1
57:020 Mechanics of Fluids & Transfer Processes
Exercise Notes for Fluid Property TM
Measurement of Density and Kinematic Viscosity
Marian Muste, Surajeet Ghosh, Stuart Breczinski, and Fred Stern
1.
Purpose
The purpose of this investigation is to provide
Handson
experience using a tabletop facility and simple
measurement systems to obtain fluid property measurements (density and kinematic viscosity), comparing results
with manufacturer values, and implementing standard EFD uncertainty analysis.
Additionally, this laboratory will
provide an introduction to camera settings and flow visualization for the ePIV system with a circular cylinder model.
2.
Experimental Design
2.1
Part 1:
For Determination of Fluid Properties
Common methods used for determining viscosity include the rotatingconcentriccylinder method (Engler
viscosimeter) and the capillaryflow method (Saybolt viscosimeter).
In the present experiment we will measure the
kinematic viscosity through its effect on a falling object in still fluid (figure1).
The maximum velocity attained by
an object in free fall (terminal velocity) is inversely proportional to the viscosity of the fluid through which it is
falling.
When terminal velocity is attained, the body experiences no acceleration, and so the forces acting on the
body are in equilibrium.
Figure 1.
Schematic of the experimental setup
The forces acting on the body are the gravitational force,
g
6
D
=
mg
=
F
sphere
g
3
π
ρ
(1)
the force due to buoyancy,
g
6
D
=
F
fluid
b
3
(2)
and the drag force, the resistance of the fluid to the motion of the body, which is similar to friction.
For
Re
<< 1 (
Re
is the Reynolds number, defined as
Re
=
VD
/
ν
), the drag force on a sphere is described by the Stokes expression,
D
V
3
=
F
fluid
d
ν
(3)
where,
D
is the sphere diameter,
fluid
is the density of the fluid,
sphere
is the density of the falling sphere,
is the
kinematic viscosity of the fluid,
V
is the velocity of the sphere through the fluid (in this case, the terminal velocity),
and
g
is the acceleration due to gravity (White 1994).
Once terminal velocity is achieved, a summation of the vertical forces must balance.
This gives:
λ
18
t
1)

/
(
g
D
=
fluid
sphere
2
/
)
(
(4)
where
t
is the time taken for the sphere to fall the vertical distance
λ
.
Using equation (4) for two different materials, Teflon and steel spheres, the following relationship for the
F
F
F
λ
V
Sphere
falling at
terminal
velocity
b
d
g
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density of the fluid is obtained, where subscripts
s
and
t
refer to the steel and Teflon spheres, respectively.
)
/(
)
(
2
t
D

t
D
t
D

t
D
=
s
2
s
t
t
s
s
2
s
t
t
2
t
fluid
ρ
(5)
In this experiment, we will drop spheres (Steel and Teflon), each set of spheres having a different density
and diameter, through a long transparent cylinder filled with glycerin (Figure 1).
Two horizontal lines are marked on
the vertical cylinder.
The sphere will reach terminal velocity before entering this region, and will fall between these
two lines at constant velocity.
We will measure the time required for the sphere to fall through the distance
λ
.
The
measurement system includes:
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 Fall '10
 FredrickStern
 Fluid Dynamics, Fluid Mechanics, mechanics, kinematic viscosity

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