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ESM 3024 Lab:
Experiment #1
Measurements of Fluid Properties – Density and Viscosity
Authors:
Drew Lovell
John Naessens
Date: 9/9/14 Time: 2:00 – 4:50 p.m.

Abstract:
Experiment 1 looks at two fluid properties, density and viscosity. Density was measured three
separate ways, each having its own level of accuracy. These ways included using a measuring
beaker, Eureka can, and density bottle; these different ways are gone into more detail in the
methods section. Viscosity of these specimens was then found by using a falling sphere
viscometer, which will also be explained in the methods section. The reason this experiment
was conducted is that all fluids experience forces which cause motion throughout the flow.
Understanding how fluids work and react to forces is important in many areas of life and across
many fields. The results that were found displayed these characteristics and showed how
density and viscosity can be calculated through a variety of procedures.
Introduction:
This experiment was performed to see how fluids are affected by their density and viscosity.
Density is the measure of mass per unit volume and is denoted by the symbol, ρ. This
measurement allows Newton’s Second Law to be applied to fluids on a “per unit volume” basis.
The mass of the object is generally measured by a balance or scale, as where volume can be
measured by water displacement, or by simply by calculating it using the objects parameters.
Viscosity on the other hand is the measure of a fluids resistance to deformation. The more
viscous a fluid is, the more resistance or thickness it will display. Viscosity is found through an
equation which utilizes the object’s radius, densities of both the fluid and object suspended,
and gravitational force. Both of these fluid properties can be seen in daily life since everything
has density and every fluid has a viscosity.
Motivation:
The reason for completing this experiment was to learn how to calculate these fluid properties
and to gain a better knowledge on measuring them accurately. Knowing how density and
viscosity work is important for flotation, mixing of materials, fluid dynamics, and many other
real world cases one might come into contact with. When measuring densities, the error of the
experiment’s calculations compared to actual values shows which method of taking density is
more reliable. And when using the falling sphere viscometer it was also seen how accurate the
gathered values were in comparison to actual known values. Comparing the data in this way
indicates how close one can get to the actual values and how calculating viscosity and density is
necessary for other practices.

Methods:
1.1.1 Density of Water using Measuring Beaker
Density of water was calculated using a measuring beaker. Density is mass over volume.
The mass of water was determined by using a scale and finding the difference in the mass of
the beaker and the mass of a beaker with a designated volume of water.
a) Measure mass of beaker
b) Fill beaker with water, record volume
c) Measure mass of beaker and water
d) Calculate mass H2O
e) Calculate density (Mass/Volume)
f) Record possible error sources
1.1.2 Density of Water using Eureka Can
Density of water was calculated using a Eureka can. A
Eureka can is a metal can with a spout coming out the side. The
can was filled with water until the water came out of the spout.
The volume of three solid spheres was calculated by measuring
their diameter and using the volume equation for a sphere. The
volume of the spheres was the volume of water displaced from
the Eureka can. The spheres were dropped into the Eureka can
and the displaced water was collected in a beaker. The mass of
water was determined by using a scale and finding the difference
in the mass of the beaker and the mass of a beaker with a
designated volume of water. The density was calculated using
mass/volume.
a) Calculate volume of three solid spheres provided
b) Fill eureka can until water flows through spout, wait for flow to stop.
c) Measure mass of beaker
d) Place beaker under eureka can spout and place three spheres into eureka can. Allow
beaker to collect water overflowing out of the spout and wait for the flow to stop.
e) Measure mass of beaker and collected water.
f) Calculate mass H2O
g) Calculate density Mass/Volume
h) Record possible error sources

1.1.3 Density of Water using Density Bottle
Density of water was calculated using a density bottle. The
mass of the dried density bottle was measured using a scale. The
bottle was filled with water and the outside was dried. The mass of
the density bottle and water was measured using a scale. The mass
of water was determined by finding the difference in the mass of
the density bottle and the mass of the density bottle filled with
water. The volume of the density bottle was 25ml. The density of
the water was calculated using mass/volume.
a) Obtain 25 ml bottle and stopper, measure mass
b) Fill density bottle with water until it overflows, place stopper on top
c) Dry outside of density bottle
d) Measure mass of density bottle with water
e) Calculate mass H2O
f) Calculate density Mass/Volume
g) Record possible error sources
1.1.4 Specific Weight of Glycerin and Castor Oil using a Hydrometer
The specific weight of gylcerin and castor oil was
calculated by using a hydrometer. A hydrometer was placed
into each fluid to record the specific gravity. The specific gravity
was used to calculate the density by multiplying the specific
gravity by the density of water. The specific weight was
calculated by multiplying the specific gravity with the specific
weight of water. Calculated specific weight was compared to
known specific weight to obtain percent error.
a) Obtain two tall glass cylinders, one filled with castor oil and the other filled with glycerin
b) Insert hydrometer into each fluid without contacting glass cylinder walls and wait for it
to settle
c) Record hydrometer level at bottom of meniscus
d) Calculate density, specific weight, error

1.1.5 Data Analysis
The three values for density of water obtained in methods 1.1.1-3 were compared to
the standard density of water. The most accurate method was determined and explained.
Specific weights of glycerin and castor oil were compared to standard specific weights.
Percentage error was explained.
1.3.1 Viscosity using falling spheres
The viscosity of castor oil and glycerin were obtained using falling spheres.
Spheres of three different sizes were individually dropped into each fluid. The
distance they traveled through the fluid and the time it took to travel that distance
was recorded. Each sized sphere was dropped three times in each fluid and the
values were averaged. The velocities were calculated and used to determine the
dynamic and kinematic velocities.
a) Measure the mass of 10 spheres of each size and record, calculate mass of a single
sphere and record. Calculate the volume of each sized sphere and record.
b) Measure distance between timing bands on each cylinder (castor oil and glycerin) and
record
c) Drop each sized ball three times in each fluid. For every drop record the time it takes the
ball to drop from one timing band to the other
d) Calculate viscocity, dynamic and kinematic
Results & Discussions
1.1.1 Density of Water using Measuring Beaker
See Table 1.2 in appendix for data
Mass of water = Mass of Beaker and Water – Mass of Empty Beaker
Density of water = Mass Water / Volume Water * 103
Density of water = 963.83 kg/m3
1.1.2 Density of Water using Eureka Can
See table 1.3 in appendix for data
Volume of sphere = 4/3*π*r3
Mass of Displaced Water = Mass of Beaker and Water – Mass of Empty Beaker
1.1.3 Density of Water using Density Bottle

Mass of water = Mass of Bottle and Water – Mass of Empty Bottle
1.1.4 Specific Weight of Glycerin and Castor Oil using a Hydrometer
Density Calculated = Specific Gravity * 1000 kg/m3
Specific Weight Calculated = Specific Gravity * 981 N/m3
% error = abs((Actual – Calculated)/Actual)
Specific Weight Glycerin Calculated = 9466.65 %Error = .521
Specific Weight Castor Oil Calculated = 12360.6 %Error = .318
Error due to accuracy of meniscus reading
1.1.5 Data Analysis
The most accurate density achieved was the density of water using the density bottle.
The true density of water is 1000 kg/m3. The second most accurate density achieved was the
density of water using a measuring beaker. The least accurate density achieved was the density
of water using a Eureka can. The most accurate density was the density bottle because the
density bottle is built to have an exact volume of water, removing human error in reading a
meniscus, which is done using the measuring beaker of Eureka can.
1.3.1 Viscosity using falling spheres
See Table 1.6 in Appendix for Sphere density data
Volume of sphere = 4/3*π*r3
Density of Sphere = Mass of one sphere / Volume * 102
See Table 1.7 in appendix for Viscosity of Glycerin data, 1.8 for Castor Oil
Velocity = Distance/Time
μ = 2/(9u)*r2*(9.81)(ρs- ρf) ρf = 1126.1 kg/m3
ν = μ/ρ
Re = ρUD/μ
μ calculated Glycerin = 1.00, 1.08, 1.08
% error = 32.9, 27.5, 27.5
μ calculated Castor Oil = .891, .961, .966
% error = 9.6, 9.5, 9.5
Glycerin held a high percentage error. This was due to human error in recording the
time it took to travel through the time bands and a low level of glycerin (there was no more
glycerin to raise the level). The low level of glycerin caused the spheres to drop past the first
time band very quickly and prevent an accurate starting time. The percentage error of Castor oil
was relatively low compared to that of Glycerin.

Conclusion
The density of water was calculated using a measuring beaker, eureka can, and density
bottle. The density bottle was the most accurate way to measure the density of the water with
a density of 988.08 kg/m3. The density bottle accuracy was followed by the measuring beaker
then eureka can, which had error due to reading the meniscus. The specific weight of glycerin
and castor oil were measured using a hydrometer. The hydrometer was very accurate with a
percentage of error for glycerin of .521% and .318% for castor oil. The specific weight values
obtained were 9467 (unitless) for castor oil and 12361 (unitless) for glycerin. The viscosities of
glycerin and castor oil were measured using falling spheres. The viscosity of glycerin had a high
average percentage error of 29.3% due to a lack of glycerin, which caused a misreading of the
time it took to travel from time band to time band. Castor oil had a low average percentage
error, relative to glycerin, at 9.5%. The values for viscosities and Reynold’s numbers can be seen
in tables 1.7 and 1.8 of the appendix.

References:
i. For Accepted Standard Values
A. www.simmetric.co.uk/si_liquids.htm
B. www.science.uwaterloo.ca/~cchieh/caet/c123/liquid.htm
ii. Virginia Tech ESM 3024 Experiment 1 Lab Manual
iii. Pictures
A. Eureka Can
http://www.andersonscientific.co.uk/images/medium/6165-01.jpg
B. Density Bottle http://www.mrs-scientific.
com/images/products/pics/WJ76.jpg
C. Hydrometer http://avogadro-lab-supply.
com/images/eBay/Hydrometer%20Reading.JPG
D. Falling Sphere
http://upload.wikimedia.org/wikipedia/commons/7/7b/Falling_Sphe
re_Viscometer.gif

Appendix
Castor Oil Density at 25˚C, ρ 956.12 kg/m^3
Absolute Viscocity μ .986 kg/(ms)
Glycerin Density at 25˚C, ρ 1126.10 kg/m^3
Absolute Viscocity μ 1.49 kg/(ms)
Table 1.1: Accepted Standard Values
Mass of Empty
Beaker
Measured (g)
Volume of
Water in
Beaker
Measured (ml)
Mass of Beaker
and Water
Measured (g)
Mass of
Water
Calculated (g)
Density of
Water
Calculated
(kg/m)
52.705 80 129.811 77.106 963.825
Table 1.2: Water Density Using the Measuring Beaker
Volume of
Solid Object
Calculated
from
Measured
Dimensions
(cm^3)
Mass of Empty
Beaker
Measured (g)
Mass of Beaker
and Water
Measured (g)
Mass of
Displaced
Water
Calculated (g)
Density of
Water
Calculated
(kg/m^3)
20.0424 52.705 71.506 18.801 938.061
Table 1.3: Water Density Using the Eureka Can
Volume of
Density Bottle
known (ml)
Mass of Bottle
Measured (g)
Mass of bottle,
stopper, and
water
Measured (g)
Mass of
Water
Calculated (g)
Density of
Water
Calculated
(kg/m^3)
25 21.802 46.504 24.702 988.08
Table 1.4: Water Density Using the Density Bottle

Liquid
Specific
Gravity
Measured
(unit-less)
Density
Calculated
(kg/m^3)
Specific
Weight
Calculated
(N/m^3)
Standard
Specific
Weight
Known
(N/m^3)
% Error
Between
Stand and
Calculated
S.W.
Calculated
Castor Oil 0.965 965 9466.65 9417.6 0.521
Glycerin 1.26 1260 12360.6 12400 0.318
Table 1.5: Specific Weights of Glycerin and Castor Oil
Diameter
Measured
(cm^3)
Volume
Calculated
(cm^3)
Number of
Spheres
Massed
Total Mass of
all Spheres
Measured (g)
Mass of
one
Sphere
Calculated
(g)
Density of
Spheres
Calculated
(kg/m^3)
0.199 0.00413 10 0.3 0.03 7270.49
0.299 0.0139 10 1.1 0.11 7859.24
0.399 0.0333 10 2.6 0.26 7817.29
Table 1.6: Data Sheet for Sphere Density
Diameter
Measured
(cm)
Time
i (s)
Time
ii (s)
Time
iii (s)
Table 1.7: Viscosity of Glycerin
Dist.
Sphere
Falls
(mm)
Table 1.8: Viscosity of Castor Oil
Vel I
(m/s)
Vel ii
(m/s)
Vel iii
(m/s)
Mean
Vel
(m/s)
μ
(Ns/
m^2)
ν (m^2/s)
Re
Calc'd
Stand
ard μ
(Ns/
m^2)
%
Error
for μ
0.199 18.06 18.4 18.47 242 0.0134 0.0132 0.0131 0.013 1.00 8.88*10^-4 0.0296 1.49 32.9
0.299 7.93 7.97 7.94 242 0.0305 0.0304 0.0305 0.031 1.08 9.59*10^-4 0.0951 1.49 27.5
0.399 4.53 4.47 4.47 242 0.0534 0.0541 0.0541 0.054 1.08 9.59*10^-4 0.2240 1.49 27.5
Diameter
Measured
(cm)
Time
i (s)
Time
ii (s)
Time
iii (s)
Dist.
Sphere
Falls
(mm)
Vel I
(m/s)
Vel ii
(m/s)
Vel iii
(m/s)
Mean
Vel
(m/s)
μ
(Ns/
m^2)
ν (m^2/s)
Re
Calc'd
Stand
ard μ
(Ns/
m^2)
%
Error
for μ
0.199 15.75 16.13 16.06 250 0.0150 0.015 0.016 0.015 0.89 9.32*10^-4 0.0327 0.986 9.6
0.299 7.93 7.97 7.94 242 0.0305 0.0304 0.0305 0.031 1.08 1.01*10^-3 0.0807 0.986 9.5
0.399 4.53 4.47 4.47 242 0.0534 0.0541 0.0541 0.054 1.08 1.01*10^-3 0.1904 0.986 9.5

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