vertically. In the case of sensors 0, 6 and 7 this is not
without problem as the active sensing element is only a few millimetres below the water
level. More interesting perhaps would have been to have the sensors horizontally as to just
detect temperature changes in the surface water. A vertical placement, although the easiest to
achieve with respect to other limitations, is however not expected to produce non-
representative data. No heat leakage into or out of the water is expected as the stainless steel

casing is a poor heat conductor and the experiments performed never lead to a temperature
difference larger than 2 °C between water and air.

In order to simulate exaggerated heat flow through the glass wall into and out from the inner
bath the outer bath was completed with a heating/cooling spiral of copper, which was
connected to a separate temperature control bath via short plastic hoses. In some
measurement situations sensor 3 and 6 were used to measure the temperature in this control

5            Experiments and result interpretation
The purpose of the following experiments is to establish various conditions under which
changing temperatures can induce convection flow in the inner bath. Gradients at rather
stable situations should indicate in what direction a convection flow is directed and how it
could intervene with the weighing performed in the bath.

5.1          Undisturbed situation after preparation
Before starting the temperature measurements the inner bath was newly prepared with water
at room temperate. The water levels were height adjusted. The outer bath was insulated at
the bottom, the outer wall and on top. No insulation was put on top of the inner bath as this is
closer to the ordinary situation. The lifting cylinder and the holder were removed for
simplest possible configuration. At average the temperature in the inner bath was 1,8 °C
below the air temperature.

After an initiating start phase all measuring points showed almost linear and parallel in-
creasing temperatures during eight hours of measurement. The rate of temperature increase
was 9 to 10 mK/h. Table 1 contains the data representative for a 40 minutes average from the
temperature log c found in the appendix.

Table 1: Temperature characterization some hours after adjustment of bath (information
         from temperture log ?). For characterizing an equilibrium situation only the
         temperature differences are of interest. They persist almost all the time.
 Temperature difference       Temp. gradient
         [mK]                    [mK/cm]
Ch-3 – Ch-4         82          5,4 vertical
Ch-7 – Ch-5         62          4,2 vertical
                                                            3       ( )
                                                                       6   0   20,331

Ch-0 – Ch-1          7          1,4 vertical                               1   20,324

Ch-0 – Ch-2         15          1,0 vertical
Ch-5 – Ch-2          7        0,5 horizontal       20,388
                                                            4   520,475    2 20,467
Ch-4 – Ch-5         65         65 horizontal
Ch-7 – Ch-0         54        4,2 horizontal
Ch-3 – Ch-7         84         84 horizontal
Higher Ÿ lower temperature

As indicated in table 1 the temperature in the outer bath is always higher than in the inner
bath at corresponding height (84 mK at top and 65 mK at half height). The vertical gradient
point (3) to (4) is largest in the outer bath and lowest in the centre (1,4 mK/cm and 1,0
mK/cm). The horizontal gradient is largest over the separating glass wall.

The interpretation starts from the assumption that the thermal energy for the temperature
increase must originate from the air through the vertical walls despite the insulation. A large
temperature fall (54 mK) at the top point (7) to the centre (0) compared to 7 mK at half
height (5) to (2) must mean that the water in the top centre gets colder, has higher density
and is sinking towards the bottom leaving the coldest spot at (2) and the warmest measured
at (7). At the inside wall the direction should be the opposite one as the water is heated and
streaming up due to lower density. This situation seems to persist after an initial phase
throughout the temperature increase indicating a toroid like flow pattern with a downward
directing in the centre. But the temperature differences are small, thus one must expect that
up and down movements of water is slow and leads to a mixing that cannot maintain an
extended convection pattern.

However the picture is not clear as sensor 6 for quite some time showed the lowest and most
fluctuating temperature before it was removed to measure the air temperature (not knowing
this result at that time). A first guess to understand this behaviour is to assume evaporation at
the air/water interface that would take the necessary energy in form of a temperature
decrease in the surface water. The water temperature at point (6) is more exposed than at
point (0) and (7), due to the acrylic protection pipe and the glass wall respectively. And the
fluctuation of around 40 mK seen in temperature log M could indicate a real layering
movement at the sensor.

5.2          Continued undisturbed insulated bath
After 24 hours from start a new registration phase lasting 24 hours was started and an
ongoing temperature rise in the range of 0,145 to 1,61 °C was registered in the water (se
temperature log d in the appendix). The rate of temperature increase during working hours
was 8,7 mK/h and became slower during night 6,2 mK/h partly due to slowly decreasing air
temperature, that had increased 0,35 °C since the end of the first measurement series. At
early morning hours a steady state condition was observed before the rising air temperature
(ventilation start) again increased the water temperature. In the centre of the inner bath
actually a beginning decrease of temperature was observed in contrast to the insulated outer
bath. This indicates a more pronounced energy loss from the inner bath.

Table 2: Temperature characterization after 48 hours undisturbed observation. Only the
         relations between temperatures are shown. The data from temperature log @
         represents the average values of a 2-hour interval.
 Temperature difference        Temp. gradient
         [mK]                     [mK/cm]
Ch-3 – Ch-4         85           5,7 vertical
                                                     20,470       720,385   0            6
Ch-7 – Ch-5         65           4,3 vertical                 3    20,539       20,477
                                                                                20,331   21,981

Ch-0 – Ch-1          8           1,6 vertical                               1   20,324

Ch-0 – Ch-2         10           0,6 vertical
Ch-5 – Ch-2          8         0,6 horizontal        20,388
                                                              4   520,475   2 20,467
Ch-4 – Ch-5         70          70 horizontal
Ch-7 – Ch-0         63         4,8 horizontal
Ch-3 – Ch-7         91          91 horizontal
Higher Ÿ lower temperature

As important observation one can state that the gap between air and water temperature fell
from 1,7 to 1,5 °C over a 24-hour period, but it seems that this gap will never get smaller as
long as the experimental conditions are kept this way. That means loss of energy from the

inner bath, predominantly due to evaporation keeps the water temperature lower than in the
outer bath. One probably also must assume that the inner bath in uncontrolled condition
permanently gains energy from the outer bath, which is cooled. The energy transfer to the
inner bath determines the gap between the temperature of the air and the outer bath.

Compared to the situation 24 hours earlier marginal differences are observable. The vertical
gradient has increased in the outer bath from 5,4 to 5,7 mK/cm and at the inner wall from 4,2
to 4,8 mK/cm. In the centre (0= to (2), however, it has decreased from 1 to 0,6 mK/cm.
Simultaneously the gradient in the top of the centre (0) to (1) has increased from 1,4 to 1,6
mK/cm. This can be interpreted as being the result of a cooling process, that despite steady
state condition is still ongoing but does not reach equally long below the water level.

Interestingly one also can state a small increase of the fluctuation (standard deviation in the
temperature) from 8 to 9 mK at point (0) at the top, from 2 to 4 mK and 1 to 2 mK at point
(1) and (2) respectively. This can be taken as an argument for the assumed cooling by
evaporation. Evaporation increases with low water vapour pressure in air, but also decreases
with lower temperature difference to the air.

5.3          Continued undisturbed non insulated bath
As the ordinary measurements are performed in the bath without insulation around the walls
the rubber material was taken away and the observation without active control started 64
hours after preparation at late afternoon. The air temperature was more than 0,5 C warmer
during working hours than during the preceding and following night. The temperature log e
is contained in the appendix. It shows that although the air temperature falls quickly within
the first hour, all water temperatures start a new increasing phase that ends next morning in a
new stable situation. This is a consequence of the better thermal contact with the air after
removing the outside insulation.

Table 3: Temperature characterization after 80 hours observation. The latest 16 hours
         without mantle insulation. Temperature log A

 Temperature difference        Temp. gradient
         [mK]                     [mK/cm]
Ch-3 – Ch-4         107          7,1 vertical
Ch-7 – Ch-5          22          1,5 vertical        21,144
                                                              3   7 20,930   0   20,899

Ch-0 – Ch-1          -3         -0,7 vertical                                1   20,902

Ch-0 – Ch-2          -2         -0,2 vertical
Ch-5 – Ch-2          7         0,5 horizontal
Ch-4 – Ch-5         129        129 horizontal        21,037
                                                              4   5 20,908   2   20,901

Ch-7 – Ch-0          31        2,4 horizontal
Ch-3 – Ch-7         214        214 horizontal
Higher Ÿ lower temperature

The removal of the outer insulation reduces the temperature gap between the air and the
water to just below 1 °C. But at the same time the new established equilibrium looks dif-
ferently. The temperature difference between the outer and inner bath has grown and the
better thermal coupling to the warmer air has generated a larger vertical gradient 7,1 mK/cm
(point (3) to (4)) compared to 5,7 before. At the inside wall (point (7) to (5)) it has decreased
from 4,3 to 1,5 mK/cm. This must mean the heat exchange through the wall has increased
and produces now at steady state condition with a larger flow of warm water at the inside
wall in upwards direction. Looking to the vertical gradient in the centre shows now a change

from 0,6 to –0,2 (point (0) to (2)) and even stronger from 1,6 to –0,7 mK/cm (point (0) to
(1)). Thus point (1) is now the warmest in the centre. This trend is confirmed by the
horizontal gradient in the top that is reduced from 4,8 to 2,4 mK/cm (point (7) to (0)),
whereas not so much has changed at half height (point (5) to (2)) 0,6 to 0,5 mK/cm.

Interpreting these observation means that, in contrast to that one would expect as a stable
layered situation, the coldest water is now found in the top of the centre at point (0). This
situation is valid over one hour period (average). Looking into more time resolved intervals
one can find even point (1) being the coldest one during a sample over 40 minutes. In other
words table 3 above seems to described a mixing pattern, which might be interpreted to stem
from persisting driving convection currents, that do not involve the whole of the interesting
measurement volume in one toroid geometry, but might consist of minor eddies as indicated
in the picture above.

It also seems most probable that this situation is a superposition of an energy flow through
the outer bath, which has an increased driving temperature gradient towards the inner bath,
and a continuing energy loss to the air above, which must stem from permanent evaporation.

The sensor fluctuations in the most stable phase has also increased giving a standard de-
viation of 10, 5 and 3 mK for the measurement points (0), (1) and (2) respectively over a
period of 2 hours and 45 minutes. Correlation analysis shows a clearly positive covariance
with a coefficient of 0,72 between point (2) and (1), 0,65 between point (1) and (0), and 0,49
between point (2) and (0). This indicates that the measured fluctuations really are physical
effects of sinking colder water followed by a new mixing.

5.4          Undisturbed bath falling temperatures
The observations so far are based on the situation of rising temperatures suggesting a
variable convection pattern having predominantly a downward direction in the centre. The
next measurement phase was selected to be at Friday afternoon to Monday morning as this is
the most predictable phase for decreasing room temperatures. So it was not even measured.
Instead sensor 6 was inserted in a 45 ° position in order to reveal if the sensor casing could
induce the large fluctuations near the water surface. Sensor 3 was inserted in the inner bath.
Another change was to hang the empty object holder in its original place during the
temperature logging. The simple idea was to see if after taring the assumed varying
downward movement could be found as a corresponding signal from the balance, especially
compared to an initially equilibrium situation.

Unfortunately the measurements were stopped already Saturday afternoon with increasing
scanning interval due to problems with the computer.

Of the limited temperature change only two periods can be used for comparison, one with a
stable water temperature over 3,5 hours and one with a very linear, but small decrease over
2,7 hours. The whole situation is presented in the temperature log f in the appendix.

The observed temperature fall is only in the range of 0,02 °C, largest in point (4) and lowest
in point (0). Most of the gradients seem unchanged by this small change. However, as seen
from the vertical gradients in the centre it reaches deeper when temperature is generally
falling compared to a constant temperature situation. In a more than two-hour average point
(1) shows actually the lowest measured temperature. Eventually the introduction of the
holder interferes with a convection movement downwards, directing the flow out of the
centre thus leading to a comparably higher temperature in point (2) than in the earlier
situations described. The difference is not big, 3 mK in the first and 4 mK in the second
period with falling temperatures.

Table 4: Temperature characterization of two roughly three-hour periods with stable and
         decreasing temperature. Temperature log B.

                       Temperature gradient [mK/cm]
                        Stable tem-    Decreasing
                         perature      temperature                               21,015
                                                                   20,996   7 6           0   20,970
Ch-7 – Ch-5 vertical        0,5            0,5
                                                                        20,970   3        1   20,962
Ch-0 – Ch-1 vertical        1,4            1,4
Ch-0 – Ch-2 vertical        0,8            1,4
Ch-5 – Ch-2 horizontal      0,0            0,3            21,099    4       5 20,975      2   20,966

Ch-4 – Ch-5 horizontal      0,7            0,7
Ch-7 – Ch-0 horizontal      125            124
Ch-7 – Ch-6 horizontal      2,3            2,1
Ch-6 – Ch-0 horizontal     -18,9          -18,7
Ch-3 – Ch-1 horizontal      7,0            6,5
Higher Ÿ lower temperature

Looking at the balance signal over time one can observe a clear tendency of rising load. At a
first glance it seems correlated with the falling temperature in the bath. Assuming a balance
with no drift at all and disregarding convection there are two possible effects that could
change the balance indication with falling temperature. Increasing water density would
increase the buoyancy effect and thus show the opposite behaviour. Volume shrinking of the
holder on the other hand would lower the buoyancy. But both of these effects are far too
small to explain the behaviour of the actual balance signal. Moreover they would rather
cancel out each other.

Would this leave convection as a possible course? Not really, the changes are far too large
that they would not have been detected much earlier during density detereminations. What
one would expect is that the signal from a stable temperature situation with certainly varying
loads would go over to a possibly higher, but varying load at “constant” level during the
linear temperature fall. This is not the case. The behaviour is not easy to explain. Not even a
measurable evaporation induced water level decrease and a somewhat longer suspension
wire in air could possibly give such increasing loads. The same argument is valid for the
possible shrinking of the length of the suspension wire with falling air temperature. This
leaves drift as the most probable possibility. The open surface of course also collects dust of
various kind that easily can fasten at the suspension wire and change the meniscus in the
water/air interface.

A repeated measurement under undisturbed night hours did not give any more reasonable
data. The temperature log g is shown in the appendix. However the obvious spread in the
balance signal was analysed for correlation with the fluctuations in the temperature signals
(at point (0), (1) and (2)). Generally a negative correlation with correlation coefficients
between –0,03 and –0,53 for various randomly selected time intervals of roughly one hour
was observed. Looking for correlation the results of several separate periods were combined
showing values of –0,62, –0,74 and –0,84 (shown below) between sensor 1, 2 and 3
respectively with the balance signal, which indicates that the balance signal generally is
influenced by temperature changes in the measurement volume. It also means that colder
water is related with higher loads whereas warmer water leads to lower load values. This
gives reason to believe that there is a common physical explanation for both fluctuations,
which could be caused by evaporation and induced convection.

            For controlling reasons also the covariance between the temperature signals from sensor 1, 2
            and 3 were checked for several one-hour periods. Here even stronger correlation effects were
            found, this time with positive coefficients +0,81, +0,78 and +0,90 (shown below) between
            sensor signals 0 and 1, 0 and 2 and 1 and 2 respectively. This is interpreted as being the same
            cold-water stream to influence all of the sensors.

            The correlation diagrams below are constructed by overlaying five single series and not just
            taken over a longer period. The reason was to avoid false influences due to the assumed
            balance drift at decreasing temperatures mentioned above. By this accumulation a weak
            correlation valid for a short period can be confirmed as exemplified in figure 3.

                                 Correlation over 5 different time intervals                                                       Correlation over 5 different different time intervals
                   0.0020                                                                                                  0.04

                                                                                                                                               y = 0.00070686 + 0.75353x R= 0.90259
                   0.0015                                                                                                  0.03

                   0.0010                                                                                                  0.02

                                                                                                Sensor 2 variations [°C]
                   0.0005                                                                                                  0.01
Balance load [g]

                   0.0000                                                                                                  0.00

                   -0.0005                                                                                                 -0.01

                   -0.0010                                                                                                 -0.02

                   -0.0015           y = 0.00012739 - 0.044462x R= 0.84953                                                 -0.03

                   -0.0020                                                                                                 -0.04
                         -0.03    -0.02     -0.01        0          0.01     0.02   0.03                                       -0.04   -0.03   -0.02     -0.01     0       0.01   0.02   0.03   0.04

                                                    Sensor 2 [°C]                                                                                      Sensor 1 variations [°C]

            Figure 3: Two correlation plots combining five separate one- hour intervals each showing
                      positive covariance between two temperature measurements and negative
                      covariance between balance load and in this case temperature changes in
                      measurement point (2).

            5.5                    Non-insulated forced cooled bath
            Instead of waiting for a room temperature drop producing falling bath temperatures the
            external control bath was used to cool the outer and in turn the inner bath. After a stable
            period with bath temperatures around 21,07 °C and declining values the control was
            switched on and sensor 3 removed to follow the control bath temperature, which nominally
            was 20,5-°C but after 2,3 hours reached a stable value at 20,45 °C. The outer bath stabilized
            after 6 hours and the temperature in the centre after more than 9 hours. The average
            temperature drop is 0,45 °C with the smallest drop at point (0).

            Temperature log 4 reveals that the outer bath forced to lower temperature after roughly two
            hours again has a higher temperature than the inner bath (see templog 4a). The gap however
            has reduced from 0,12 to 0,09 °C, showing that the energy loss from the inner bath by
            evaporation must have reduced, which seems reasonable. The fluctuations markedly have
            reduced as well.

            Table 5: Temperature situation before and after start of temperature control. The belong-
                     ing temperature log h is contained in the appendix.

Channel     No temperature   Active temperature
                control            control
          Temperature Stdav Temperature Stdav
             [°C]       [mK]    [°C]       [mK]                                         20,899

Ch-0        21,081       19    20,649        1                                      7 6
                                                                                  20,656 20,639
                                                                                                  0   20,649

Ch-1        21,072       14    20,628        2                                                    1

Ch-2        21,072       10    20,616        2                       20,724
Ch-3        21,079        8    20,440       15
                                                                              4    5              2   20,616
                                                          20,440 3

Ch-4        21,203        9    20,724        1
Ch-5        21,087        9    20,644        1
Ch-6        21,081       16    20,639        3
Ch-7        21,106        8   20,6563        1

Temperature             Difference Gradient            Difference Gradient
                         [mK]      mK/cm]              [mK]       mK/cm]
Ch-7 – Ch-5 vertical       19        1,3                 12         0,8
Ch-0 – Ch-1 vertical        9        1,8                 21         4,2
Ch-0 – Ch-2 vertical        9        0,6                 33         2,2
Ch-5 – Ch-2 horizontal     15        1,1                 28         2,1
Ch-4 – Ch-5 horizontal    116       116                 80         80,3
Ch-7 – Ch-0 horizontal     25        1,9                 7          0,6
Ch-7 – Ch-6 horizontal     25        3,5                 17         2,4
Ch-6 – Ch-0 horizontal      0         0                 -10        -1,4
Higher Ÿ lower temperature

Looking to the data in table 5 the two situation exhibit clear differences. There is a much
more distinct layering in the controlled bath with considerable less fluctuation compared to
the situation before starting control. The bigger vertical gradient in the controlled case with a
higher temperature in point (6) than in point (0) indicates a stronger convection despite less
evaporation, which the lower fluctuation also seems to tell. A detailed temperature picture of
these two situations is given in the temperature log ha and hb in the appendix.

During the actual temperature change the gradients look different. All temperatures are much
closer to each other with the warmest temperature at point (0) and point (5) as the coldest
one, which might indicate a reversed flow pattern with colder water sinking down at the
wall, eventually pushing water up in he centre. But from the moment the outer bath is not
any longer colder than the inner one the final layering is established with pronounced
weight. A fist conclusion to draw might therefore be that upstream convection in the centre
seams rare and is mainly connected with reversed temperature conditions between inner and
outer bath.

5.6           Effect of insulation to prevent evaporation
With persisting control of the outer bath at 20,5 °C a thick insulation was put on top of the
inner bath as well. This experiment should demonstrate the effect of drastically reduced
energy loss by evaporation. The corresponding temperature log 5 below shows the situation.

                                                                                                         Ch 0
           put thick insulation
           on top of the inner                                    Balance
                                        mät02okt22_23                                                    Ch 1
   21.00                                                                              0.0015             Ch 2

                                                                                                         Ch 3
   20.90                                                                                                 Ch 4

                                                                                      0.0005             Ch 5

   20.80                                                                                                 Ch 6
                                                                                                         Ch 7

   20.70                                                                              -0.0005




   20.40                                                                              -0.0025

                                                                                switch of temperature
                                                                                control - put sensor 3
                                                                                from control bath to
                                                                                top of outer bath

Figure 4: The temperature curves show the effect of insulating the water/air interface.
The reduced energy loss at continuing cooling leads to marked temperature increase.

Table 6: Change of temperature equilibrium due to insulation on top. The graphical
         situation is shown in the temperature log i below.

Channel           no insulation at insulation at top
                 top (cooling on)    (cooling on)
               temperature stdav temperature stdav
                    [°C]      [mK]   [°C]       [mK]
                                                                      7 6   0
Ch-0                 20,657 2          20,973 3
Ch-1                 20,634 2          20,854 2                             1

Ch-2                 20,621 1          20,778 2
Ch-3                 20,447 15         20,453 12            3     4   5

Ch-4                 20,732 1          20,800 2
Ch-5                 20,649 2          20,781 2
Ch-6                 20,645 2          20,936 3
Ch-7                 20,662 1          20,920 2

Temperature                 Difference Gradient         Difference Gradient
                              [mK]         mK/cm]       [mK]         mK/cm]
Ch-7 – Ch-5 vertical             13           0,9        139            9,3
Ch-0 – Ch-1 vertical             23           4,7        119           23,8
Ch-0 – Ch-2 vertical             36           2,4        195           13,0
Ch-5 – Ch-2 horizontal           28           2,1          3            0,2
Ch-4 – Ch-5 horizontal           82           82          20           19,5
Ch-7 – Ch-0 horizontal            5           0,4        -53           -4,1
Ch-7 – Ch-6 horizontal           17           2,5        -16           -2,4
Ch-6 – Ch-0 horizontal          -12          -1,7        -37           -5,3
Higher Ÿ lower temperature
From the moment the insulation is in place (the logging was not stopped) all temperatures
rise. The effect is strongest in point (0), which also has the shortest time constant. The others

are following in the expected order point (6), point (7), i.e. at the top layer where point (7) is
slowed down by the continuously cooled outer bath, that is also slowly rising. At last follow
the points (5) and (2). For the first time we have now a situation where most of the
temperatures in the inner bath are higher than in the outer bath. The temperature rise
indicates the amount of energy loss which, due to the new insulation, is strongly reduced.

Looking to the data collected in table 6 all vertical gradients increase drastically and all
horizontal ones decay or change in opposite direction. This would suggest that the con-
vection flow permanently is inverted giving rise for cooler water to sink along the walls and
warm water to be pressed up in the centre. The balance signal seems to reflect the
temperature behaviour, which might be explained by an upward force. And it is also correct
that this force should lower the load quickly when temperature changes suddenly. However,
as soon as a new equilibrium is establishing the convection should cut down and the lifting
force should decay, which is not seen in the above plot.

Compared to earlier measurements it is striking that the fluctuation in the temperature signal,
especially at point (0) and (1) is lacking. This is most probably a separate confirmation that
the earlier spread is caused by evaporation. The balance signal as well is lacking its
pronounced variation. This is indirectly a confirmation of the correlation between balance
variation and temperature fluctuation in the measurement volume.

5.7          Insulation on top and no cooling
With lacking energy loss to the air on top the pronounced layering is kept due to the driving
force of the cooled outer bath. Switching of the forced cooling would mean that a new
temperatures distribution will take place. And that is what happens and it is documented in
temperature log j in the appendix.

Table 7: Temperature pattern after switching of cooling and afternoon and night for
         stabilization . Ttemperature log j.

    Temperature difference and gradient
                         [mK] [mK/cm]
Ch-3 – Ch-4 vertical       41         2,7
Ch-7 – Ch-5 vertical       45         3,0
Ch-0 – Ch-1 vertical       17         3,4              21,374         7 6           0   21,378
Ch-0 – Ch-2 vertical       54         3,6                           21,373 21,374
Ch-5 – Ch-2 horizontal      3         0,2
Ch-4 – Ch-5 horizontal      6         5,6
Ch-7 – Ch-0 horizontal     -5        -0,4              20,724
                                                                4    5              2   21,324

Ch-7 – Ch-6 horizontal     -1        -0,1
Ch-6 – Ch-0 horizontal     -5        -0,7
Ch-3 – Ch-7 horizontal      1         0,7
Higher Ÿ lower temperature

All temperatures rise quickly to a new state producing meanwhile even somewhat larger
gradients. With sensor 3 back in the top of the outer bath it can be seen that there is the
warmest spot as the energy is taken up from the air through the wall. After point (3) point (0)
and (7) mark the warmest areas with point (6) very close. Even point (4) is warmer than
points (5) and (2), which suggest that the inner water is heated at the walls to the outer bath
producing even larger vertical gradients during some hours. Then equalisation takes place

and all points strive to smaller gradients. This is due to lacking decreasing energy input with
falling air temperature during night hours.

Even though much of the balance signal is difficult to analyse in detail the temperature log
j shows a marked shift in the falling trend to a positive load change the moment the cooling
is switched off and thus the cooling inner wall changes to a heating wall. This must be taken
as a confirmation that a changing convection pattern influences the weighing.

The drastically smaller vertical gradients in the new equilibrium indicate that there is a much
lower driving force for convection. This is true for the horizontal gradients as well. The
small gradients probably tend to small movements, which mostly produce small mixing
eddies and no larger convection patterns. Generally the above situation seems to be a more
favourable one for density determinations. That point (0) shows lower temperature than
point (6) or (7) is probably due to the fact that there is still small evaporation within the
acrylic pipe that is not insulated.

5.8          Insulation on top and heating to room temperature
So far the heat transport through the outer bath in connection with the existence/absence of
energy loss to the air has been the driving forces characterising the temperature and thus a
variable convection pattern. The most stable and thus convection free situation is considered
to have no losses and no supply of energy to the system. This could possibly be achieved by
heating the outer bath to a temperature equivalent to the varying air temperature.
Unfortunately this control is difficult to achieve without more sophisticated controlling
devices, but a rough trial should show if this idea would hold.

After some hours of rather stable conditions the external control bath was turned on striving
to the momentary air temperature. However none of the sensors was used to follow either air
or control bath temperature.

Figure 5 displays the heating from one stable to a new stable situation. Firstly the differences
between all temperatures increase starting mixing convection. After ten hours, however, all
gradients seem reduced and a more homogeneous temperature pattern established. To
achieve this situation the driving gradients must first increase and then decay. The result at
the end of this phase is collected in table 8.

Again the balance signal reacts momentary on the temperature change, but the effect is short.
Also at the point of largest gradients, with probably largest convection there is fast balance
signal decay. The expected reaction is however an increase.

                                                                                           Temperature control to air temperature
                     22.1                                                                                                                                                                                                            0.0010
                                               Ch 0                    Ch 2                 Ch 4                Ch 6                                                                                Balance
                                               Ch 1                    Ch 3                 Ch 5                Ch 7

                     21.9                                                                                                                                                                                                            0.0005

                                                                                                                          10,4 hours
 water temperature

                                                                                                                                                                  7 6         0

                     21.7                                                                                                                                                     1                                                      0.0000

                                                                                                                                                          4       5       2


                     21.5                                                                                                                                                                                                            -0.0005


                                                                                     Switching on control bath to 21,7 °C                                                                                   Templog 9

                     21.3                                                                                                                                                                                                            -0.0010










Figure 5:The temperature log 7 showing the effect of heating the outer bath to the same
         temperature as the surrounding air.
Table 8: Temperature pattern before and after switching on heating to keep the outer bath
         at room temperature. Temperature log 7
Channel                                    No temperature   Active heating to
                                               control      room temperature
                                         temperature stdav temperature stdav
                                             [°C]      [mK]    [°C]     [mK]
Ch-0                                        21,398      0,5     21,958 0,9                                                                                            3
                                                                                                                                                                          7 6              0

Ch-1                                        21,378      1,1     21,951 0,8                                                                                                                 1

Ch-2                                        21,350      1,3     21,943 0,9
Ch-3                                        21,398      1,4     21,968 0,7                                                                                            4   5                2

Ch-4                                        21,361      0,4     21,954 0,8
Ch-5                                        21,352      1,4     21,945 1,3
Ch-6                                        21,392      0,4     21,958 0,8
Ch-7                                        21,394      0,5     21,963 0,7

Temperature             Difference Gradient                                                                                                 Difference Gradient
                         [mK]      mK/cm]                                                                                                   [mK]       mK/cm]
Ch-3 – Ch-4 vertical       37        2,4                                                                                                     14          1,0
Ch-7 – Ch-5 vertical       41        2,8                                                                                                     18         1,2
Ch-0 – Ch-1 vertical       20        4,0                                                                                                      8         1,5
Ch-0 – Ch-2 vertical       48        3,2                                                                                                     15         1,0
Ch-5 – Ch-2 horizontal      2        0,2                                                                                                      1         0,1
Ch-4 – Ch-5 horizontal      9        9,0                                                                                                      9         9,0
Ch-7 – Ch-0 horizontal     -4       -0,3                                                                                                      5         0,4
Ch-7 – Ch-6 horizontal      1        0,2                                                                                                      6         0,8
Ch-6 – Ch-0 horizontal     -5       -0,8                                                                                                     -1         -0,1
Ch-3 – Ch-7 vertical        4        4,3                                                                                                      5          4,9
Higher Ÿ lower temperature

The information in table 8 compares the start and end conditions. It combines low fluc-
tuation with the smallest over-all gradients of all discussed experimental situations. The
temperature range has reduced to half of the start situation from 48 mK to 25 mK. The
vertical gradient in the centre is now lowered to one third. This should mean that convection
also is reduced and possibly only encircle smaller eddies.

This control mode should thus give the best possible conditions for density determination in
non-surrounding insulation applications. Additional experiments using mantle insulation and
heating of the outer bath to existing room temperature did not lead to lower overall gradients
as shown in temperature log 11 in the appendix. The actual measurement, that was aimed to
demonstrate a long-term stability under control, was unfortunately disturbed due to the fact
that the room temperature control was adjusted two times during the logging period. This
was done without notice and first understood after analysis of the measurement data.

As a summary of the various conditions one can state that the most stable weighing con-
ditions are those using insulation both on top and around the outer bath and using external
temperature control. Most likely the expectable convection error reduction leads generally to
a lower uncertainty when working at elevated temperature level. The uncertainty con-
tribution connected with a density correction to standard 20 °C conditions is doubtless of
lower importance.

6            Conclusions
The observation of the temperature behaviour in several points in the bath under various
conditions seem to reveal an important result, namely that even small temperature differ-
ences can drive convection. Under ordinary density measurements with no insulation on top
the energy loss, inherently connected with evaporation, is the major source for vertical
temperature differences, which can start convection. There is a quite significant coupling
between the varying temperatures at different heights in the bath on one hand and the
varying balance signal on the other hand. Thus we can assume that evaporation, even under
perfect stable outer temperature conditions, can add a small convection force onto the holder.
Just because of permanent fluctuations in case of no insulation on top the convection is also
varying all the time. In consequence this means that it is possible that the two weighing
situations in the hydrostatic technique might be influenced randomly with different strength.

The experiments have also shown that only in one situation, namely when the outer bath is
kept in forced cooling, that the expected convection is directed downwards at the wall and
upwards in the centre. This is very unlike all actual measurement conditions experienced so
far, when the water is expected to warm up striving upwards at the walls and downwards in
the centre. We therefore always can count on an additive force to the load on the balance.

If this overlaying force results in the same extra load for both situations A and B of the
repeated ABBA weighing scheme then this will not affect the density measurement.
Moreover small variations in the extra load may average out over the measurement series. If
on the other hand convection induced forces are not neutral to the two weighing situations A
and B shown in figure 6 below the density determination will suffer from an error. The sign
of this error is not self-evident. It may lead to higher and lower density values compared to
the ideal situation with no convection at all. Thus natural convection could explain the
slightly higher density values for SP found in an inter-comparison with Finland.

In which direction the overlaying force will act is not only dependent on the size and
direction of the convection flow. The design of the holder and the measurement object

certainly will influence the situation. Depending of its relative size an object in step A could
lead the downward flow as shown in figure 6 aside, producing a lower load in weighing step
A as in step B when TB is weighed in the holder. In this case the resulting density would be
lower. But the opposite can happen as well if the flow pattern does look different.

Thinking of the shaded objects being weighed in the same holder may lead to differences in
the convection induced effects, tht are clearly seen but not necessarily understood.



                        A                                       B


                    Lifting                                         Lifting

                   Cylinder                                       Cylinder

                                       Measurement bath

Figure 6:   The two weighing steps A left and B right making up a ABBA weighing scheme
            for density determination. In the case of the small cylinder TB a situation is
            assumed giving a higher convection load in B than in A resulting in a higher
            density. The shaded objects indicate that the relation between object and holder
            might lead to different reaction on the density.

This study is of course only a qualitative one in that sense as the temperature data are used to
reveal the possible causes and direction but not the size of the currents in terms of flow
speed etc. and the additional force in gram equivalents. Anyhow, in comparison to the
situation before starting this project convection was not even mentioned as a problem.
Temperature homogeneity was more important under the aspect of accurate knowledge of
the density of water that is the most important source of uncertainty. Thus the existence of
convection is directly linked to water as a traceable density standard at this accuracy level.

The major design idea in the density measurement shown above is to compare two weighing
situations aiming at eliminating the meniscus effect around the suspension wire. With a
holder suitably well shaped for the object in question also unexpected convection might to a
large extend be neutralized. In many designs, especially when liquid density is measured, no
comparison is performed. Instead a solid density standard is directly fixed to the suspension
wire. Given an overlaying convection force in downward direction a systematic error will
always produce too low density values for the liquid in question.

The experiments mentioned in this report allow improving the measurement situation in
order to produce lower uncertainties. Insulation on top is beneficial in two respects. It
reduces evaporation-induced convection and as a consequence it reduces variation in the
temperature and the balance signal. Insulation on the outside, although not very practical,
helps to reduce horizontal gradients and keeps the bath more stable on a one-hour basis.

Given convection never can be totally avoided the holder design should be changed to
minimize its effect thus not risking its neutrality in the hydrostatic weighing technique. This
is most definitely important when low uncertainty is important as in determining the liquid
density (especially of water) with artefacts working as solid density standards.

The experience gained by this study can qualitatively explain the variability of measurement
results produced on the same object and the holder in question at different points in time and
under what was assumed constant conditions, which is a satisfying statement. Nevertheless it
would be of interest to study convection by means of mathematical modelling. With the
experimental data of this study one would have good material to vary the border conditions.
One benefit would be to predict the numerical effect on the weighing. Especially the
modelling of the relation between the holder and the object could be very beneficial to
optimise the design of holders.

But other metrological benefits could be expected as well. The situation in the mentioned
bath is a very stable one compared to large volume standards used in volume and flow
calibration. The uncertainty in temperature measurement is mostly one of the biggest
contributions in these metrological fields and an understanding of convection is beneficial to
find representative spots for temperature measurement.

The situation is quite analogue in large standing cylinders of tenth of meters in diameter at
refineries that are used for metrological measurements. Despite the large temperature shift in
the outdoor environment the contained liquid volume is often determined using only one
thermometer in the bottom. As evaporation is prevented the model also could be applied in
those situations leading to better temperature and in turn more accurate liquid volume

7            References
[1] Lau P. Study of traceability to the density of water. Interim Report to Nordtest,
    NORDTEST PROJECT 1543-01, SP Technical Notes : 2001:43
[2] Gläser M. Change of the apparent mass of weights arising from temperature differences.
    Metrologia; 1999, 36 no 3, 183-197
[3] Gläser M., Do J.Y. Effect of Free Convection on the Apparent Mass of 1 kg Mass
    Standards. Metrologia, 1993, 30, n°2, 67-73
[4] Gläser M. Response of Apparent Mass to Thermal Gradients. Metrologia, 1990, 27, n°2,
[5] Rosby P. Temperaturgradienters inverkan vid viktkalibrering. 30 s. SP AR 1994:14
[6] Källgren H, Lau P., Myklebust T, Nielsen L., Riski K. Testing of weights OIML
    Bulletin Volume XXXVIII, Number 2. Part 3 - Magnetism and convection (Oct. –97)
Appendix: Temperature logs 1 to 11

  Short descriptions of the different temperature measurements

  All diagrams have a time scale specifying a day from start (0:) and the real time (10:05:37), which
  indicates the end of the temperature scan in order to distinguish between working and night hours.

  Temperature log 1:
  Bath insulated on outside (mantle) but not on top (except for outer bath that is always insulated).
  Sensor 6 measures first water and then air temperature. Relative stable temperature relation
  between measurement points when no direct control is applied. Increasing air temperature leads to
  increasing water temperatures. No indication for changing gradients and thus forced mixing.

  Temperature log 2:
  Bath insulated on outside but not on top. Sensor 6 measures air temperature, which shows short-
  term fluctuations in the range of 0,05 °C and a total range of 0,2 °C over a 24 hour period. The
  water temperature increase is still an adjustment to the higher air temperature.
  The temperature in the outer bath (sensor 3 and 4) is clearly higher than in the inner one. Highest
  temperature (sensor 7) at the surface close the inside wall. Clearly observable fluctuations at the
  surface (sensor 0).

  Temperature log 3:
  Rapid air temperature fall (0,4 °C) at the end of the working day. Slow decrease (0,1 °C) during
  night hours. Increasing water temperature due to removal of mantle insulation around outer bath
  and thus better thermal coupling to surrounding air. Outer bath temperature 0,1 to 0,2 °C higher
  than inner bath.

  Temperature log 4:
  Clearly observable fluctuations (sensor 0 and 1) as well as balance signal. Sensor 6 in water just
  below surface under 45 ° angle seems not to “see” the same amount of fluctuation. Might indicate
  that fluctuation is strongest closest to surface. Drifting balance signal, but not related to decreasing
  water temperature.

  Temperature log 5:
  Unexpected temperature increase in both outer and inner bath, probably due to increasing air tem-
  perature that was not measured here, but constant temperature gap 0,2 °C between inner and outer
  bath. Remarkable fluctuation. Relative stable balance signal. Suspected correlation between
  balance- and temperature signal.

  Temperature log 6:
  Cooling of outer non-insulated bath after an undisturbed phase of 5 hours. Sensor 3 taken from the
  outer bath and transferred to the separate control bath, which was set to 20,5 °C. The control tem-
  perature establishes after 1,5 hours at 20,44 °C. For approximately the same time the outer bath
  (Ch 4) gets colder than the inner one. Then after en intensive mixing phase the cooled inner bath
  gets colder than the outer one (-0,035 °C). Due to forced cooling the fluctuations have mainly dis-
  appeared. But this also means permanent convection within the bath.

  Temperature log 7:
  The inner bath is insulated at top, which lowers the energy loss. This leads at continued cooling to
  a slowly increase of the inner bath. All fluctuation is disappeared. The inner bath is actually per-
  manently warmer then the outer one (Ch 4). Water in the inner bath is cooled and a large vertical
  gradient is generated with warmest water at the top.

  Temperature log 8:
  With insulation on top of the inner bath the cooling is stopped. Sensor 3 is introduced into the
  outer bath again. All temperatures rise driven by the higher (but not logged) air temperature. In a
  new equilibrium all temperature differences tend to minimize. Still the inner bath is warmer than

Appendix: Temperature logs 1 to 11

  the outer one although the energy transport is through the outer bath. When the temperature in-
  crease starts the balance signal is clearly affected. The regions marked by arrows are compared.

  Temperature log 9:
  The situation exhibiting smallest temperature differences is expected to be the one where the outer
  bath is controlled to the same temperature as the surrounding air with minimized energy loss via
  evaporation. The outer bath (CH 3 and 4) reacts fastest to the control temperature 21,7 °C and it is
  always the warmer one. Actually the lowest gradients seem to be reached that way.

  Temperature log 10:
  Switching off the heating (inner bath insulated on top, no mantle insulation) leads immediately to
  a mixing situation followed by a slow decrease 0,75 °C during more than 48 hours. All gradients
  get smaller during the stabilization to new equilibrium.

  Temperature log 11:
  In order to reshape the smallest gradients the bath, insulated on top and around the mantle, was
  controlled to existing room temperature using the external control bath and the heating coils in the
  outer bath. However, without notice the air temperature in the laboratory was adjusted two times
  (22,2 °C and 22,8 °C) by the management. Thus the enlarged gradient to the surrounding air in-
  creased the water temperature two times as well, leading to larger gradients in the water too. Any-
  how the start conditions indicate that the assumption is correct.

  The density measurement bath with insulation and definition of the various temperature sensor po-

                                               130 mm
                                            70 mm
                                                                 Acrylic glass pipe

                                                                     Suspension wire

                                                                      top insulation inner bath

                    30 mm
                                            7    6      0
                            80 mm


                               180 mm

                                                                                                      420 mm
                                                                                             375 mm

                                        4   5           2

     Control bath

       mantle insulation
                                                            290 mm
                                                            370 mm

                           Appendix: Temperature logs 1 to 11
                                                                                                                                      Temperature log 1 - undisturbed bath after preparation
                                                3         720,385
                                                                6( )               0   20,331
                                                                                                                                  21,636                                                                                                              Ch    0
                                                                                                                                                                                                                                                      Ch    1
                                                                                   1   20,324
                                                                                                                                                                                                                                                      Ch    2
                        20.80                                                                                                                                                                                                                         Ch    3
                                                                                                                                                                                                                                                      Ch    4
                                                            520,323                2                                                                                                                                                                  Ch    5
                                                4                                       20,316
                                                                                                                                                                                                                                                      Ch    6
Air/Water temperature

                                                                                                                                                                                                                                                      Ch    7
                        20.20                                                                                                                                                                                                                         40 min
                                           Templog1                                                                                       Sensor 6 removed from bath to monitor air temperature















                           Appendix: Temperature logs 1 to 11
                                             Temperature log2 - Undisturbed bath - increasing temperature during working hours
                                                                                                  Ch 0                      Ch 3                Ch 7                                     Ch 6 air
                                                                                                  Ch 1                      Ch 4                                                                                            22.4
                                                                                                  Ch 2                      Ch 5
Water temperature (C)


                                                                                                                                                                                                                                   Air temperature (C)
                                                                                                                                                                      stable                                                21.6
                                                                                                                                                                    conditions                     templog 2












                                       Appendix: Temperature logs 1 to 11
                                                                                      Temperature log 3 - Removed mantle insulation
                                                                                                                                                                                                                                                         Ch 0                        Ch 4
                                                                                                                                                                                                                                                         Ch 1                        Ch 5
                                                                                                                                           7 20,930            0   20,899                                    6                                           Ch 2                        Ch 6
                                                                                                                          3                                                                              21,981
                                                                                                                                                                                                                                                         Ch 3                        Ch 7
                                                                                                                                                               1   20,902
                                                                                                             21,037                                            2
                                                                                                                          4            5 20,908
Air / water temperature [°C]

                                            Removal of
                                            mantle insulation
                                                                                                                                                                                                                                                                       one hour
                               20.50        2:16:00:00                                                                                                                                                                                                                    Templog3
















                                 Appendix: Temperature logs 1 to 11
                                   Temperature log 4 - Time series friday afternoon to saturday afternoon - no laboratory activity
                         21.30                                                                                                                                                       0.0015
                                                                                 y = -0.01106 + 3.1092e-08x R= 0.90454
                         21.25                  Ch 0                Ch 3                      Ch 6                                                                                   0.0010
                                                Ch 1                Ch 4                      Ch 7
                                                Ch 2                Ch 5                                                                                          Balance
Water temperature [°C]


                                                                                                                                                                                               Balance [g]
                                                                                                                          3-hour                                                     -0.0005
                                                                                                                  falling temperature
                                                                                                                                               Ch-6 tilted to 45 angle
                                                  stable interval                                                                                                Templog4
                         20.90                                                                                                                                                       -0.0020







                            Appendix: Temperature logs 1 to 11
                                                    Temperature log 5 - Undisturbed temperature drift over night
Water temperature (C)

                                                                                                                                                              Balance signal (g)
                                                                                                  Ch 0                Ch 3                 Ch 6
                                                                                                  Ch 1                Ch 4                 Ch 7     -0.0040
                                                                                                  Ch 2                Ch 5






                           Appendix: Temperature logs 1 to 11
                                                                                          Temperature log 6 - Starting forced cooling
                                                                                                                                                                                                                                         Ch 0
                        21.20                                                                                                                                                                                                            Ch 1
                                                                                                        Starting the control of                                                                                                          Ch 2
                                                                                                        the outer bath to 20,5 C
                                                                                                                                                                                                                                         Ch 3
                        21.10                                                                                                                                                                                                            Ch 4
                                                                                                                                                                                                                                         Ch 5
                                                                                                                                                                                                                                         Ch 6
                                                                                                                                                                                                                                         Ch 7
Water temperature (C)

                                                4-hour                                                                                                                                    4-hour
                                                period                                                                                                                                    period
                        20.40   Switch Ch-3 to separate
                                temperature control bath
















                                Appendix: Temperature logs 1 to 11
                                 put thick insulation
                                 on top of the inner                           Temperature log 7 - Insulation on top of bath at forced cooling
                        21.00                                                                                                                                                                                                                                                             0.0015
                                                                      Ch 0                               Ch 3                         Ch 6
                                                                      Ch 1                               Ch 4                         Ch 7
                                                                      Ch 2                               Ch 5
Water temperature (C)


                                                                                                                                                                                                                                                                                                    Balance (g)
                        20.70                                                                                                                                                                                                                                                             -0.0005
                                                                                                                                                                                                                                  insert sensor 3
                                                                                                                                                                                                                                  from control bath
                                                                                                                                                                                                                                  to outer bath
                                      templog 7
                        20.40                                                                                                                                                                                                                                                             -0.0025
                                        6 08:03:55

















                                                                                                                                                                                                                                                                                      switch of
                                Appendix: Temperature logs 1 to 11
                                                                                                         Temperature log 8 - After switching off cooling
                        21.40                                                                                                                                                                                                                                                                               0.0015
Water temperature (C)

                        20.90                                                                                                                                                                                                                                                                               -0.0005

                                                                                                                                                                                                                                                                                                                      Balance (g)
                                                                                                                                                                                                                                                                                     Ch 0
                                                                                                                                                                                                                                                                                     Ch 1
                                                                                                                                                                                                                                                                                     Ch 2                   -0.0010
                                                                                                                                                                                                                                                                                     Ch 3
                                                                                                                                                                                                                                                                                     Ch 4
                        20.60                                                                                                                                                                                                                                                        Ch 5
                                                                                                                                                                                                                                                                                     Ch 6
                        20.50                                                                                                     Inserting sensor 3 to the outer bath                                                                                                               Ch 7
                                                                                                                                 Switching off cooling
                        20.40                                                                                                                                                                                                                                                                               -0.0025

















                               Appendix: Temperature logs 1 to 11
                                                                               Temperature log 9 - Control to air temperature
                        22.1                                                                                                                                                                                                        0.0010
                                                Ch 0                    Ch 2                 Ch 4                Ch 6                                                                             Balance
                                                Ch 1                    Ch 3                 Ch 5                Ch 7
                        21.9                                                                                                                                                                                                        0.0005
                                                                                                                               10,4 hours
Water temperature (C)

                                                                                                                                                                      7 6   0

                                                                                                                                                                                                                                              Balance (g)
                        21.7                                                                                                                                                1                                                       0.0000
                                                                                                                                                                  4   5     2
                        21.5                                                                                                                                                                                                        -0.0005
                                                                                                                                                                                                          Tem plog 9
                                                                                       Switching on control bath to 21,7 °C
                        21.3                                                                                                                                                                                                        -0.0010










                            Appendix: Temperature logs 1 to 11
                                                             Temperature log 10 - Temperature decrease after switching off heating
                                                                                                                                                                     Ch    0
                        21.90                                                                                                                                        Ch    1
                                                                                                                                                                     Ch    2
                                                                                                                                                                     Ch    3
                        21.80                                                                                                                                        Ch    4
                                                                                                                                                                     Ch    5
                                                                                                                                                                     Ch    6
                        21.70                                                                                                                                        Ch    7
Water temperature (C)










                               Appendix: Temperature logs 1 to 11
                                    Temperature log 11 - Insulated outer bath - heated to previous measured room temperature
                            23.00                                                                                                                                                                                            1200
                            22.50                                                                                                                                                                                            1150
                                                                                                                                           Ch 0                         Ch 3                             Ch 6
                                      first adjustment of
                                                                                                                                           Ch 1                         Ch 4                             Ch 7
Water/air temperature (C)

                                      air temperature control
                                                                                                                                           Ch 2                         Ch 5

                                                                     second adjustment of
                                                                     air temperature control
                                                       Start heating insulated outer bath
                                                       to existing air temperature                                                                                                                                           1000











                                                                     Appendix: Temperature logs 1 to 11
                                 20.97                                                                                                                                                                                                                                                                                                                                                     Temperature log 41 - stable equilibrium                                                                                                                                                                                                   Temperature log 42 - starting falling
                                                                                                                                                                                                                                                       Templog31                                                                                                21.15                                                                                                                                                                                                  21.15
                                 20.96                                              Ch 0                                                  Ch 4
                                                                                    Ch 1                                                  Ch 5
                                 20.95                                              Ch 2                                                  Ch 6
                                                                                    Ch 3                                                  Ch 7
                                                                                                                                                                                                                                                                                                                                                                21.10                                              Ch 0                               Ch 4                                                                                                             21.10                                                                                    Ch 0                                                            Ch 4
                                 20.94                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Ch 1                                                            Ch 5
Water temperature [°C]

                                                                                                                                                                                                                                                                                                                                                                                                                   Ch 1                               Ch 5
                                                                                                                                                                                                                                                                                                                                                                                                                   Ch 2                               Ch 6                                                                                                                                                                                                      Ch 2                                                            Ch 6
                                 20.93                                                                                                                                                                                                                                                                                                                                                                             Ch 3                               Ch 7                                                                                                                                                                                                      Ch 3                                                            Ch 7

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Water temperature (C)
                                                                                                                                                                                                                                                                                                                                        Water temperature (C)

                                                                                                                                                                                                                                                                                                                                                                21.05                                                                                                                                                                                                  21.05
                                                                                                                                                                                                                                                                                                                                                                21.00                                                                                                                                                                                                  21.00
                                                                                                                                                                                                                                                                                                                                                                20.95                                                                                                                                                                                                  20.95
                                 20.88                                                                                                                                                                                               one hour
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            templog 42

















                                                                                                                                                                                                                                                                                                                                                                                                                                                                           templog 41
                                                                                                                                                                                                                                                                                                                                                                20.90                                                                                                                                                                                                  20.90










Largest fluctuation in the top of the bath.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Temperature log 61 - Before starting forced cooling
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Ch 0
                                                                              Temperature 51 - Correlation in fluctuation                                                                                                                                                                                                                                                                Temperature 51 - Correlation in fluctuation                                                                                                                                                                                                                                                                                                                                                                                 Ch 1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               21.12                                                                                                                                                                                                                                                                 Ch 2
                                 21.02                                                                                                                                                                                                               0.0020                                                                             21.02                                                                                                                                        0.0020
                                         Templog 51                                                                                                                                                                                                                                                                                                               Templog 51                                                                                                                                                                                                                                                                                                                                                                                                                                         Ch 3
                                                                                                          Ch 0                          Ch 1                         Ch 2                                             Balance                                                                                                                                                                               Ch 0             Ch 1       Ch 2                       Balance                                                                                                                                                                                                                                                                                                                                           Ch 4
                                                                                                                                                                                                                                                     0.0015                                                                                                                                                                                                                          0.0015                                                                                                                                                                                                                                                                                                                          Ch 5
                                 21.01                                                                                                                                                                                                                                                                                                  21.01                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Ch 6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               21.10                                                                                                                                                                                                                                                                 Ch 7

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Water temperature (C)
                                                                                                                                                                                                                                                     0.0010                                                                                                                                                                                                                          0.0010
                                 21.00                                                                                                                                                                                                                                                                                                  21.00

                                                                                                                                                                                                                                                                                                                Water temperature (C)
         Water temperature (C)

                                                                                                                                                                                                                                                     0.0005                                                                                                                                                                                                                          0.0005

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Balance signal (g)
                                                                                                                                                                                                                                                                             Balance signal (g)
                                 20.99                                                                                                                                                                                                                                                                                                  20.99                                                                                                                                                                                                  21.08
                                                                                                                                                                                                                                                     0.0000                                                                                                                                                                                                                          0.0000
                                 20.98                                                                                                                                                                                                                                                                                                  20.98
                                                                                                                                                                                                                                                     -0.0005                                                                                                                                                                                                                         -0.0005
                                 20.97                                                                                                                                                                                                                                                                                                  20.97
                                                                                                                                                                                                                                                     -0.0010                                                                                                                                                                                                                         -0.0010
                                 20.96                                                                                                                                                                                                                                                                                                  20.96
                                                                                                                                                                                                                                                     -0.0015                                                                                                                                                                                                                         -0.0015                                                   21.04
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Templog 61
                                                                                                                                                                                                                                                                                                                                        20.95                                                                                                                                        -0.0020                                                   21.03
                                 20.95                                                                                                                                                                                                               -0.0020


























                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Large fluctuation in undisturbed bath – no insulation.
Large fluctuation in temperature and balance signal.                                                                                                                                                                                                                                                           Large fluctuation in temperature and balance signal.
                                                                  Appendix: Temperature logs 1 to 11
                                                              Temperature log 63 - After starting forced cooling
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Temperature log 10-1 - Heating switched off
                           21.19                                                                                                                                                                                                                                                                                                                                                                 Temperature log 61 - After forced cooling                                                                                                                                                                                                                           21.98
                                                                                                                                                                                                                                                                      Ch 0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Ch 0
                           21.15                                                                                                                                                                                                                                      Ch 1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Ch 1
                                                                                                                                                                                                                                                                      Ch 2                                                            20.73                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Ch 2
                                                                                                                                                                                                                                                                      Ch 3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Ch 3
                           21.10                                                                                                                                                                                                                                      Ch 4                                                                                                                                                                                                                                                                                                                                                                                           21.96                                                                                                                                                                                                                                    Ch 4
                                                                                                                                                                                                                                                                      Ch 5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Ch 5
                                                                                                                                                                                                                                                                      Ch 6                                                                                                                                                                                                                                                                                                                        Ch 0                                                                                                                                                                                                                                                                                                        Ch 6
 Water temperature (C)

                                                                                                                                                                                                                                                                      Ch 7                                                            20.71                                                                                                                                                                                                                                                       Ch 1                                                                                                                                                                                                                                                                                                        Ch 7

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Water temperature
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Ch 2
                                                                                                                                                                                                                                                                                                                                      20.69                                                                                                                                                                                                                                                       Ch 3                                                               21.94
                                                                                                                                                                                                                                                                                                            Water temperature (C)

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Ch 4
                           20.97                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Ch 5
                                                                                                                                                                                                                                                                                                                                      20.68                                                                                                                                                                                                                                                       Ch 6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Ch 7
                                                                                                                                                                                                                                                                                                                                      20.66                                                                                                                                                                                                                                                                                                                          21.92
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 switch off heatig
                                                                                                                                                                                                                                                                                                                                      20.64                                                                                                                                                                                                                                                                                                                          21.90
                                           Templog 63                                                                                                                                                                                                                                                                                 20.62
















                                                                                                                                                                                                                                                                                                                                      20.61                Templog 62

























Mixing after starting the cooling – changed gradients
                                                                                                                                                                                                                                                                                                            Low fluctuation during external cooling control                                                                                                                                                                                                                                                                        Mixing due to stopped heating – changed gradients.
                                                                                              Temperature log 10_2 - Stability in decay
                           21.40                                                                                                                                                                                                                                                                                                                                Temperature log 10_3 - Stable gradient despite decay                                                                                                                                                                                                                                                                                                                                                 Temperature log 11_2                                                                                                    Ch 6
                                                                                                                                                                                                                                                                                                                                      21.24                                                                                                                                                                                                                                                                                                                          21.60                                                                                                                                                                                                                                                   23.0
                                                                                                                                                                                                                                                                                            Ch 0
                                                                                                                                                                                                                                                                                            Ch 1
                           21.38                                                                                                                                                                                                                                                            Ch 2
                                                                                                                                                                                                                                                                                            Ch 3
                                                                                                                                                                                                                                                                                            Ch 4                                      21.23                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  22.8
                                                                                                                                                                                                                                                                                            Ch 5                                                                                                                                                                                                                                                                                                                                                                     21.55
                                                                                                                                                                                                                                                                                            Ch 6
   Water temperature (C)

                                                                                                                                                                                                                                                                                            Ch 7

                                                                                                                                                                                                                                                                                                              Water temperature (C)

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             Water/air temperature
                                                                                                                                                                                                                                                                                                                                      21.22                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  22.6

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           air temperature
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  outer bath higher energy loss
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     21.45                                                                                                                                                        despite new outside insulation
                           21.30                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             22.2
                                                                                                                                                                                                                                                                                                                                                                                  Ch 0                        Ch 2                                Ch 4                               Ch 6                                                                                                                                                                                                                                                 outer bath heated                                                                  Ch 0                                         Ch 3                           Ch 7
                                                                                                                                                                                                                                                                                                                                                                                  Ch 1                        Ch 3                                Ch 5                               Ch 7                                                                                                                                                                                                                                                 by inceasing air                                                                   Ch 1                                         Ch 4
                                                                                                                                                                                                                                                                                                                                      21.19                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Ch 2                                         Ch 5










                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     21.40                                                                                                                                                                                                                                                   22.0





















Rather stable gradients in cooling after heating stopp.                                                                                                                                                                                                                                                     Small changes when establishing equilibrium.                                                                                                                                                                                                                                                                           Effect of air temperature increase in insulated bath.
Peter Lau

Study of traceability to the
density of water
Interim Report to Nordtest

SP Technical Notes : 2001:43
Measurement Technology
Borås 2001


The result of an experimental study is presented that was aimed to explore and describe
the presumed buoyancy effect of an air layer in hydrostatic weighing not visible to the
experimenter eye. The expected result was thought to have relevance for the traceability
in all hydrostatic weighing, especially in the volume/density determination of weights. An
earlier inter-comparison had brought forth a deviation beyond the estimated measurement
uncertainty between two Nordic National Laboratories. The seeked effect was found to
have a different experimental explanation. Disturbances both induced and natural ones
generate convection currents in the measurement bath, which add an erroneous force onto
both the weighed artefact and the holder, which can explain the discrepancies in the inter-
comparison. The hypothesis of a gas layer leading to extra buoyancy for a solid immersed
into water without preceding de-aeration could however not be verified. More extensive
plans to study this buoyancy component as a function of the solid material and liquid
viscosities were therefore cancelled.

Key words: hydrostatic weighing, density, de-aeration, buoyancy, convection, water air

SP Sveriges Provnings- och                         SP Swedish National Testing and
Forskningsinstitut                                 Research Institute
SP AR : 2001:43                                    SP Technical Notes : 2001:43
                                                   Postal address:
                                                   Box 857,
                                                   SE-501 15 BORÅS, Sweden
                                                   Telephone: +46 33 16 50 00
                                                   Telex: 36252 Testing S
                                                   Telefax: +46 33 13 55 02

Abstract                                                                        2

1          Background                                                           5
1.1        Water as a reference in volume and density determination             5
1.1.1      The problem of undetected gas bubbles                                5
1.1.2      Technique for de-aerating                                            5    De-aerating of water                                                 5    De-aerating of test object and holder                                6
1.2        Density inter-comparison with Mikes (Finland)                        6
1.3        The Euromet project 339 outcome                                      7
1.4        The effect of different artefact treatment on the measured density   8
1.5        The hydrometer inter-comparison outcome between MIKES and IMGC       8
1.6        Formulation of a hypothesis                                          9

2          Purpose of the Experiment                                            10

3          Experimental method                                                  11
3.1        The density determination of solid artefacts                         11
3.2        The experiment layout                                                11
3.2.1      The test objects                                                     12
3.2.2      The measurement program                                              13
3.3        De-aerating procedure                                                13
3.4        The thermal stability of the bath                                    14

4          Results                                                              15
4.1        Table over results obtained without de-aeration                      15
4.2        Table over results obtained with de-aeration                         16
4.3        Graphic result                                                       16
4.3.1      The ring results                                                     16
4.3.2      The cylinder results                                                 18
4.3.3      The acrylic glass results                                            19
4.4        The mass stability of the artefacts                                  19

5          Observations and interpretations                                     20

6          Convection as an explanatory model for the searched but              21
           not found effect

7          Conclusions and suggestions                                          24

8          References                                                           25

1             Background
1.1          Water as a reference in volume and density
The magnitude of volume is defined by a measurement of length. The litre is equivalent
to a cubic decimetre. However, in all traceable calibration of volumes, regardless if it is a
contained quantity of a volume standard, the volume of a certain amount of gas or liquid
or the volume of a solid, it is determined by means of a gravimetric measurement. The
delivered volume is weighed either directly or as the mass change of a container before
and after emptying.

With the knowledge of the density of the used liquid, the measured mass or mass change
can be converted to volume. Most practically very pure water is used in calibration labo-
ratories to achieve this conversation. Although originally the water density as a function
of its temperature was established using a solid density standard traceable to length and
mass, for all practical work thoroughly prepared water is used as a secondary reference
standard. The reason is twofold. It is relatively simple to get proper water and it is defi-
nitely not a simple job to determine the water density with the same low uncertainty that
one can assume just from a correct temperature measurement of pure water [1].

1.1.1        The problem of undetected gas bubbles
Water always contains a certain amount of solved air. This does slightly lower the
specified density. However, a second effect of the contained air is more serious. Even in
very carefully filled containers it is the rule rather than the exception that after a short
time air bubbles will show up clinging to the inside container wall. For stability reasons,
larger volume standards (≥ 5 litres) are produced in stainless steel and one cannot see
whether or not air bubbles form part of the contained volume. However, even in small
volume standards of glass, where air bubbles can be seen it is unwanted and troublesome
to remove them. In addition, it would of course lead to considerable measurement errors
in the volume determination to weigh air and to regard it to be contained water volume.

1.1.2        The technique of de-aerating
The risk of air bubble generation on the inside wall of volumetric calibration objects can
almost be neglected if the water previously is de-aerated and poured very carefully from
the bottom using thin hoses.      De-aerating of water

The de-aeration is achieved collecting the freshly produced pure water in a large flask and
applying a low pressure at its top for a time of roughly 15 minutes. Due to the low atmos-
pheric pressure, the water will boil at room temperature and release the solved air. At the
same time an evaporation process starts, which finally would remove all water if not
stopped. The process is not as effective as ordinary boiling but has the big advantage that
a thermal equilibrium at room temperature is much faster reached.
                                              6      De-aerating of test object and holders

Water has a very high surface tension. In order to get rid of all water from the inside wall
of a container the water level must be reduced very slowly. This is also true for water
droplets on solids when lifting them out of the water. It is reasonable to assume that the
opposite is also true, namely to insert a solid very slowly into a water bath in order to wet
the whole surface. This is however the most risky moment in density and volume deter-
mination experiments and it is desirable to perform the immersion as quickly as possible,
but without risking air bubbles to form. Due to the very same reason at SP the artefacts
for these determinations have been regularly de-aerated too. This is done by putting those
objects into a vessel with pure and de-aerated water and applying a low pressure for some
minutes. Despite making the water air-free a lot of existing air bubbles can be released
from the surface of the artefact during this preparation. Thus to avoid the risk of having
air bubbles in the test bath both on the test object and the necessary holder are de-aerated
in advance either together or separately.

When the de-aeration process is over the object is moved very fast out of the de-aeration
vessel and into the bath and holder, exposing it very wet for very few seconds to air

The process of density/volume determination is briefly described in chapter 3.1 and in
greater detail in [2] and [3]. Compared to the weighing procedure in water the prepa-
rations and the handling of the object in question is a rather time consuming procedure.
Occasionally a density determination was repeated or a fast density check had preceded a
standard measurement without applying the de-aeration procedure. A slightly lower den-
sity value was gained and ascribed to those deviations from the written method. However,
the differences were so small that they were within the uncertainty margin connected with
the measurement.

1.2          The density inter-comparison with Mikes
In the middle of the nineties, the four Nordic laboratories JV (Norway), DFM (Denmark),
Mikes (Finland) and SP (Sweden) were engaged in a Nordic task group developing test
methods for the verification of weights according to IR 111 [4], [5]. Among the inter-
comparisons conducted between these institutions concerning mass, density, magnetic
behaviour and surface roughness only Mikes and SP were at that time able to perform a
density measurement. After further development of the density/volume calibration
capabilities a new inter-comparison between these laboratories in 1999 lead to the result
shown below.

This resulted in a difference between the laboratories that was larger than acceptable con-
cerning their corresponding uncertainties, especially as the last of the four SP-measure-
ments was reported to be the most reliable one with the most careful preparation. The two
first were performed in a hurry before summer vacation and the third one was done for
experimental reasons with a water sample that was not changed during the vacation. The
fourth measurement was done with freshly prepared water and conducted in total agree-
ment with the written method.

The difference in density being significant in the 5 th position cannot be ascribed to dif-
ferences in the mass determination (agreement to the 7 th position) or corrections to a
common temperature of 20 °C (sensitive in 7 th position).

                                     Density com parison of a 1 kg w eight
                                                                U        =0,2

      Density(kg/m )

                                                                                    ∆ ρ =0,32

                                                                U           =0,13
                       7,996.8                                      MIKES

                                 06-30   07-01    08-13 08-16                   Mikes

Figure 1: The result of a density inter-comparison between Mikes and SP (four discrete
          measurements) on a standard 1 kg weight with a less good surface roughness.
          The relative deviation from MIKES is 4 units in the 5 th position.

1.3                       The Euromet project No 339 outcome
During January 1996 and January 1999 SP was the second of 12 European laboratories to
take part in a Euromet-project to determine the mass and volume of three ceramic
spheres, which is exactly the same experiment as to determine the density of these arte-
facts. The report finalized in August 2000 settled the capability of the participating labo-
ratories to determine the volume. As a final model, the median in this European inter-
comparison was chosen as the best reference value. The outcome for SP is specified in
the table 1 below containing also the deviations if the mean or the weighted mean from
all laboratories is chosen [6]. Mikes was not ready to take part in this exercise when the
project was started, but Force (Denmark) took part.

Table 1: SP result in comparison to various references for the inter-comparison.
Artefact              Stated     Deviation from Deviation from Deviation from
                     volume           median              mean         weighted mean
                      [cm3]          rel. units         rel. units        rel. units
large ceramic                              .   -5             .   -5
                    315,50242       -1,13 10          -1,31 10           -1,07 . 10-5
medium ceramic
                    220,17827        9,08 . 10-8      -1,05 . 10-6        1,35 . 10-6
small ceramic
                    87,16507         2,52 . 10-6       1,27 . 10-8        1,53 . 10-6

The handling of the large sphere was problematic due to the large holders used in this
volume/density measurement. A deviation of 1 unit in the 5 th position in negative direc-
tion could very well mean a corresponding deviation of density to higher values. On the
other hand, the volume of a 1 kg weight with 125 cm3 lies in the middle of the small and
medium sphere. There the SP result had a much better uncertainty declaration and devi-
ated positively with only one unit in the 7 th and 2,5 units in the 6 th position. Thus, the
outcome rather would confirm the density value from SP being closer to the European
metrological community (compare 2.10-6 with 4.10-5!)

The outcome of the inter-comparison also exhibits an interesting trend. Five of the labo-
ratories refer their results to solid density standards whereas the rest like SP has its trace-
ability to the density of water. The volume values given by SP are generally lower than
those given by those other laboratories and correspond better to the values of the labora-
tories using solid references. This would mean that if the experiment had asked for den-
sity instead of volume the SP-values and those from the laboratories using solid density
standards would have been higher than those values from the rest of laboratories. This
trend might indicate a systematic difference in density determination.

1.4            The effect of different artefact treatment on the
               measured density
In finding possible explanations for the differences in artefact density between Mikes and
SP, although in the vicinity of the measurement uncertainty, the suspicion was raised it
could have been caused by different treating before the weighing in water.

From the analogy of changing moisture on weight surfaces when moving them from one
temperature to an other and the assumption of a moisture stabilization time one could
expect to also have some natural air layer on a weight when immersing it into water.
Thus, the idea was that SP and Mikes actually might have worked with different experi-
mental definitions of a weights “volume”. A hypothesis was raised that an air layer in the
Mikes-experiment involved a small but additional buoyancy effect on the 1 kg-weight.

For checking this thesis in a first test series of experiments a 100 g weight was treated
with and without de-aeration in different combinations. The result of this preliminary test
showed at average a 0,6 kg/m3 higher density after de-aerating. However, the variation,
probably due to variations in the de-aeration procedure (time, static pressure etc), was so
high that no conclusion could be drawn. The reason for choosing a 100 g weight was the
ability to use a 200 g balance with a hundredfold increased resolution. Anyhow, the effect
seemed so large that it was considered to be a possible explanation for the inter-compari-
son result on the 1 kg weight. Considering the surface area of a 1 kg weight and that of a
100 g weight and what this could imply on the buoyancy, one has to compare the area to
volume relation between the two weights (se table 2). Thus the assumed “buoyancy ef-
fect” should for a 1 kg weight amount to 0,6 kg.m-3/ 2,18 = 0,28 kg.m-3, which is reason-
able close to the experienced 0,32 kg.m-3 from the offset between Mikes and SP.

Table 2:       Surface - volume relations between two weights of different size.
                             1 kg weight       100 g weight        175 g sphere
Surface area                 14259 mm2             3115 mm2            3782 mm2
Volume                      125676 mm3             12568 mm3           21868 mm3
Relation area/volume         0,113 mm-1            0,248 mm-1          0,173 mm-1
Difference in relation     (100 g/1 kg): factor 2,18     (100 g/174 g): factor 1,44

1.5            The hydrometer inter-comparison outcome
               between Mikes and IMGC
Parallel to the density inter-comparison between Mikes and SP, Mikes also took part in an
inter-comparison with IMGC (Italy) and LNE (France) concerning hydrometer calibra-
tion. The outcome shows a satisfactory overlap between the two laboratories. However,

one eventually could recognize a slight offset of 0,2 kg/m3 to lower values for Mikes [7].
Of course, this inter-comparison is about hydrometers, but the hydrostatic weighing tech-
nique is very similar. An offset possibly might come from the reference density meas-
urement of the liquid using an artefact, a sphere of stainless steel with 174 g that in turn is
traceable to the density of water via hydrostatic weighing. With the same argumentation
as above the “air layer effect” might have produced a density which is 0,4 kg/m3 lower or
a sphere volume that is correspondingly larger, thus leading to an underestimation of the
liquid density used in the hydrometer calibration. However, this is quite speculative. If
there is an “air layer effect,” it should occur two times and thus cancel out each other. On
the other hand, it might be different in different liquids dependent on the surface tension
and contribute with various amounts to the buoyancy in these liquids, which could result
in a reduced underestimation of the density of the second liquid.

1.6          The formulation of a hypothesis
Based on the visual observation of releasing air bubbles on the surface of objects when
keeping them in water under low pressure and further on some preliminary experiments
comparing the density result of a 100 g weight and different treating leading to somewhat
higher artefact density after de-aerating, it is proposed that artefacts have a gas layer
which not necessary is totally removed when the artefact is quickly immersed into a liq-
uid. This unresolved gas layer, not visible to the eye, still produces a displacement of
liquid that is larger than just that of the artefact itself, i.e. it is experienced as a larger
volume. In consequence, the hydrostatic weighing value, due to this small difference in
volume but insignificant difference in mass leads to a lower balance reading.

The hypothesis can be extended. The formation of a gas layer is dependent on the mate-
rial, the surface roughness and the size of the artefact. It also depends on the surface ten-
sion of the liquid, the speed with which it is brought into the liquid, its solubility of gas
and time it has been kept there. Probably by waiting a considerable stabilisation time the
remaining gas is dissolved in the liquid and the extra buoyancy effect disappears.

2            Purpose of the Experiment
The main purpose of the suggested Nordtest-project was to verify the hypothesis of an
existing air layer on an immersed artefact at least originally when immersing it into water.

The second aim was to determine its size and dependence on the hydrostatic weighing
concerning the characteristics of the artefact like surface size and roughness. Equally
important the influence of various liquid properties like surface tension and viscosity
especially of water should be investigated. In consequence, the project was aimed to im-
prove the hydrostatic weighing technique and to clear up the differences in density deter-
mination between Mikes and SP and further to support an improved traceability of den-
sity- and volume calibrations back to the density of water.

3            Experiment Method
3.1          The density determination of solid artefacts
In normal weight calibration, the gravimetric and buoyancy forces acting on two weights
are compared using a balance. As both share the same density, the mass of the unknown
weight is given by the mass of the know weight and the reading of the difference on the
balance. In the density (volume) determination of a solid body, both the mass and the
volume are unknown. Thus, two different conditions are needed to retrieve the unknowns
from two experimental equations. This is usually achieved by two comparison weighings,
first in air and then in water providing a large buoyancy difference. In the easiest experi-
mental set up the water weighing is performed with the unknown object placed in a
holder and immersed in water hanging on a thin suspension wire beneath the pan. The
reference weight(s) however is (are) placed on the pan in air. In this model of the experi-
ment, the artefact in the water experiences a lifting force due to the displaced liquid. If
there is a remaining air layer more water is displaced giving rise to less mass to balance
the total action force on the artefact.

3.2          The experiment layout
The basic idea of the experiment was to perform a series of usual density measurements.
However, in order to observe the roll of the supposed “air layer effect” the determination
was done at least two times with each of several artefacts. In the first measurement-round,
no trial was undertaken to remove the air from the surface of the artefacts in advance,
while in the second determination-round all artefacts were carefully de-aerated as de-
scribed below. In the first round the weighing procedure in water was repeated after a
delay of several hours in order to experience a possible dissolving of the “surface air” in
the water bath. The expectation was to eventually receive a lower real volume and thus a
higher density value, whereas no such indication was expected to occur in the second

As the presumed “air layer effect” is expected to depend on both the material and the
surface size of the artefact, initially two different materials and all together 5 geometric
shapes were planned for studying the expected behaviour. The choice of stainless steel
and acrylic glass was mainly due to the fact that these materials in combinations are used
in various holders in hydrostatic weighing experiments at SP. They also have a large dif-
ference in density. Dependent on the outcome further materials were planned to be incor-
porated in the survey, in the first place glass and ceramic, as these materials are predomi-
nantly used for sinkers and density standards.

Water, being de facto a density reference, was the most important liquid to examine.
Nevertheless, other liquids, especially alcohol providing different wetting properties and
hydrocarbons having different surface tension and viscosity were planned for repeated

3.2.1        The test objects
As the presumed air layer is correlated to the surface 5 artefacts were produced of a stain-
less steel alloy typically used for the production of weights. Starting from a common
target mass of 100 g, three different configurations were achieved exhibiting a large dif-
ference in surface size (factor 2,5 and 1,6) at identical volume. From the two artefacts
with the smallest and largest surface two samples were produced one with a polished face

and one with a coarse grinded one. The hypothesis expected that more air could be
trapped in the second case.

Initially seven artefacts were produced for the project. Their data are collected in table 3
and figure 2.

Table 3:     Comparable data of the studied artefacts.
Detail         Name             Mass        Volume          Surface area     Material/surface
no                               [g]          [cm3]            [cm3]
1        Artefact A           99,5964       12,5167           2,9844         Stainless steel /
         Polished cylinder                                                   polished
2        Artefact A           99,8027       12,550,8           2,9898        Stainless steel /
         Grinded cylinder                                                    grinded
3        Artefact B           99,6512       12,573,9           4,6174        Stainless steel /
         Grinded thick ring                                                  grinded
4        Artefact C           99,8259       12,605,8           7,6814        Stainless steel /
         Polished thin ring                                                  polished
5        Artefact C           99,7585       12,595,0           7,6248        Stainless steel /
         Grinded thin ring                                                   grinded
6        Artefact D            4,3125        3,6884            3,4017        Acrylic glass /
         Acrylic ring                                                        polished
7        Artefact E            9,2917        7,8145            6,4063        Acrylic glass /
         Acrylic pipe                                                        polished

The mass is determined by ordinary calibration. The volume and surface area are calcu-
lated from the geometric measurements.

 Artefact A      d = 25,000mm
                                                                        dy = 42,000 mm
                                         Artefact B             dy      di = 24,000 mm
                     h = 25,465 mm                                           h = 13,397 mm

                         Artefac C                         dy = 46,000 mm
                                                  dy       di = 36,000 mm

                                                             h = 19,409 mm

Figure 2:     Nominal parameters for the stainless steel artefacts having the same mass
              and volume but different surface.

3.2.2         The measurement program
After the production, all artefacts were carefully cleaned and all relevant form parameters
were measured. After this procedure they were cleaned once more with alcohol and water
and tempered over more than 24 ours before the weighing in air took place.

For the weighing in water the total equipment was cleaned, pure water newly produced,
de-aerated and then transferred to the experiment bath. The lifting device was cleaned and
the holder de-aerated and brought in place in the bath hanging below the balance. Two
thermometers T1 and T2 were introduced in their place after having covered the bath and
the surrounding buffer bath with a protection against dust and air convection.

After more than 24 hours of stabilization time, the first artefact from table 3 was brought
into the water and holder using a suitable pair of tongs. As soon as the disturbed bath was
considered stable enough, which typically demands for one to two hours, the weighing
procedure started in the standardised way.

A typical measurement lasted somewhat more than one hour and was normally performed
in one sequence either in the morning or the afternoon. In this first round, the artefact was
kept in place and the measurement was repeated at least 12 hours later once more in the
same way. Generally a more stable vertical temperature gradient could be observed after
that time.

At the end of the second weighing sequence each artefact was placed on the bottom and
kept inside the bath for eventually a third weighing.

This handling scheme was repeated for every artefact on the list. The holder and part of
the lifting device had to be changed after the first two cylindrical artefacts, but nothing
else was done, that experimentally could influence the measurement outcome.

After the first round all artefacts were dried and in some cases their mass re-measured.
The bath was emptied and cleaned and new test water was prepared. The second round
very closely followed the first concerning the measurement layout with the exception that
every artefact was de-aerated before the first weighing sequence in water.

3.2          The de-aeration procedure
In standard procedure the artefact is placed in the de-aeration vessel containing pure wa-
ter. The lid is closed and a low pressure is applied for a time long enough to release all
air, typically 10 minutes. Thereafter the lid is opened and the artefact is lifted out with a
pair of tongs and put into the measurement bath as quickly as possible. This takes some-
thing between 2 and 10 seconds in which there is a contact of the wet artefact surface
with air.

Due to the variation in a preliminary study now a more well defined attempt was tried. A
main goal also was to prevent the artefact surface to come into contact with air during the
transportation from the de-aeration vessel to the measurement bath. Therefore a small
bowl with water was placed in the de-aeration vessel which did not contain water other-
wise. After opening the lid the whole bowl was lifted out and immersed into the water
bath so that the artefact could be transferred into the holder always immersed in water.

An advantage of this procedure was that the applied low pressure on the artefact was not
dependent on the static pressure of the water column in the de-aeration vessel. The de-
aeration time could also be kept shorter. A clear disadvantage however, was that the
evaporation remarkably lowered the temperature of the de-aeration water, which became
a function of time. A temperature reduction of 4 °C in the water was an extreme example.
It therefore was necessary to wait or actively increase the water temperature before im-
mersing the bowl into the measurement bath. A second disadvantage was the larger dis-

turbance of the measurement bath. Thus a longer delay than in the first round, more than
two hours, was necessary before a first weighing sequence could take place.

                                      to ejector

                                           acrylic glass

         air at low                  O-ring

           bowl with water and artefact (ring)

       rod of

                                       vessel                   Figure 1: Scheme and picture of the de-aera-
                                       of glass
                                                                          tion vessel with a small bowl and a
                                                                          stainless steel ring.

3.4              The thermal stability of the bath
In spite of the possibility to perform hydrostatic measurements at various controlled bath
temperatures the most accurate measurements are performed without any active tem-
perature regulation of the outer bath (se figure 11). At room temperature the experience is
that there is no control as effective to keep a stable temperature or temperature gradient as
to have a large thermal buffer and await thermal stability, which typically means very few
mK fluctuations at the spot of the thermometers and about 40 mK temperature difference
between the thermometers being roughly 10 cm apart in height.

4              Results
The experimental results are collected in the two following tables and then shown graphi-
cally for a better overview over the observed effects.

4.1            Table over results obtained without de-aeration
Table 4:       Results from the first round in order of their determination. The stated den-
               sity is valid for a temperature of 20 °C. The results are shown graphically in
               figures 4 to 8.
Meas.      Artefact         Density      Average     Temperature Temperature Measurement
No         shape            [kg/m3] Temperature Gradient               Stability    Uncertainty
                                           [°C]           [°C]           [°C]         [kg/m3]
1          A polished 7960,333           19,556          0,046          0,037          ±0,48
2          Cylinder        7960,150      19,869          0,012          0,003          ±0,21
3          A grinded       7960,040      19,913          0,013          0,006          ±0,19
4          Cylinder        7960,044      19,907          0,011          0,001          ±0,25
5          B grinded       7960,665      19,811          0,029          0,012          ±0,33
6          Ring thick      7960,799      19,940          0,011          0,004          ±0,29
7          C polished 7951,727           19,944          0,016          0,003          ±0,23
8          Ring thin       7951,624      19,936          0,011          0,001          ±0,28
9          C grinded       7951,516      19,966          0,013          0,001          ±0,23
10         Ring thin       7951,412      19,911          0,010          0,001          ±0,23

11         D Ring        1190,959       19,941         0,011        <0,001           ±0,10
11b        Acryl glass   1191,138       19,957         0,012         0,001           ±0,10
12                       1192,209       19,928         0,010         0,001           ±0,10

13         A polished    7959,896       19,882         0,016         0,004           ±0,41
14         Cylinder      7959,915       19,956         0,010         0,001           ±0,20

15         E Pipe        1193,447       19,168         0,062         0,023           ±0,10
16         Acryl glass   1193,795       19,919         0,010         0,003           ±0,10

31         A grinded     7960,314       21,255         0,032         0,001           ±0,18
32         cylinder      7959,891       21,211         0,017        <0,001           ±0,18
33                       7960,122       21,173         0,021         0,001           ±0,22

The density, as indicated in the table was always measured close to 20 °C. Yet, all experi-
mental values were then transformed to be valid for a temperature of 20 °C using a proper
thermal volume expansion coefficient. The average temperature is the mean value of the
water temperature from two sensors placed 5 cm above and 3 cm below the artefact and 5
cm on either side (se figure 11). The temperature gradient is simply the difference between
the two temperature sensors T1 and T2 separated approximately 11 cm in vertical and 10 cm
horizontal direction. For the stability measure the largest of the standard deviations from
the two temperature sensors was chosen, each comprising 10 readings during the weighing
phase in water with durations from one to one and a half hours typically. The stated meas-
urement uncertainty is calculated by the evaluation program used, which takes care of the
experimental conditions and some basic assumptions with the water density being one of
the main uncertainty contributions.

After a new preparation of the water in the measuring bath the temperature gradient can
reach 60 mK and the stability up to 37 mK. After several hours however, typically a
temperature difference of 10 to 12 mK and standard deviations of 1 mK are reached.

4.2           Table over results obtained with de-aeration
As soon as the first results from the second round became available, the planned scheme
of measurements was changed. As the proposed effect could not be seen in the results
immediately only those artefacts were examined carefully that were expected to produce
the largest differences between the de-aerated and the non-de-aerated treatment. These
are documented in the table below.

Table 5:       Results from the interrupted second round in order of their determination.
               The stated density refers to a temperature of 20 °C.
Meas.      Artefact        Density     Average      Temperature Temperature Measurement
No         No              [kg/m3] Temperature Gradient             Stability     Uncertainty
                                          [°C]           [°C]         [°C]          [kg/m3]
17         C polished 7951,775          19,969          0,016         0,005          ±0,20
18         Ring thin      7951,317      20,023          0,011         0,003          ±0,21
19         C grinded      7952,058      20,089          0,013         0,005          ±0,57
20         Ring thin      7951,374      20,091          0,010         0,001          ±0,23
21         C grinded      7951,219      20,155          0,027         0,001          ±0,21
22         C polished 7951,308          20,182          0,022         0,001          ±0,25
23         D Ring         1195,672      20,125          0,015         0,004          ±0,10
24         Acryl glass 1195,966         20,131          0,009         0,001          ±0,10
25         A polished 7959,159          19,829          0,011         0,003          ±0,21
26         cylinder       7959,305      19,746          0,007        <0,001          ±0,32

27         A grinded     7960,705       21,204          0,023          0,003           ±0,20
28                       7960,344       21,197          0,028          0,004           ±0,19
29         A polished    7959,913       21,164          0,024          0,001           ±0,18
30         cylinder      7960,032       21,209          0,037          0,001           ±0,20
30b                      7960,042       21,223          0,034          0,001           ±0,26

In contrast to all other results, the measurement number 27 consists of a series of 10
shorter weighing series, which were repeated over two days in order to record tempera-
ture stability conditions. Here only the average values are given.

4.3           Graphic results
4.3.1         The ring results
The effect of de-aeration was first applied to the artefacts C, i.e. the rings with the largest
surface in polished and grinded form. The result is shown in the figures 4 and 5.

                                                        Artefact C - P olished thin ring

                         7952.0                                                                  (17)
                                               (7)                                                                             de-areated
                                                             (8)                                                               artefact
       Density [kg/m ]

                         7951.6                                                                            ~0,5                     (22)

                         7951.2      artefact
                                    Polished thin ring                                                           (18)
                         7951.0                              01-mar

                                                                                                 06-m ar

                                                                                                                     07-m ar

                                                                      Measurement date

Figure 4: The density of the polished ring – two measurements (7,8) without any prepa-
          ration – three measurement after de-aeration (17, 18, 22). Between the first
          two measurements the ring stayed in the measurement bath all the time. The
          three de-aerated measurements are shorter series with the ring left in the wa-
          ter. The de-aeration was only applied before measurement (17).

                                                          Artefact C - Grinded thin ring

                         7952.0        non-de-areated                                                                     de-areated
                                       artefact                                                                           artefact
  Density [kg/m ]

                                                                                       (19)                                      (21)
                         7951.2                                   (10)
                                  Grin ded thin rin g
                                                                                       07-m ar


                                                                                                                                  08-m ar

                                                                  28-f eb

                                                                            Measurement date

Figure 5: The density of the grinded ring – same procedure as in figure 4. The measure-
          ment series after de-aeration are shorter, which is reflected in an increased
          uncertainty. As in (18 and 22) above the measurements (21 and 22) refer only
          to a repeated weighing series not to a repeated de-aeration.

4.3.2                              The cylinder results

                                                          Artefact A - Polished cylinder
                                                                                                                               (30) (30b)
                                                                           (14)                                        (29)
  Density [kg/m ]

                                          (1)     (2)
                                7959.7                                                         (26)

                                           non-de-areated                              (25)                    de-areated
                                7959.3     artefact                                                            artefact
                                         res blank cylinder2
                                                                      02-m ar


                                                                            Measurement date

Figure 6: Two measurements (1,2) of a cylinder in a holder at one day are repeated
          after a one week stay in water at the bottom of the bath (13,14). A measure-
          ment (25) after de-aeration is repeated during one day (26.) Four totally new
          measurements several months later with the first (28) de-aerated the others
          (29,30,30b) are repeated weighings.

                                                          Artefact A - G rinded cylinder
                                                                                                                       res matt cylinder2
                                7960.7                   de-earated
                                7960.6                                                                           (31)
              Density [kg/m ]


                                7960.4                                                                                         (33)

                                7960.3            (3)      (4)
                                7960.2                                                                                      (32)




                                                                     Measurement date

Figure 7:                          Two measurements (3,4) of a cylinder in a holder at two following days are
                                   repeated several months later (31-33). In between a series of shorter
                                   weighings (27) after a de-aeration. Here only the weighed mean at a 0,65
                                   kg/m3 higher value is given. A detailed picture is shown in figure 9.

4.3.3                            The acrylic glass results

                                       Artefact D and E - ring and pipe of acrylic glas
                                                            Acryl. ring non-de-areated
      Density at 20 C (kg/m )
                                                            Acryl. ring de-areated

                                                            Acryl. pipe non-de-areated
                                1195                                                                    (15)    (16)
                                1194                                                 (23)

                                1193                                       (12)

                                1192              (11)            (11b)

                                        Plexig las ring och rör






Figur 8:                         Three measurements without (11, 11b, 12) and two after de-aeration of an
                                 acrylic glass ring (23,24). The two measurements on an acrylic pipe (15, 16)
                                 were not repeated with de-aeration.

4.4                              The mass stability of the artefacts
As the density results varied between measurements the mass of some of the artefacts was
re-determined. Whereas the stainless steel artefacts are stable enough to be excluded as a
source for a density change, the acrylic glass ring shows a very distinct mass change due
to water absorption.

Table 6: Mass stability of used artefacts.
Artefact         Before density deter-                                        After density determi- Date
                 mination date 20 Feb.                                        nation
A cylinder       99 596,4 ± 0,07 mg                                           99 596,47 ±0,065 mg 9 Mar
A cylinder       99 802,7 ± 0,07 mg
B thick ring     99 651,2 ± 0,07 mg
C thin ring      99 825,9 ± 0,07 mg                                           99 825,9 ± 0,07 mg         9 Mar.
polished                                                                      99 826,02 ± 0,066          12 Mar
C thin ring      99 758,5 ± 0,07 mg                                           99 758,6 ± 0,07 mg         9 Mar
D acrylic ring   4 312,49 ± 0,044 mg                                          4 332,41 ± 0,044           12 Mar
E acrylic pipe   9 291,71 ± 0,047 mg

5            Observations and interpretations
At first glance, the figures 4 to 7 for the stainless steel artefacts A and C all show a simi-
lar behaviour. The second value (measurements no 2, 4, 8 and 10 respectively) in the non
de-aerated case is lower than the first one (measurements no 1, 3, 7 and 9). This seems to
be a systematic behaviour although this difference is within the measurement uncertainty.
Typically, the spread is also higher in the first measurement series. With the exception for
the first result after de-aeration (measurement 17, 19, 25, 26 and 27 respectively), the
repeated values (figure 6 and 7) are almost the same as without preparation. For the two
rings under stable thermal conditions, the density (figure 4 and 5) turned out to be even

The first and most important conclusion that must be drawn from those observation is
that the hypothesis of a gas layer exhibiting extra buoyancy must be rejected.

There are some more similarities in those four figures. The first measurement after de-
aeration leads to a measurable shift in density. In three cases the first value is roughly 0,5
to 0,8 kg/m3 higher compared to the final situation after more than one day in the water.
In one case figure 6, however, the immediate result received was roughly 0,8 kg/m3 lower
than for the repeated measurements. This is an unexpected result but valuable for finding
an explanation.

The second important conclusion to draw is that the expected “buoyancy” effect, giving a
higher density, can occur under certain conditions, however, the explanation must be a
different one.

First, one has to declare that if there does not exist a gas layer directly after de-aeration
and immersion in the water bath, then there is no possibility that after a longer time gas
from the liquid might adhere on the surface giving additional buoyancy thus lowering the
density of the artefacts. The polished cylinder was de-aerated a second time (figure 6
measurement (28)) and this time a somewhat higher first value resulted in analogy with
measurement (27) in figure 7, which indicates that the results (25) and (26) in figure 6
were caused by a different process.

The density of the two rings (artefact C) varied round a value of 7951,4 kg/m3, the
density of the two cylinders (artefact A) around 7960,1 kg/m3, whereas the thick ring
(artefact B) has a density of 7960,7 kg/m3. These values indicate that at least two of the
stainless steel artefacts were fabricated from a different bar.

Compared to stainless steel the density results of acrylic glass deviated much more, both
in time and between different parts from the same physical piece. The interpretation is
more complicated, but having stated that there is no “air-layer induced buoyancy effect”,
the analysis of the acrylic glass results is of less interest. From the re-measurement of the
mass of the acrylic artefacts, it is proven that the material is hygroscopic. Thus, the in-
creasing density rather reflects the water absorption than anything else. This effect in-
creases most probably with surface, which might explain the difference between the ring
and the larger pipe piece. For the sake of the actual study, no further measurements were

6            Convection as an explanatory model for the
             searched but not found effect
It was known before that the de-aeration applying a low pressure does slightly cool down
the water in the de-aeration vessel. With a large water volume the decrease in temperature
is in the order of a few tens of a degree when waiting longer than 15 minutes. However,
the change in artefact temperature is expected to be less pronounced. Transferring the
artefact alone from the de-aeration vessel to the holder in the measuring bath disturbs the
local temperature gradient in the water around the holder. But those small temperature
differences causing disturbance in the bath for some time were considered to last not
longer than one to two hours, which is the usual start for a weighing series. Most com-
monly, measurements are prepared the day before the actual measurement. As can be
seen in table 4 and 5, a typical temperature gradient over the measured artefact and holder
is in the range of 10 to 12 mK, when waiting long enough and the stability in temperature
at either points of the thermometer is in the range of the instruments resolution, i.e. 1 mK.
In this study, two things differ from standard handling. First, the artefact is not removed
from the de-aeration vessel and immersed wet through the air to the water in the bath.
Instead, the whole bowl with the water and artefact inside was immersed into the bath and
the artefact never came into contact with air before it was placed on the holder under the
water level. Second, the bowl had a very small water volume; the reason being a more
well defined low-pressure condition and a more suitable transportation. This situation led
primarily to lower liquid temperatures of roughly 2 degrees in the bowl compared to
standard conditions, which forced an imperative heating process of the bowl for at least
an hour at a warmer place to counterbalance this temperature decrease. It is very likely
then, that the artefact itself both could have a higher temperature (measurement 25, 26
figure 6) and lower one (measurement 17, 19, 27 in figure 4, 5 and 7) than the water in
the measuring bath.
The somewhat warmer or cooler artefact will start a convection stream in the bath around
its body. Due to friction with the surface, an upward or downward directed impulse is
transferred to the artefacts resulting in a lower respectively higher weight indication,
which is synonymous with a calculated decrease or an increase of the density of the arte-
The first values after de-aeration are interpreted by this convection effect. Due to the
changed de-aeration conditions, the convection disturbance is more serious than expected.
To reach a temperature equalization and to establish a stable gradient, it needs obviously
several hours. First after the induced convection process has stopped an undisturbed
weighing series can render more reproducible density values.
As can be deducted from figure 4, 5 and 6 despite of a quite long stabilization time, over
24 hours with newly prepared water at room temperature, the fist measurement even
without especially induced convection mostly produces higher density results. Looking to
the average temperatures reported in table 3 and 4 this must be interpreted by a perma-
nently ongoing convection in the inner measurement bath. The general trend is that the
water temperature is significantly increasing in the beginning. The driving force is to seek
in the slightly higher room temperature. As the energy transport predominantly is through
the outer bath, a convection pattern like the one shown in figure 11 is most probable. As a
consequence, the inner bath exhibits a downward directed flow in the centre, which adds
an additional force onto the artefact. With a larger convection, a larger effect on the cal-
culated density of the artefact must be expected.
The situation gets worse if a holder like the one shown in figure 11 is involved, as was the
case with the two cylinder artefacts A and which is the standard situation for the majority

of solid density determinations. The calculation is based on a comparison weighing where
the holder is assumed to be totally neutral. In reality, the convection pattern also will
influence the holder but not necessarily equally in the two compared weighings, which
must be considered as a varying systematic measurement error, which so far has not been
included in the mathematical model of the weighing situation. In contrast to the ring
measurements (figure 4 and 5) where the holder just consists of a hook (se figure 10), a
larger variation in the cylinder measurements (figure 6 and 7) must be expected. This is
definitely exhibited in figure 9, which is a close up of figure 7.

                                                     G rinded cylinder                 + W ater den sity
                               79 61.2                                                                        998.3
                                                                                           m att cylinder 2
   Artefact density [kg /m ]

                               79 61.0

                                                                                                                        W ater density [kg/m ]
                               79 60.8
                                       non-de-                                           non-de-
                               79 60.6 aerated                                           aerated
                               79 60.4

                               79 60.2                        de-aerated                                      998.0

                               79 60.0

                               79 59.8                                                                       997.9
                                         0   10      20       30      40         50        60              70
                                                               T ime sca le

Figure 9:                           Close up of the results after de-aeration of the grinded cylinder shown in
                                    figure 7 (measurement 27). The large symbols are the same as earlier. The
                                    small ones comprise a series of repeated short measurements over a time of
                                    two 8-hour periods. For comparison the corresponding but not correlated
                                    water densities are shown as well. The open circle is the weighed mean.

                                                                        suspension wire               to balance
                                                                                                                    outer bath
                                                          2                                                      bath

                                                          3                       T1

                                                          5                                Cylinder

Figure 10: Polished ring on hook          Figure 11: Measuring bath with cylinder on holder
1: suspension, 2: hook, 3: thermometers, 4: lifting cylinder, 5: surrounding water

Compared to the partial results of any complete 1-hour series of standard measurement
type the short series of measurement 27 show a much larger variance. Fluctuating water
temperature does not cause this directly. The calculation takes care of the corresponding
density as displayed in figure 9. It is more likely that the varying convection during day
and night, caused by changes in air temperature, generates the observed spread.

As mentioned above also the acrylic holder absorbs water thus changing its mass. This
effect, however, cannot be responsible for the observed variation. As an ABBA weighing
scheme is used throughout the whole exercise a drift in holder mass is experimentally
cancelled out.

7            Conclusions and suggestions
The main conclusion from the reported experiments is that there is no evidence for a
buoyancy effect generated by a gas layer not visible to the operator’s eye.

The expected and occasionally earlier observed deviations in repeated density determina-
tions are most probably caused by convection, natural or induced. For the cylinder arte-
facts a temporary increase of roughly 0,5 kg/m3 was found. A corresponding value 0,6
kg/m3 for an OIML-shaped 100 g-weight with larger vertical mantle surface was found
earlier. This value is surely larger than under standard measurement conditions. The rea-
son is twofold. Here the disturbance of the bath was larger and the first measurement was
started earlier than usual. Considering the difference in friction area between the used
cylinders and the 1 kg-weight from the inter-comparison with MIKES an overlaid con-
vection there can have been responsible for a larger part of the 0,32 kg/m3 higher density
value from SP. Taking this aspect into account would bring the inter-comparison in rea-
sonable agreement.

In routine measurements, when water in the bath is freshly prepared it takes quite a long
time, one to two days, before a good thermal stability is reached, even if the water is tem-
pered in advance. Up to now experience has told that the best thermal stability at room
temperature is reached using a passive water buffer rather than controlling the outer bath

Even though water very quickly establishes a layered structure with a stable vertical tem-
perature gradient (1 mK/cm height difference), the new experiments seem to indicate that
the convection process in the bath never really stops. It is not only, as so far assumed, the
handling of putting the artefact into the holder that temporarily disturbs the temperature
gradient. One must expect that the changing room temperature, which has a cycle of
roughly ±0,2 to ±0,5 °C per day, acts like a generator.

This convection can generate systematic effects leading to over- and underestimations of
the artefact density, depending on the current relation between the temperature of the bath
and the surrounding air. If the air is warmer, as during day, there is a convection pattern
as indicated in figure 11 resulting in an overestimation of density values. During the
night, the pattern seems to be reversed. This convection cannot be detected using the inert
thermometers. Not even point speed measurements using a laser-doppler anemometer can
resolve this movement in the bath as the optically introduced energy directly would
warm-up the tiny measurement volume thus starting to generate a punctual movement in
the measurement spot.

This disturbance to the density measurement must be avoided. One way is to insulate the
outer bath, another one to stir it in order to destroy the existing gradient and convection
there and to produce a homogeneous temperature distribution. Both techniques have
drawbacks. With the first suggestion, it will be difficult to observe the measurement,
which is almost necessary. With the second suggestion probably vibrations are generated
that will reduce the weighing accuracy.

In any case, an uncertainty component needs to be added to the existing uncertainty
budget to reflect the experience gained by this research study.

Further, a re-design of the common holders should be considered to minimize the risk for
a non-symmetric convection effect. Due to the large horizontal bottom plate, convection
also can add a force to the holder that could be different depending whether or not an
artefact rests on the plate or not. Despite the comparison technique, where such forces

experimentally are tried to cancel out, the form of the used holder might add a significant
error force, which so far was not understod.

The varying results of the density measurement seem directly coupled to the size of the
convection, whether it is induced by colder or warmer test bodies, the introduction of
water with differing temperature or an ongoing convection driven by outside air tem-
perature changes.

Further experiments with warmer and colder artefacts of different surface sizes could give
valuable data for adjusting a model to predict convection induced forces and use it to
estimate corresponding errors in hydrostatic weighing. This knowledge would be
beneficial in the density determination of artefacts as well as of liquids and also in the
calibration of hydrometers as these have an extremely large surface.

8            References
[1]   Betin, H., Spieweck, F. Die Dichte des Wassers als Funktion der Temperatur nach
      Einführung der Internationalen Temperaturskala von 1990. PTB-Mitt. 100, 1990, 2.
[2]   Lau P. Heierli, R. Density Determination of Reference Mass Standards, NCSL
      Annual Workshop and Symposium 1998, Albuquerque.
[3]   Lau P. Density Determination - OIML Workshop on Weights, Borås, Sweden 13-
      15 October 1999
[4]   Källgren H., Lau P. Mycklebust T. Nielsen L. Riski K. Testing of weights, OIML-
      Bulletin Vol. XXXVIII. No 2.
[5]   OIML R 111-2 Weights of classes E1, E2, F1, F2, M1, M2, M3, Committee Draft,
      OIML/2 nd CD R111, Feb. 2000.
[6]   Richard P., Intercomparison of volume standards by hydrostatic weighing, Euromet
      Project no 339 – Final report, Aug. 2000.
[7]   Lorefice S.,Heinonen M.,Madec T. Bilateral comparisons of hydrometer
      calibrations between the IMGC-LNE and the IMGC-MIKES
      Metrologia, 2000, 37, n°2, 141-147

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