MECHANICS of FLUIDS LABORATORY - Mechanical Engineering

EXPERIMENT 2
FLUID PROPERTIES: VISCOSITY
One of the properties of homogeneous liquids
is their resistance to motion. A measure of this
resistance is known as viscosity. It can be
measured in different, standardized methods or
tests. In this experiment, viscosity will be
measured with a falling sphere viscometer.
The Falling Sphere Viscometer
When an object falls through a fluid medium,
the object reaches a constant final speed or
terminal velocity. If this terminal velocity is
sufficiently low, then the various forces acting on
the object can be described with exact expressions.
The forces acting on a sphere, for example, that is
falling at terminal velocity through a liquid are:
Weight - Buoyancy - Drag = 0
ρ s g 4 3 πR3 - ρg 4 3 πR3 - 6πµVR = 0
where ρ s and ρ are density of the sphere and
liquid respectively, V is the sphere’s terminal
velocity, R is the radius of the sphere and µ is
the viscosity of the liquid. In solving the
preceding equation, the viscosity of the liquid can
be determined. The above expression for drag is
valid only if the following equation is valid:
average the results. With the terminal velocity
of this and of other spheres measured and known,
the absolute and kinematic viscosity of the liquid
can be calculated. The temperature of the test
liquid should also be recorded. Use at least three
different spheres. (Note that if the density of
the liquid is unknown, it can be obtained from any
group who has completed or is taking data on
Experiment 1.)
Questions
1. Should the terminal velocity of two
different size spheres be the same?
2. Does a larger sphere have a higher
terminal velocity?
3. Should the viscosity found for two different
size spheres be the same? Why or why not?
4. If different size spheres give different
results for the viscosity, what are the error
sources? Calculate the % error and account
for all known error sources.
5. What are the shortcomings of this method?
6. Why should temperature be recorded.
7. Can this method be used for gases?
8. Can this method be used for opaque liquids?
9. Can this method be used for something like
peanut butter, or grease or flour dough?
Why or why not?
ρVD
µ < 1
where D is the sphere diameter. Once the
viscosity of the liquid is found, the above ratio
should be calculated to be certain that the
mathematical model gives an accurate
description of a sphere falling through the
liquid.
Equipment
Hydrometer cylinder
Scale
Stopwatch
Several small spheres with weight and
diameter to be measured
Test liquid
FIGURE 2.1. Terminal velocity measurement (V =
d/time).
V
d
Drop a sphere into the cylinder liquid and
record the time it takes for the sphere to fall a
certain measured distance. The distance divided
by the measured time gives the terminal velocity
of the sphere. Repeat the measurement and
9