EXPERIMENTAL ENGINEERING - Duygu Erdem Viscometer Experiment Semih Kalma 110180729 - Mehmet Batuhan Başyiğit

EXPERIMENTAL ENGINEERING
 Duygu Erdem

 Viscometer Experiment

 Semih Kalma
 110180729

 Buğrahan Bayraktar
 110170150

 Mehmet Batuhan Başyiğit
 110160121

Introduction
 The purpose of this experiment is measuring the viscosity of a selected fluid. This
selected fluid in our case is honey. The viscosity of a fluid is a measure of its resistance to
deformation at a given rate. To better observation, we want a uniform and non-turbulent flow,
another expression we want to do our experiment in creeping flow conditions. Flows with
Reynolds number is close to 0 (less than 1) are called creeping flows, and they occur at low
flow speeds of viscous fluids past small objects.

 Experimental Setup and Method
 Our experimental setup was inspired from Höbbler’s falling ball viscometer, so we
followed the same principles. The Falling Ball Viscometer is based on the measuring
principle by Höppler for simple but precise dynamic viscosity measurement of transparent
Newtonian fluids. The basic concept is to measure the elapsed time required for the ball to fall
under gravity through a sample-filled tube. Höbbler’s experimental setup is used a tube
inclined with an angle, commonly 80 degrees, but in our experiment our tube is perpendicular
to the surface so we expect a free fall from the object in the fluid.
 Where ∆ is measuring distance and ∆ is the time required for the ball to pass through
this measuring distance. To obtain better data in the time of falling we used our phone’s slow
motion camera feature. 240 Frame per second camera footage gave us a more precise falling
time. The velocity of the spherical object in the fluid can be calculated as given below.
 ∆ 
 =
 ∆ 

The physicist George Gabriel Stokes derived the following equation, which shows the
relationship between the speed v at which a sphere of radius r is drawn through a fluid of
viscosity η and the resulting frictional force
 = 6 

 If a ball is dropped in a viscous liquid, the speed increases at first until the opposing
frictional force is as great as the weight force of the ball. For more accurate measurements,
the upward buoyant force must also be taken into account. frictional force, gravitational
force, buoyant force, all three forces balance each other in the steady case and a constant
sinking speed is obtained.
 = + 

 The weight force of the ball can be determined via the volume and the density of
the ball 
 4
 = = = 3 
 3
 The buoyant force Fb is determined on the principles of Archimedes from the weight
force of the displaced liquid, whereby the displaced volume corresponds exactly to the
volume of the ball.
 4
 = = = 3 
 3

 When viscous forces, buoyancy force and gravitational forces are combined we can
obtain equations below
 4 3 4
 ∗ = 6 + 3 
 3 3

 4 4
 6 = 3 ∗ − 3 
 3 3

 4 3
 6 = ( − )
 3

 2 2 
 = ( − )
 9 

Finally, viscosity can be found as below
 
 = ( − )∆ 
 ∆ 

 As we mentioned at the beginning of this section, to obtain creeping flow conditions
Reynolds number must be close to zero. In other words, situations where the Reynolds
number is below 1 meet this condition.

 Our balls radiuses are 10mm, 16mm, 25mm respectively.
 Marbles are made of glass and density of glass is 2500 / 3
 The density of honey at 20 degree Celsius is 1419.8 / 3 .
 And, where at 20 degree Celsius dynamic viscosity of honey is 14.095 . 
 Formula of Reynolds number is
 
 =

fluid, else there will be flow effects between the ball and the wall of graduated cylinder that
can no longer be neglected such as shear forces. In our cases the radius difference between
marbles and graduated cylinder is not so high, so we add another parameter in calculation
which is called Ladenburg Factor.
 Where L, Ladenburg Factor, can be calculated as
 
 = 1 + 2.1
 
 R is the inner diameter of graduated cylinder and r is the diameter of marbles.
Eventually the viscosity can be calculated as below
 
 = ( − )∆ 
 ∆ 

Results
 Our experiment was done at 20 degrees Celsius, and the viscosity and density of
honey at this temperature is 14.095 ∗ and 1419.8 / 3 respectively.

 Marble Diameter (m) 0.01 0.016 0.025

 ∆ (second) 28 17 11

 V (m/s) 0.00393 0.00647 0.01

 Ladenburg Factor 1.525 1.84 2.3125

 Viscosity (Pa.s) 11.890 12.658 15.911

 Reynolds Number 0.00469 0.01161 0.02231

 Difference % -15.6% -10.2% 12.9%

 The blue line is real absolute viscosity value of honey at 20 degrees Celsius which is
14.095 Pa.s and blue dots are calculated values by using data obtained from experiment.

Evaluation of Results
 First of all, we have to mention about reasons for errors in this experiment. First of all,
we don’t know the exact value of density of our marbles. We assume it is ordinary glass,
which density is 2500 / 3 . Also, this experiment was done at home conditions. That
means we don’t have a precise scientific equipment to measure variables in this experiment.
Falling time of marbles was observed with human eye. We used slow motion footage to get
better results but still our results are accurate in seconds.
 Now the interpretation of results. Our graduated cylinder’s diameter is not too much
higher than our marbles, especially biggest one. Due to this situation, there is an additional
friction of the liquid flowing past and a reduction in the sinking speed of the ball. We call this
principle of hydraulic damping. Because of the finite radius of the graduated cylinder, the
sinking speed of the ball is therefore always measured smaller in practice so we added an
empirical correction factor to viscosity calculation, which is called Ladenburg factor.
 We have obtained viscosity value of honey by using a research paper about
temperature effects on the viscosity of honey. In this paper there are eleven different types of
honey and we choose the one whose properties are most similar to our honey, but still we
don’t know the exact value of our honey’s absolute viscosity. However, first two experiment
was relatively correct, because the results of these two are close to each other and real value
of viscosity of honey.
 There is one more point we need to pay attention to, when the marble diameter is
increasing calculated absolute viscosity is also increasing. The biggest value of calculated
viscosity is 15.911 and this is our biggest marble. We have mentioned about Ladenburg factor
and difference between radius of marble and inner radius of graduated cylinder before. When
we increasing the size and Ladenburg factor is bigger than 1.1 than it leads to a compression
in the fluid. Falling marbles compress the fluid below it and the fluid tries to escape the
borders. This compression is the cause of an additional force. In addition to that, the shear
effects of fluid and inner side of graduated cylinder is also affected the falling marble. When
all of these effects combined there are some errors occur for biggest marble, and there is an in
uptrend in viscosity.

Conclusion
 A graduated cylinder with bigger inner radius and smaller marbles may give us better
results but in home conditions there are all we can do. For all three marble, the absolute
viscosity of honey was calculated as accurate as possible. And at the end error factors was
added to calculations. As a result, after all these simplifications and assumptions, the best
possible result was obtained.

References
Diego Gómez-Diaz, José M. Navaza & Lourdes C. Quintáns-Riveiro (2009). Effect of
Temperature on the Viscosity of Honey. International Journal of Food Properties, 12:2, 396-
404, DOI: 10.1080/10942910701813925

Sutterby, L. J. (1972). Falling Sphere Viscometer. Journal of Physics E: Scientific
Instruments, 22.

Francis, A. W. Arthur, L. D. (1933). Wall Effect in Falling Ball Method for Viscosity,
American Institute of Physics.

Munson, B. R. Young, D. F. Okiishi, T. H. Huebsch W. W. (2009). Fundamentals of Fluid
Mechanics (6th ed.). Wiley.

Kundu, P. Cohen, I. Dowling, D. (2016). Fluid Mechanics (6 th ed.). Elsevier.

Fulmer, E. I. Williams, J. C. (1935). A Method for the Determination of the Wall Correction
for the Falling Sphere Viscometer.