ME317L Fluid Mechanics Lab 1: Hydrometers
Group members: Steven Dunkleberger, Carmen Sowers, Aubrey Pierce
Due: 02/13/2025
Professor: Dr. Larsen
TA: Ranjith Janardhana
Tuesday Lab
Group #1
Table
of
Contents
I. Objective ............................................................................................................................. ......................................3
II. Experimental Setup ................................................................................................................................................3
III. Theory ................................................................................................................. ...................................................4
IV. Procedure ............................................................................................................... ................................................5
V. Data ..........................................................................................................................................................................6
VI. Results/Calculations..................................................................................................... .........................................7
VII. Conclusion.............................................................................................................................................................8
VIII. Discussion Questions.................................................................................................................... ......................8
IX. References.............................................................................................................................................................11
List
of
Figures
Figure 1. Hydrometers used during experiment.......................................................................................................3
Figure 2. Graduated Cylinders with liquids used during experiment....................................................................4
List of Tables
Table 1. All the collected data from the experiment and the theoretical data found online
Table 2. The calculated percent error of the specific gravity of each of the fluids
Table 3. The calculated specific weight of all the fluids used in the experiments
I. Objective
This lab was used to understand the process of measuring the specific gravity of four different fluids. To do this, two
different types of hydrometers (heavy and light) were used.
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II. Experimental Setup
A. Equipment

Hydrometers
o
Coarse/fine

Graduated Cylinders Filled with One of these Fluids:
o
Ethylene Glycol
o
Water
o
Red Gage Oil
o
Unknown Mixture/Fluid

Thermometer
B. Setup
Four clean hydrometers were placed on the lab counter. Figure 1 shows the setup. Four graduated cylinders filled with
either Ethylene Glycol, water, Red Gage Oil, and an unknown mixture/fluid were also placed on the same counter. A
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graduated cylinder with water was placed to the side with a thermometer inside to monitor the room temperature.
Figure 2 shows the graduated cylinder and thermometer setup.
Figure 2: Graduated cylinders and thermometer
III. Theory
A. Nomenclature

γ = Specific Weight

ρ = Density

ρSTD = Density of pure water

v = Specific Volume

m = mass

g = Acceleration due to Gravity

SG = Specific Gravity of a Liquid

̊Be = Degree Baume Scale
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
SI = International System of Units

BG = British Gravitational System of Units
B. Theory
The lab’s purpose is to demonstrate a phenomenon known as the Archimedes Principle. The principle is
basically when an object is immersed in a fluid the buoyant force that acts on the object is equal to the weight of the
displaced fluid. Most know the story about when Archimedes discovered/realized this, he was in the bath and
immediately got out and began running naked in the streets shouting Eureka [1-2].
An object's density determines its specific gravity and specific weight, which also determines the degree on the Baume
scale since it’s directly related to specific gravity. Equations 2 and 3 are used to find specific gravity and weight,
respectively [3].
C. Pertinent Equations
𝜌 = 𝑚𝑣 (Eq. 1)
𝜌=
𝑚
𝑣
(Eq. 2)
𝜌𝑓𝑙𝑢𝑖𝑑 = 𝑆𝐺𝑓𝑙𝑢𝑖𝑑 × 𝜌𝑤𝑎𝑡𝑒𝑟 (Eq. 3)
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐷𝑖𝑠𝑐𝑟𝑒𝑝𝑒𝑛𝑐𝑦 (𝐸𝐷𝑃) =
𝑆𝐺𝑚𝑖𝑥 =
1
1
1
𝑥×
(1−𝑥)
𝑆𝐺𝑒𝑡ℎ𝑦𝑙𝑒𝑛𝑒 𝑔𝑙𝑦𝑐𝑜𝑙
𝑆𝐺𝑤𝑎𝑡𝑒𝑟
|𝑆𝐺𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 −𝑆𝐺𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙
𝑆𝐺𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
(Eq. 4)
(Eq. 5)
𝛾 = 𝜌𝑔 (Eq. 6)
IV. Procedure
1. All members of group 1 donned gloves upon entry into the fluids laboratory.
2. Lab members were briefed on the safety procedures and given an introduction to the lab procedures.
3. A clean, light hydrometer was inserted into the first liquid (if the reading was outside of the hydrometer’s range
then the heavy hydrometer would be inserted instead) and the reading was confirmed by two lab members.
4. The third lab member records the reading
5. The hydrometer was removed, cleaned, and dried.
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6. Repeat steps 3-5 for the rest of the liquids.
7. Recorded water at room temperature
V. Data
Table 1. Below is the table of all the collected data from the experiment and the theoretical data
Experimental (Water Temperature = 22.00 C)
̊Be
Fluid
Theoretical
Density
Density
SG
Water
̊Be
Density
Density
(H or L)
(kg/m3)
(slugs/ft3)
SG
(H or L)
(kg/m3)
(slugs/ft3)
1.00
L
997.77
1.936
1.00
L
1000
1.94
1.11
H
1107.5247
2.14896
1.1
H
1100
2.134
1.06
H
1057.6362
2.05216
1.05
H
1050
2.037
0.825
L
823.16025
1.5972
0.825
L
825
1.60244
Ethylene
Glycol
Mixture
Red
Oil
Gage
To determine specific gravity, the number is read off the appropriate (light or heavy) hydrometer that is suspended in
the liquid. Table 1 shows both the experimental and theoretical values for specific gravity, Baume values, and density
in both SI and English unit.
Table 2. The calculated percent error of the specific gravity of each of the fluids
Experimental SG
Water
Red Gage Oil
Ethlyene Glycol
Mixture
1.000
0.825
1.110
1.060
Theoretical SG
1.000
0.826
1.100
1.050
Experimental Percent
Discrepency
0
0.121065375
0.909090909
0.952380952
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Table 2 shows the discrepencies between the theoretical and experimental values collected during this experiment.
All values procurred during the experiment are within less than a 1 percent of the theoretical values.
VI. Results/Calculations
Once readings were taken from the hydrometers, the team identified the graduated cylinder with water based
off its specific gravity. To calculate the experimental density of each liquid for Table 1., Eq. 3 was used for both SI
and British units.
𝜌𝑅𝑒𝑑𝐺𝑎𝑔𝑒 = 𝑆𝐺𝑅𝑒𝑑𝐺𝑎𝑔𝑒 × 𝜌𝑤𝑎𝑡𝑒𝑟 = .825 ∗ 997.77
𝜌𝑅𝑒𝑑𝐺𝑎𝑔𝑒 = 𝑆𝐺𝑅𝑒𝑑𝐺𝑎𝑔𝑒 × 𝜌𝑤𝑎𝑡𝑒𝑟 = .825 ∗ 1.94
𝑘𝑔
= 823.16025
𝑚3
𝑠𝑙𝑢𝑔𝑠
𝑓𝑡 3
= 1.6005
𝑘𝑔
𝑚3
𝑠𝑙𝑢𝑔𝑠
𝑓𝑡 3
To find the SG of the mix, Eq. 5 was used.
𝑆𝐺𝑚𝑖𝑥 =
1
1
𝑆𝐺𝑒𝑡ℎ𝑦𝑙𝑒𝑛𝑒 𝑔𝑙𝑦𝑐𝑜𝑙
𝑥×
1
𝑆𝐺𝑤𝑎𝑡𝑒𝑟
(1−𝑥)
=
1
1
1
𝑥×
(1−𝑥)
1.1100
1.00
= 𝑥 = 57% 𝐸𝑡ℎ𝑙𝑦𝑒𝑛𝑒 𝐺𝑙𝑦𝑐𝑜𝑙
To find the experimental percent discrepancy, Eq. 4 was used. In this instance the table values for Red Gage oil were
used. The results were recorded in Table 2
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐷𝑖𝑠𝑐𝑟𝑒𝑝𝑒𝑛𝑐𝑦 (𝐸𝐷𝑃) =
|𝑆𝐺𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 − 𝑆𝐺𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 |
. 826 − .825
=
× 100%
𝑆𝐺𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
. 826
= .12%
VII. Conclusion
The purpose of this lab was to use a hydrometer to measure the specific gravity (SG) of various fluids and
use that measurement to calculate density (ρ), specific weight (γ), Baume scale values (°Be), and the percent
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discrepancy between the theoretical and experimental values for each. In addition, the specific gravity of an unknown
mixture of ethylene glycol and water was measured. This measurement was then used to determine the percentage of
ethylene glycol in the mixture. The calculated values are summarized in Table 3, and the percentage of ethylene glycol
in the mixture was determined to be 57%.
VIII. Discussion Questions
1. What is the difference between a fluid’s specific weight and its specific volume?
The difference between a fluids-specific weight and a specific volume is mainly found in the units used to
describe each property. Specific weight is defined as weight per unit of volume for a fluid and is calculated using γ=ρg
with Newtons per cubic meter as measuring units. On the other hand, specific volume is the reciprocal of density and
measures the space a unit of mass of the fluid occupies. The units are typically cubic meters per kilogram [4].
2. Is there a more practical or suitable way to measure the density of a fluid than using a hydrometer?
There are a few different ways to measure the density of a fluid. One way would be to use a pycnometer or
density bottle which allows for a more accurate measurement. It works by using a calibrated flask and an alreadyknown volume of fluid to find the mass. Another way is using an oscillating U-tube density meter which determines
density by measuring a change in oscillation frequency with the fluid fills the U-shaped tube. This way might be a
little more complicated based on others' skill strengths and the tools required. There are two other ways, mass flow
meters and hydrostatic weighing that can also work [5].
3) When would a hydrometer be used in engineering practice? (Name at least two applications)
The need for a hydrometer is when a fluid's density or specific gravity is necessary for the system. An example
of this would be in the petroleum fields, to help determine the density of fuels and oils since most are brought up from
the ground they need to be checked to meet industry standards. Another example where hydrometers are used is in
water treatment plants to monitor salinity levels and quality of water [6].
4) Compute the specific weight (kN/m3 and lbf/ft3) for both the theoretical and experimental
values of each fluid
Table 3. The calculated specific weight of all the fluids used in the experiments
Experimental
Fluid
Theoretical
Specific Weight ɤ Specific Weight ɤ Specific Weight ɤ Specific Weight ɤ
8
(kN/m3)
(lbf/ft3)
(kN/m3)
(lbf/ft3)
9787.437
2007.3222
9810
2011.470
10864.817
2228.128
10791
2212.617
Mixture
10375.411
2127.762
10300.5
2112.043
Red Gage Oil
8075.202
1656.041
8093.25
1661.474
Water
Ethylene
Glycol
Table 3 shows the experimental specific weight and theoretical specific weight calculated using the values found
during the experiment. While there is some deviation from the experimental to theoretical, the discrepencies are
minimal
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IX. References
[1] Dwyer Instruments, “Red Gage Fluid Safety Data Sheet,” URL:
https://www.dwyerinst.com/PDF_files/MSDS/Red_Gage_Fluid.pdf [Accessed 24 September 2019]
[2] Engineering ToolBox, (2003). Liquids - Specific Gravities. [online] Available at:
https://www.engineeringtoolbox.com/specific-gravity-liquids-d_336.html [Accessed 24, September 2019]
[3] ThoughCO.com, “ What is Specific Volume.” 2018, URL : https://www.thoughtco.com/specific-volumedefinition-and-examples-4175807 [retrieved 24 September 2019]
[4] LibreTexts. (n.d.). Density, Specific Volume, Specific Weight, and Specific Gravity. Retrieved from
(eng.libretexts.org)
[5] METTLER TOLEDO. (n.d.). Density Measurement. Retrieved from (mt.com)
[6] Scientific Laboratory Supplies. (n.d.). 3 Ways to Measure Density: Know-How, Hints, and More. Retrieved from
(scientificlabs.co.uk)
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