Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
Page 1
Grading Sheet
~~~~~~~~~~~~~~
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Experiment №. 5
VISCOSITY
Students’ Names / Section №
POINTS
APPEARANCE, ORGANIZATION, ENGLISH, & GRAMMAR (Applicable
to both MS Word and Mathcad sections)
5
ORDERED DATA, CALCULATIONS & RESULTS—MATHCAD
FALLING SPHERE VISCOMETER
VARIABLE DEFINITIONS AND RAW DATA
CALCULATIONS (INCLUDING REYNOLDS NUMBER) WITH
DETAILED EXPLANATIONS
VISCOSITY VALUES
5
10
5
SAYBOLT VISCOMETER
5
5
5
VARIABLE DEFINITIONS AND RAW DATA
CALCULATIONS WITH DETAILED EXPLANATIONS
VISCOSITY VALUES
STORMER VISCOMETER
5
10
5
5
VARIABLE DEFINITIONS AND RAW DATA
CALCULATIONS WITH DETAILED EXPLANATIONS
CALIBRATION CHART FOR 2 MASSES
VISCOSITY VALUES
TECHNICAL WRITTEN CONTENT
TABLE OF 3 VISCOSITY PAIRS (W/IN RED BOX OVER MATHCAD)
5
DISCUSSION OF RESULTS
WHY FILL SAYBOLT CONTAINER TO OVERFLOWING …?
HOW WOULD ONE INTERPOLATE TABLE 1 DATA?
WHY MUST THE GLYCERIN & OIL BE AT THE SAME TEMPS?
WHICH METHOD IS BEST? WHY?
CONCLUSIONS
ORIGINAL DATASHEET
TOTAL
COMMENTS
d
GRADER—
5
5
5
5
5
5
100
SCORE
TOTAL
Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Experiment №. 5
VISCOSITY
~~~~~~~~~~~~~~
LAB PARTNERS: NAME
NAME
NAME
SECTION
№
EXPERIMENT TIME/DATE:
NAME
NAME
NAME
TIME, DATE
~~~~~~~~~~~~~~
OBJECTIVE—This experiment is performed to familiarize the
future engineer with three of the many methods of measuring
viscosity. In particular, a falling sphere viscometer, a Saybolt
viscometer, and a Stormer viscometer will be used to measure
viscosity of the same fluid (a motor oil) at room temperature.
INTRODUCTION—One of the properties of homogeneous fluids
is its resistance to motion. A measure of this resistance is known as
viscosity1. The engineer has to have knowledge of viscosity for a wide
range of applications. For example, it is very important to select a fluid
of proper viscosity for use in a hydraulic machine. Furthermore, viscosity enters into the calculation of pressure losses through pipes, the
determination of pump sizes, the calculation of fluid forces, etc. Thus,
it is helpful for the engineer to have a physical awareness of viscosity
and a background in how viscosity is measured. A viscosity measurement is generally made with a device known as a viscometer. There
are several methods of determining viscosity, three of which will be
demonstrated in this experiment. These methods are 1) Falling
sphere method, 2) Saybolt viscometer, and 3) Stormer viscometer.
It is worth noting that viscosity is a measure of relative fluidity at some
definite temperature. Since viscosity varies considerably with temperature, it is essential that the fluid be at a constant and uniform temperature when a measurement is being made. The scope of this experiment will not include the varying effect of temperature on viscosity.
Viscosity can be reported as dynamic viscosity, , or kinematic
viscosity,  = /f, where f, is the density of the fluid. In SI
measure, dynamic viscosity is reported in units of centipoises
where 1 cP = 1 mPas while kinematic viscosity is reported in
units of centistokes where 1 cSt = 1 10–6 m2/s.
1. FALLING SPHERE VISCOMETER—This type of viscosity
measurement is based on Stokes’ law and terminal velocity.
Stokes’ law is applicable for extremely low Reynolds number
flow; i.e., creeping or drifting flow (Re < 1).
Procedure—Fill the graduated cylinder with motor oil of unknown
viscosity all the way to the top graduation. Drop a sphere into the oil
and record the time it takes the sphere to travel a given distance within
the cylinder. The distance can be easily laid out by applying tape at
two locations along the cylinder. Remember that it takes the sphere
a few moments to reach terminal velocity; thus, the upper tape
demarcation should not be at the level of the free surface. Using a
stop watch, the constant (terminal) velocity between the tape-marked
locations is determined. Using the calculated velocity, the Reynolds
number can be obtained. The inside diameter. Dcyl, of the graduated
cylinder should also be measured.
In order to obtain spheres of a density that is slightly greater than the
density of the fluid, plastic spheres are used. To determine the density
of the sphere material, measure the diameter of ten spheres. Then, use
the average of each of these measurements and the measured mass of
all ten spheres to compute a density of the sphere material. Also
measure a mass of a known volume of the fluid using a balance and a
1
viscosity: < Latin, viscosus, sticky (also viscum, bird lime, a sticky substance made from mistletoe berries that is spread on twigs to capture birds)
Page 2
graduated flask. This can be done using the 60cc flask for the Saybolt
viscometer, weighing it empty and full.
Calculations and Results—A blank Mathcad object has been
supplied for the viscosity calculations of this experiment in the
section entitled ORDERED DATA, CALCULATIONS AND RESULTS.
There, the student should compute a Reynolds number based on the
terminal velocity to verify that, indeed, Re < 1. In cases where Re > 1,
charts of drag coefficients versus Reynolds number for spheres can be
found in any fluids textbook. The Reynolds number is defined as
 f VtermD
(1)
Re 

where,
f  density of the fluid
Vterm  terminal velocity of sphere in the fluid
D  diameter of the sphere
  unknown viscosity of the fluid.
The unknown viscosity is determined from Stokes’ law using the
measured terminal velocity calculated as
Vterm 

D2 g    f

(2)
18
where,
g  acceleration of gravity
  density of the sphere.
Report both dynamic and kinematic viscosities in the space
provided in the Mathcad object.
Note that Stokes’ law only applies to spheres and it assumes an infinite
fluid around the sphere. The presence of the cylinder walls will cause a
higher fluid velocity around the sphere. If D/Dcyl > 1/3, this wall effect
can be approximately accounted for by using
2
 9D 
9D


(3)
Vterm
4 Dtube  4 Dtube 
where,
V  true fluid velocity as experienced by the sphere
Dtube  inside diameter of the graduated cylinder or tube.
V
 1
2. UNIVERSAL SAYBOLT VISCOMETER—The Saybolt method
requires the measurement of time for a certain volume of fluid to flow
through a capillary or a tube of very small diameter. The Saybolt
viscometer consists of four containers of constant volume capacity
with capillary outlet tubes at the bottom. The containers are immersed
in an oil bath for which the temperature can be closely controlled (this
experiment will be carried out at room temperature). A container
must be filled all the way up to the edge (with a bit of overflow) with
the oil of unknown viscosity. Excess oil must be removed from the
annulus. A pipette is recommended for the removal. Explain in the
discussion why filling the oil to overflowing is important and why the
annulus needs to be cleaned. Once the excess oil has been removed, oil
is allowed to flow through the capillary tube into the constant volume
flask (60 ml) placed below it. Simultaneously, the time it takes the oil
to fill the flask is recorded. The time recorded can be converted into
units of viscosity by making use of the provided chart (see Figure 2).
OVERFLOW ANNULUS
OIL
FILL TO HERE
THERMOMETER
HEATING
UNIT
RESERVOIR
CONTAINER
LIQUID BATH
60 CC
CORK
Figure 1—Saybolt viscometer
Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
Procedure—Three of the four tubes have Universal orifices and one
tube has a Furol2 orifice. The oil, whose viscosity is to be determined,
is placed in one of the containers having a Universal orifice. The
container must be filled to the edge. The temperature of the unknown
oil may be controlled by means of an oil bath surrounding the cylinder.
However, in all three parts of this experiment the fluid will be tested at
room temperature. With the fluid at room temperature, the oil in the
cylinder is allowed to flow through the capillary tube into the 60cc
container below. As soon as the oil begins to flow, the stopwatch is
started. Timing stops when the oil in the container below reaches a
specified volume of 60cc. The elapsed time is known as Saybolt
Universal Seconds, SUS, or Saybolt Furol Seconds, SFS, depending
on which orifice is used. The Saybolt seconds can be converted to SI
viscosity units of centistokes or English Gravitational units of ft2/s by
means of the following formulae:
Page 3
 – uniform shearing stress over width of annulus
 – absolute viscosity
Vx – velocity in direction of shearing, for the annulus,
this is the tangential velocity
y – direction normal to the shearing (radial direction)
dVx/dy – velocity gradient due to shearing—in this case, it is
constant (linear profile)
The rotational speed under an applied constant torque is inversely
proportional to the fluid viscosity. The principal difficulty with
this type of viscometer is that mechanical friction must be
accounted for, and this is difficult to determine accurately.
where,
SI cSt   0.226  SUS 
195
,
32s  SUS  100s
SUS
135
cSt   0.220  SUS 
,
SUS  100s
SUS
English Gravitational
1 
195 
 ft 2 / s 
 0.226  SUS 
 , 32s  SUS  100s
929 
SUS 




 ft 2 / s 
1 
135 
 0.220  SUS 
 ,
929 
SUS 
SUS  100s
(4)
The metric equations graph as shown below.
Kinematic Viscosity, cSt
50
45
Figure 3—Stormer Viscometer
40
Detailed Procedure—Make sure that the cylinder that holds the test
fluid is absolutely clean. Using glycerine3 as a calibrating fluid,
measure the time (seconds) for 20 revolutions using two different
masses on the hanger. This will produce two different shearing rates
and driving shearing stresses. Then, clean and dry the cylinder that
holds the liquid and load the sample of the fluid of unknown
viscosity. Test the sample using the same procedure.
35
30
25
20
15
10
Dynamic Viscosity of 100% Glycerine (Centipoises)
Temperature (°C )
5
0
20 40 60 80 100 120 140 160 180 200
Saybolt Universal Seconds, SUS
trace 1
Figure 2— Kinematic
Viscosity, cSt, vs.
trace 2
Saybolt Universal Seconds, SUS
Calculations and Results: Convert SUS reading into centistokes and
centipoises and report in the box provided over the Mathcad object.
3. STORMER VISCOMETER—is a rotational viscometer. It consists of
two concentric cylinders that are rotated with respect to one another.
The narrow annular space between the cylinders is filled with liquid
whose viscosity is to be measured. As the width of the annular space is
small compared with the diameter of the annulus, the sheared flow
produced is almost identical to the flow that would be produced by
two flat plates—Newton’s intended experiment. For a known annular
distance and relative angular velocity of the outer and inner surfaces
of the annulus, Newton’s law of viscosity can be used to determine
the absolute (dynamic) viscosity.
Newton’s law of viscosity is
dV
Shearing Force

  x
Shearing Area
dy
2
0
12070
0
furol: a contraction of “fuel and road oils”
10
3900
20
1410
30
612
40
284
50
142
60
81.3
70
50.6
80
31.9
90
21.3
100
14.8
Table 1-Temperature dependence of glycerin’s dynamic viscosity
http://www.dow.com/glycerine/resources/table18.htm,
In plotting the data listed in Table 1, one must observe the highly nonlinear viscosity-temperature dependence. This makes the evaluation
of viscosity at room temperature (20ºC) difficult. Fortunately, UT’s
Bruce Poling (Professor, ChEE) in Reference [A]4 has supplied the
following equation for the absolute viscosity of glycerol:
  3.426  1073 T 28.52 , (applicable range 273  T  303ºK)
The curve fitted data shown in Figure 4 indicates a good agreement
between experimental data of Table 1 and predictions made with
the above equation. Density data downloaded from the same URL
is shown in Table2 and is also plotted in Figure 4. As one might
expect, density is linear enough to interpolate.
In the discussion, explain how one would interpolate the data of
Table 1 if the Poling equation just above were not available.
3
4
glycerin, glycerine: [<Gr. glykeros, sweet] nontechnical term for glycerol.
glycerol: [glycer(in) + -OL { an alcohol or phenol}] an odorless,
colorless, syrupy liquid, C3H5(OH)3, prepared by the hydrolysis of fats
and oils: it is used as a solvent, skin lotion, food preservative, etc.
References [B] and [C] may have similar data.
Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
Density of 100% Glycerine, (g/cm3)
Temperature (°C)
15
15.5
20
25
30
1.26415
1.26381
1.26108
1.25802
1.25495
Table 2 – Glycerin density variation with temperature
http://www.dow.com/glycerine/resources/table4_91100.htm

1.4 10
4
1.2 10
4
1 10
4
i
 calc( TT )

8000
1 10
5
1 10
4
i
 calc( TT )
6000
1 10
4000
3
2000
0
270
280
290
300
100
270
310
280
T  TT
i
290
300
310
T  TT
i
2

jj
1.5
1
270
280
290
T den
300
310
jj
Figure 4—Fit of experimental data for the dynamic viscosity and of
glycerol. Density data is also plotted.
Calculations and Results—Calculate absolute viscosity following
the outlined procedure (which indirectly makes use of Newton’s
law of viscosity). Construct a calibration chart (Viscosity vs. Time
for 20 Revolutions) for the Stormer viscometer for each of the
driving weights. Complete the chart by joining each of the datum
points to the origin. Use markers (both vertical and horizontal) in
Mathcad to denote the intersection on each line of time and
computed viscosity. Since this is not a traditional graphical
solution, one has to calculate it and then plot it.
Now the viscosity of the unknown oil can be determined using the
constructed calibration chart. Use the same two driving weights as
before to determine two values for the unknown viscosity, then
calculate the average value of the two to be reported. One must
take extra care to insure that the temperature of the oil is the same
as the temperature of the calibrating glycerol since the calibrating
chart can only be used under these conditions. Explain why this is
so in the discussion. Report both dynamic and kinematic viscosity
in the summary box of the Mathcad calculations.
Finally, in the discussion, explain which of the three methods is
best? Why?
References
[A] Reid, Robert C., Prausnitz, John M., Poling, Bruce E., The
Properties of Gases and Liquids, McGraw-Hill Book
Company, 4th edition, 1987.
[B] Yaws, Carl L., Handbook of Viscosity, Gulf Publishing
Company, 1995
[C] Daubert, Thomas E. and Danner, R.P., Physical and
Thermodynamic Properties of Pure Chemicals: Data
Compilation, 5 Volumes, Taylor & Francis, 1996
Page 4
Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
Page 5
ORDERED DATA, CALCULATIONS, AND RESULTS THE RED BOX BELOW RESIDES OVER THE MATHCAD OBJECT & CAN BE RESIZED A/O MOVED.
MATHCAD OBJECT--DOUBLE CLICK TO OPEN
cP 
poise
100
cSt 
stokes
100
1. FALLING SPHERE VISCOMETER
2. SAYBOLT VISCOMETER
3. STORMER VISCOMETER
SUMMARY
DYNAMIC
VISCOSITY
KINEMATIC
VISCOSITY
FALLING SPHERE
sph 
cP
sph 
cSt
SAYBOLT
sau 
cP
sau 
cSt
STORMER
stm 
cP
stm 
cSt
Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
DISCUSSION OF RESULTS
In the Saybolt part of the lab, explain why filling the oil to overflowing is important and why the annulus needs to be cleaned?
Answer here
.
How one would interpolate the data of Table 1 if the Poling
equation were not available?
Answer here
One must take extra care to insure that the temperature of the oil
is the same as the temperature of the calibrating glycerol since the
calibrating chart can only be used under these conditions.
Explain why this is so.
Answer here
Explain which of the three methods is best? Why?
Answer here
CONCLUSIONS
Page 6
Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
Page 7
APPENDICES
APPENDIX A —DATA SHEET FOR VISCOSITY EXPERIMENT
Time/Date:
_______________________
Lab Partners:
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
1. Falling Sphere Viscometer
To Compute Density of Sphere Material
For 10
Spheres,
Sphere O.D.,
cm
Average
O.D. cm
.
To Compute Density of Fluid
10 Spheres
Total Mass, g
For 1 Sphere, Measure Terminal Velocity Drift Time
Fluid
Motor Oil
Fluid Temperature, ºC
Mass of Empty Saybolt 60cc Flask, g
Mass of Flask with Fluid Sample, g
.
.
.
Sphere Diameter, cm
Fall Distance, cm
Fall Time, s
Use Saybolt
60 cc flask
Fluid Sample Size, ml
I.D. of Cylinder
.
.
.
.
2. Saybolt Viscometer
Fluid
Motor Oil
Fluid Temperature, ºC
Same as above
Saybolt Universal Seconds
for 60cc Sample, s
3. Stormer Viscometer
Glycerin Calibration Runs
Run
Temperature, ºC
1
Same as above
2
Same as above
Motor Oil Runs
1
Same as above
2
Same as above
Hung Mass, g
Time for 20 revs, s
.
Last Rev.: 17 MAY 08
VISCOSITY : MIME 3470
Page 8