SOP for Falling Ball
viscometer (Höppler)
SOP-KTH-HOPVISC-Ver:1
Department of Energy Technology
2
SOP for Falling Ball viscometer (
Department of Energy Technology
Reference: e.g. KTH- XYz
Measurement of viscosity of nanofluid using Höppler viscometer
1. Purpose
1.1. Measurement of viscosity in nanofluids.
2. Scope
This protocol is applicable to all members of NanoHex project and provides a descriptive
procedure to measure viscosity with falling-ball (Höppler) viscometer in distilled water
nanofluid.
3. Principle
The principle of the viscometer is to determine the falling time of a ball of known diameter
and density through a close to vertical glass tube of known diameter and length, filled with
the fluid to be tested. The viscosity of the sample liquid is related to the time it takes for the
ball to pass a distance between two specified lines on the cylindrical tube. Turning the
measurement tube results in returning of the ball and it is possible to re-measure the time
over the same distance. The result is dynamic viscosity with the standard dimension
(mPa.s).
Velocity of a ball which is falling through a liquid in a tube is dependent on the viscosity of
the liquid. When the ball moves through the liquid, it is affected by the gravity, buoyancy and
frictional forces: Gravity as downward force, buoyancy and friction as the upward forces
(figure 1).
W=mg=Vρsg=4/3πr3ρsg
(1)
ρs :density of ball
g:gravitational acceleration
V: volume of ball
r:raduis of ball.
Buoyant force, F1, acts upward and it is dependent of the density of the liquid which is
displaced by the ball.
F1=VρLg=4/3πr3ρLg
ρL=density of liquid
(2)
The liquid has a dynamic viscosity, which produces a resistance against the ball movement.
This frictional force is derived from the Stokes's law:
F2=6πηru (3)
u:velocity of the ball
3
SOP for Falling Ball viscometer (
Department of Energy Technology
Figure 1 - Body diagram of a ball in a fluid
Whilst gravity and buoyant force are static and independent from the velocity, the frictional
force raises with the velocity. Therefore, the velocity of the falling ball raises till the net forces
is zero:
W-F1-F2=0
(4)
Combination of these equations would result in:
u=2/9 r2 g (ρs-ρL)/η (5)
Equation (5) shows that the viscosity of liquid, η, can be gained from the velocity of ball
which is going down through this liquid.
The studied liquid is in a glass tube which has two marks by distance L. In the experiment,
the time it takes for liquid to pass through these two marks is measured. Modification of
equation (5) yields:
In which the dynamic viscosity,
is:
Generally for simplification the constant coefficients are changed into a single coefficient, K:
4
SOP for Falling Ball viscometer (
Department of Energy Technology
K is viscometer constant and can be determined by using distilled water as it has well-known
viscosity [3].
3.1. Technical data for the equipment [1]:
Measuring range:
0.6-80000 mPa.s according to DIN 53015
Limit:
30-300 s
Inaccuracy of measurement:
0,5-2 % according to the diameter of ball
Temperature range:
-60...+150 oC
Measuring distance:
100mm (50mm between upper and middle
lines in both directions)
3.2. Equipment
In measuring viscosity by Höppler viscometer one needs a stop watch and a thermometer
and a water bath in order to have homogenous bath temperature besides studied solutions
and distilled water for calibration. A schematic Höppler viscometer is shown in figure 2.
5
SOP for Falling Ball viscometer (
Department of Energy Technology
Figure 2 – Falling ball viscometer [2]
1- Stand
12- Screwneck
2- Viscometer
13- Sealing washer
3- Spirit level
14- Bearing
4- Adjusting screw
15- Nuts
5- Adjustment screw
16- Upper locking plug
6- Falling tube
17- Lower locking plug
7- Upper plate
18- Cap
8- Lower plate
19- Sealing
9- Water bath jacket
20- Lid
10- Olive shaped tubes
21- Falling tube screw fitting
11- Fastening screw for
thermometer
3.3. Ball selection
Choice of ball is made on basis of the assumed viscosity of studied liquid and the
specification which is given in table 1:
Table 1- Balls characteristics [1].
Ball
No.
Material
Density
ρ(gr/cm3)
1
2
3
4
5
6
glass
glass
glass
alloy
alloy
alloy
2.228
2.228
2.411
8.144
7.909
7.907
Ball
weight
(gr)
4.599
4.816
4.454
16.055
14.536
11.073
Ball constant
(mPa. cm3/gr)
0.00891
0.0715
0.07755
0.1239
0.6523
-
Measuring
range
(mPa.s)
0.6-10
7-130
30-700
200-4800
800-10000
6000-75000
3.4. Temperature control
Falling ball viscometers allow an accurate temperature control of studied liquid through the
bath. The following is recommended thermostatic fluids [1]:
+1...+95ºC
+80...+150ºC
-60...+30ºC
Distilled water
Glycerine mixed (pure or in appropriate ratio
with water)
Methyl alcohol or ethyl alcohol (pure or
mixed in appropriate ratio with water)
4. Safety procedures and precautions
4.1. Wear rubber gloves and safety goggles during any handling of nanofluids
5. Procedure
5.1. Fill the falling tube with studied liquid and put in the ball cautiously. Add more liquid till
no air bubbles can be seen. Then close the falling tube by its cap.
6
SOP for Falling Ball viscometer (
Department of Energy Technology
5.2. Before starting the measurement, it is better to turn the falling tube up and down at least
once in order to enhance temperature uniformity along the tube.
5.3. Turn the falling tube 180 degree. Start stop watch when the ball reaches to the first
marks on the tube, and measure the time between the two marks. For better and more
accurate results it is recommended to repeat the measurement 10 times at each
temperature.
5.4. After changing the bath temperature, it’s highly recommended to wait at least 20 minutes
to ensure temperature stability for the sample.
5.5. At the end of the experiment, empty the tube from the liquid and remove the ball from
the tube very carefully. Clean the tube with suitable solvent and/or a brush.
5.6. Write down the density of liquid and ball,ρL and ρs respectively. Calculate the average t
for each temperature and calculate the viscosity using equation (9).
6. Calibration
For calculating the viscometer constant, do all the above steps with a liquid which has a
known viscosity such as distilled water but use the dynamic viscosity of distilled water in
equation (9) and calculate the viscometer constant, K [2].
Notes:
-The liquid in the falling tube should be free of bubbles.
-Generally the measurement for calibration is done at 20°C.
-Measuring of the time starts when the lower edge of the ball touches the upper mark and
ends when crosses the lower mark [2].
7. Re-calibration
7.1. As some of the nanoparticles tend to stick to the surface it is important to check the
calibration of the viscometers at regular intervals. In the initial phase of Nanohex project,
the viscometers should be checked after cleaning after each run with nanofluids. The
check should be done by measuring the viscosity of distilled water at room temperature.
The deviation from previously measured values must not be larger than 5%.
8. References
[1] - Anleitung G.,Hoppler –Viskosimeter,D.R.P.Nr.644312.
[2] - Rheo Tec Messtechnik GmbH,Operating manual, Falling Ball Viscometer
KF10,Germany.
Available at www.rheotec.de
[3] - DocStoc,2008,Using a falling-ball viscosimeter to determine the viscosity,version1.1,
Available at http://www.docstoc.com/docs/28564042/Using-a-falling-ball-viscosimeter-todetermine-the-viscosity-of/