TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES
938 Aurora Boulevard, Cubao, 1109 Quezon City

FLUID MECHANICS
CE 023
CE31S2

Experiment No. 4: FALL VELOCITY OF SPHERE

Finals

Submitted By:
1913643
MONTILLA, GLADIES JOY A.

Submitted To:
ENGR. JOSEPH ANGELO R. SABIO
Instructor

Date Submitted:
November 17, 2021
 Experiment No. 4
Fall Velocity of Sphere
Objective:
The activity aims to determine the viscosity of the fluid by measuring the fall velocity of the sphere.
Intended Learning Outcomes (ILOs):
The students shall be able to use the techniques and skills in fluid mechanics to determine the viscosity of fluid
using fall velocity measurement; and apply the techniques and skills acquired relevant to professional
engineering practice.
Discussion:

The Falling Sphere Viscometer

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 test. In this experiment, viscosity
will be measured with a 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

4 3 4 3
ρs g πR −ρg πR −6 πµVR=0 (4.1)
3 3

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:

ρVD
<1 (4.2)
µ

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.
Resources/Instruments Required:

● Graduated cylinder
● Scale
● Stopwatch
● Several small spheres with weight and diameter to be measured
● Test liquid
● Caliper
● Ruler

Procedure:

1. Fill the graduated cylinder with fluid up to about 3 cm below the rim of the tube. Drop a sphere into the
cylinder 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.
2. Repeat the measurement and average the results. With the terminal velocity of this and of other spheres
measured and known, the absolute and kinematics viscosity of the liquid can be calculated.

Terminal velocity measurement (V = d/time)

3. The temperature of the test liquid should also be recorded. Use at least three different spheres.
Data and Results:

(Oil)

Distance Absolute Kinematic

Trial Sphere Diameter (m) (m) Time (s) Weight (kg) viscosity viscosity
μ (Pa-s) Ѵ (m2/s)
1 0.015 0.185 0.14 0.004
2 0.019 0.185 0.13 0.010
3 0.026 0.185 0.08 0.023

(Diesel)

Distance
Trial Sphere Diameter (m) Time (s) Weight (kg) μ (Pa-s) Ѵ (m2/s)
(m)
1 0.015 0.185 0.42 0.004 0.3678 0.000414
2 0.019 0.185 0.33 0.010 0.6578 0.000723
3 0.026 0.185 0.23 0.023 0.728 .0008

(Kerosene)

Distance
Trial Sphere Diameter (m) Time (s) Weight (kg) μ (Pa-s) Ѵ (m2/s)
(m)
1 0.015 0.185 0.13 0.004 0.1278 0.000164
2 0.019 0.185 0.12 0.010 0.2558 0.000328
3 0.026 0.185 0.09 0.023 0.3081 0.000395

Computation:

Weight of Sphere – Buoyant force = Drag force

(msphere)g –(SG*Yw)(Vdisplaced) = 6π (μ)(R)(velocity)

For μ :

4 3
(mass sphere)(9.81) – (SG)( γ water ¿ ( π R ) = 6π (μ)(R)(velocity)
3
Documentation:
Observation:

In the experiment, the sphere was repeatedly dropped and the time was recorded. Among the three
liquids, oil has the longest settling time in all the trials using different spheres.

Conclusion:

Based on the experiment, we therefore conclude that oil has the highest viscosity among the liquids
used. Consequently, the more viscous the liquid used is, the more time it would take for an object to
settle in that liquid.
Additional Situation:

1. Given the data for oil in the conducted experiment, compute for the absolute viscosity and
kinematic viscosity in the three trials below. Use SG of oil = 0.91.
Note: To solve for the missing variables, read the manual. Provide solutions for all the
unknowns.

(Oil)

Distance Absolute Kinematic

(m) Weight
Trial Sphere Diameter (m) Time (s) viscosity viscosity
(kg)
μ (Pa-s) Ѵ (m2/s)
0.185 0.1256 1.5701×10-4
1 0.015 0.14 0.004
kg/ms m2/s
0.185 0.2591 3.2394×10-4
2 0.019 0.13 0.010
kg/ms m2/s
0.185 0.2532 3.1649×10-4
3 0.026 0.08 0.023
kg/ms m2/s

Computation:
Weight of Sphere – Buoyant force – Drag force = 0

(msphere)g –(SG*Yw)(Vdisplaced ) – 6π (μ)(R)(velocity) = 0

For μ :

4 3
(mass sphere)(9.81) – (SG)( γ water ¿ ( π R ) = 6π (μ)(R)(velocity)
3

Trial 1
Given: Solution:
msphere = 0.004 kg v = (distance(d)/time(t))
m m
g = 9.81 v = (0.185/0.14) =1.321428571
s2 s2
4 3
SGoil = 0.91 (mass sphere )(9.81) – (SG)( γ water ¿ ( π R ) = 6π (μ)(R)(v)
3

γ water = 9.81
kN
m3 [ (0.004 kg)(9.81
m
s2 ]
) -¿

D = 0.015 m [ 3
= 6 π (μ) ( 0.0075 ) (1.321428571
m
s2
)
]
R = (D/2) = 0.0075 m μ = 0.2100 (Pa-s)
 μ(Pa−s) 0.2100 kg /m∙ s
V= V=
d = 0.185 m ρoil ¿ 3
950 kg/m ¿
¿ ¿
t = 0.14 s V =¿ 2.2105×10-4 m2/s
ρoil kg
¿ = 950
¿ m3

Trial 2
Given: Solution:
msphere = 0.010 kg v = (distance(d)/time(t))
m m
g = 9.81 2 v = (0.185/0.13) =1.423076923
s s2
4 3
SGoil = 0.91 (mass sphere )(9.81) – (SG)( γ water ¿ ( π R ) = 6π (μ)(R)(v)
3

γ water = 9.81
kN
m3 [ (0.010 kg)( 9.81
m
s2 ]
)-¿

D = 0.019 m [ 3
= 6 π (μ) ( 0.0095 ) (1.423076923
m
s2
)
]
R = (D/2) = 0.0095 m μ = 0.3848 (Pa-s)
μ(Pa−s) 0.3848 kg /m∙ s
V= V=
d = 0.185 m ρoil ¿ 950 kg/m3 ¿
¿ ¿
t = 0.13 s V =¿ 4.0505×10-4 m2/s
ρoil kg
¿ = 950
¿ m3

Trial 2
Given: Solution:
msphere = 0.023 kg v = (distance(d)/time(t))
m m
g = 9.81 v = (0.185/0.08) =2.3125
s2 s2
4 3
SGoil = 0.91 (mass sphere )(9.81) – (SG)( γ water ¿ ( π R ) = 6π (μ)(R)(v)
3

γ water = 9.81
kN
m3 [ (0.023 kg)(9.81
m
s2 ]
)-¿

D = 0.023 m [ 3
= 6 π (μ) ( 0.013 ) (2.3125
m
s2
)
]
R = (D/2) = 0.013 m μ = 0.3980 (Pa-s)
Conclusion:

In conclusion, the student was able to identify the viscosity of the fluid particularly the oil by
measuring the fall velocity of the sphere by the conducted experiment. For the Additional situation,
the students are given a task to fill out the table containing computation for both unknown viscosity
wherein having the increases toward the quantity of mass and velocity as well as the volume of the
sphere will resulted in increasing value also of the Absolute Viscosity (μ) and Kinematic Viscosity
(V) and it will be accounted on how viscous the liquid it is, thus, relating to the outcome of each trial,
the third trial give a more amount of viscosity, therefore, the oil in the last trial is thicker among the
other trials and has higher resistance of the fluid flow. Thus, the activity is carried to ensure that the
student applies the techniques and skills obtained with the incline to the engineering operation.

References:

 Science Learning Hub (2007). Viscosity-Pouring liquid water. The University of Waikato.
https://www.sciencelearn.org.nz/resources/1500-viscosity
Assessment (Rubric for Laboratory Performance):
BEGINNER ACCEPTABLE PROFICIENT
CRITERIA SCORE
1 2 3
I. Laboratory Skills
Members occasionally Members always
Manipulative Members do not demonstrate
demonstrate needed demonstrate needed
Skills needed skills.
skills skills.
Members are able to Members are able to
Experimental  Members are unable to set-up
set-up the materials set-up the material with
Set-up the materials.
with supervision. minimum supervision.
Members occasionally Members always
Members do not demonstrate
Process Skills demonstrate targeted demonstrate targeted
targeted process skills.
process skills. process skills.
Members follow safety Members follow safety
Safety Members do not follow safety
precautions most of the precautions at all
Precautions precautions.
time. times.
II. Work Habits 
Time Members finish ahead
Management / Members do not finish on time Members finish on time of time with complete
Conduct of with incomplete data. with incomplete data. data and time to revise
Experiment data.
Members have defined Members are on tasks
Members do not know their
responsibilities most of and have defined
tasks and have no defined
Cooperative the time.  Group responsibilities at all
responsibilities.  Group
and Teamwork conflicts are times.  Group conflicts
conflicts have to be settled by
cooperatively managed are cooperatively
the teacher.
most of the time. managed at all times.
Clean and orderly
Clean and orderly
workplace with
Neatness and Messy workplace during and workplace at all times
occasional mess during
Orderliness after the experiment. during and after the
and after the
experiment.
experiment.
Ability to do Members require Members do not need
Members require supervision
independent occasional supervision to be supervised by the
by the teacher.
work by the teacher. teacher.
Other Comments/Observations: Total Score
(TotalScore)
Rating = x 100
24