Eastern Mediterranean University
Department of Mechanical Engineering
Laboratory Handout
COURSE: FLUID MECHANICS MENG 353
Semester: Spring ( 2012-2013 )
Name of Experiment: Determination of the viscosity
Instructor: Assist. Prof. Dr. Hasan Hacışevki
Name and Surname:
Student No:
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Date of experiment: ……………….
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EVALUATION
Activity During Experiment & Procedure
30 %
Data , Results & Graphs
35 %
Discussion, Conclusion & Answer to Questions
30 %
Neat and tidy report writing
5%
Overall Mark
Table of Contents
Object ………………………………………..………………………….…………... p. 1
Theory …………………………………………………………………………….....…p. 1
Procedure ………………………………………………………………………….........p. 2-3
Results ………………………………………………………………...……………......p. 3-4
Discussion and Conclusion …………………………………………………..……..…p.4
Appendix ……………………………………………………..…….……………...........p. 5-6
Object
The object of this fluid property experiment was to determine the viscosity of a
particular homogenous fluid using the falling sphere viscometer method.
Theory
Viscosity is a fluid property defined as the fluid’s resistance to an externally applied
shear. From this definition, it is implied that a fluid will resist any change in form. If a
solid object is placed in a fluid that has a lesser density, the object will fall through the
fluid medium. As the object falls, it exerts a shear force on the fluid. Thus, the fluid is
displaced and exerts a force on the object. The forces present during this
process are weight due to gravity, the buoyant force and the drag force as shown below in
a force balance equation (Equation 1, below).
Weight – Buoyant Force – Drag Force = 0
(Eq. 1)
ρsg(4/3)πR3 – ρg(4/3)πR3 - 6πμVR = 0
(Eq. 2)
Equation 2 is a less general form of the force balance equation and illustrates the
importance of the falling object’s geometry and motion in relation to the forces present.
A graphical representation of the above equations can be seen in Figure 1. The
components of the equation are as follows:
ρs – density of the object
ρ – density of the fluid
g – gravitational acceleration
R – radius of the object
µ – viscosity of the fluid
V – terminal velocity of the object
The force of weight in Equation 2 is due to the gravitational acceleration of the object and
acts in the downward direction. The density of the object is directly related to the
magnitude of this acceleration. The more dense object is, the greater the weight.
The buoyant force in Equation 2 is caused by the pressure gradient exerted by the fluid on
the object. The lateral forces of this pressure are equal and opposite and therefore negate
one another. The pressure on the submerged object acting in the vertical is lesser on the
top than on the bottom and exerts a net upward force on the object.
The drag force in Equation 2 acts in the opposite direction of the relative motion of the
object traveling through the fluid. Therefore, the force acts in the direction of the fluid
flow. The cause of the drag force is due to the viscous effects of the fluid on the surface
of the submerged object.
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Procedure
Equipment:
Figure 2: 28 mm diameter
rubber Sphere
Figure 3: Digital Stopwatch
Figure 1: Cylinder filled with water.
ρ = 1000 kg/m3
Figure 4: Calipers
Experiment:
1) Measure the diameter of the rubber balls with the calipers and record the measurements
onto a data sheet. It is better to select bearings that have identical diameters. Make note of
the density of the material used in the bearings.
2) Make note of the ambient temperature where the experiment is being performed, as
density is a function of the temperature of the fluid.
3) Fill a transparent tube with a particular fluid of a known density. Affixed to the tube should
be a ruler so that velocity measurements can be made. The tube should be topped with a cap
that has a hole in the center large enough for the bearing to ensure that the bearing will travel
down the center if the cylinder.
4) Drop one stainless steel bearing into the fluid filled cylinder and observe the position
relative to the ruler at which the bearing achieves terminal velocity. Let this point be the initial
point from which time measurements are made. Assign another arbitrary point at which the
time measurement will cease.
5) After the distance for time measurement has been assigned, proceed to drop another bearing
into the fluid. When the bearing reaches the assigned point for beginning time measurements,
start a stopwatch. Stop the stopwatch when the bearing has reached the assigned terminus.
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Record the time taken to travel between the two assigned points. Repeat this step four more
times and record the times.
6) Average the times recorded from Step 5. Use this time to determine the terminal velocity of
the falling sphere by the assigned distance by the averaged time. This velocity will be used to
determine the drag force.
7) Use the terminal velocity calculated in Step 6, the respective densities of the fluid and
sphere, radius of the sphere and gravitational acceleration in Equation 2. Rearrange the
expression algebraically to solve for the viscosity, µ.
µ = [ρg(4/3)πR3 - ρsg(4/3)πR3] / 6πVR
(Equation 3)
Results
Table 1: Initial Measurements
Rubber Ball Bearing Density
Rubber Ball Bearing Diameter
Water Density
Displacement on Scale
Ambient Lab. Temperature
ρs = ......... kg/m3
D = ......... mm
ρ = 1000 kg/m3
z = ......... m
T = ........ oC
Table 2: Time Trials
Trial #
Time (s)
1
2
3
4
5
tavg =
Initial conditions seen in Table 1 were measured with the exception of the density of the rubber
ball. The value for this density was pulled from a professionally published source. The density
of the water was measured using a hydrometer. The lab temperature was also recorded for the
purposes of ascertaining the temperature of the shampoo used in this experiment.
After dropping the rubber sphere into the fluid filled cylinder five successive times and
averaging the recorded times, the terminal velocity was calculated.
V = z/tave  V = ........................ m/s
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The terminal velocity was the remaining unknown value for Equation 3. Substituting
this value into the equation calculates the viscosity of the shampoo.
µ = [ρsg(4/3)πR3 - ρg(4/3)πR3] / 6πVR = ................ N.s/m2
Note: Repeat these for both rubber balls.
Discussion & Conclusion
The terminal velocity of two different size spheres would not be identical. Assuming the spheres
were made of the same material, a change in the geometry of the sphere would alter its weight
and therefore alter the force it exerted on the fluid. For this experiment, a smaller sphere
dropped from the same height would reach a higher terminal velocity due to the smaller amount
of surface area in contact with the viscous material. In turn, a larger sphere would have a larger
surface area and would therefore have more surface contact with the viscous fluid and have a
lower terminal velocity.
The viscosity would be the same for spheres of varying size because viscosity is a property of
the fluid and not of the sphere. The geometry of the sphere will influence the terminal velocity,
which is proportional to the radius of the sphere. Therefore a larger sphere, with increased mass,
would travel at a higher velocity.
There are various shortcomings in the measurements taken for this experiment. Due to human
error, the time measurements for this experiment are not exact. An observer must “eyeball”
the entirety of the sphere’s travel across the displacement. Introducing automation to this
experiment for the purposes of timing would increase its accuracy.
The temperature for this experiment needs to be recorded because it will affect the density of the
liquid medium. The higher the temperature, the less dense the material will become. This is the
result of thermal expansion. The opposite can be said of a cold fluid, which will be denser. The
density of the fluid has a direct correlation with its viscosity, which can be deduced by Eq. 2.
This method can be used for gases; however, it would not produce desirable results. It would be
difficult without automation to record the velocity of the object over a short distance such as that
in this experiment.
This method could be used for opaque fluids, though it would require specialized
instrumentation. In order to perform a falling sphere viscometer experiment with opaque fluids,
some sort of imaging technology would be required to keep track of the falling object. It is
possible to do this using, for instance, thermal imaging. If the sphere were at a different
temperature than the fluid, it could be tracked as it passed through the fluid.
As long as the sphere has a higher density than the test fluid, this experiment can be
performed on a variety of opaque fluid. However, this method will not work on
inhomogeneous fluids such.
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