ME 317 Lab 1 Hydrometers
Kimberly Rogulich
9/2/2014
Professor Truman
Matthew Baca
Caitlin O’Grady
Tuesday
II. Table of Contents
III. Objective..................................................................................................................................................................3
IV. Experimental Setup .................................................................................................................................................3
V. Theory.......................................................................................................................................................................4
VI. Procedure .................................................................................................................................................................4
VII. Data ........................................................................................................................................................................5
VIII. Results/Calculations..............................................................................................................................................5
IX. Conclusion ...............................................................................................................................................................8
X. Discussion Questions ................................................................................................................................................8
XI. References ............................................................................................................................................................. 11
Figure 1. Setup of Beakers.............................................................................................................................................3
Figure 2. Hydrometers ...................................................................................................................................................3
Table 1. Data Recorded During Experiment..................................................................................................................5
Table 2. Experimental Data ...........................................................................................................................................5
Table 3. Theoretical Data ..............................................................................................................................................5
Table 4. Baumé Scale and Density Calculations ...........................................................................................................6
Table 5. Experimental Percent Discrepancy Calculations .............................................................................................6
Table 6. Calculation of Specific Weight for Experimental Data ...................................................................................7
Table 7. Calculation of Specific Weight for Theoretical Data.......................................................................................7
2
III. Objective
The purpose of this lab is to learn how to measure the density of various liquids using a hydrometer. It is also
important to understand how different hydrometer scales work. It is also essential to learn how to calculate the
Baumé scale, density, specific weight, and the percent error of the data recorded during the experiment.
IV. Experimental Setup
Equipment:
 Beakers (5)
 Ethylene Glycol
 Glycerin
 Hydrometers (4)
 Red Gage Oil
 Thermometer
 Water
As shown below in Fig. 1, each beaker was filled with a different liquid and a paper towel was placed underneath
each beaker to catch the drips. Ethylene glycol was in the first beaker, water in the second, a mixture of the two in
the third beaker, glycerin in the fourth, and red gage oil was in the last beaker. Fig. 2 shows the hydrometers that
were placed on a paper towel next to the beakers.
Figure 2. Setup of Beakers
Figure 1. Hydrometers
3
V. Theory
Nomenclature:

ρ = density
In order to measure the density of liquids, hydrometers are used. The measurements of this device are in terms of
specific gravity (SG), which is shown in Eqn. 2. Specific gravity is ratio of the density of a liquid to the density of
water at a specified temperature. Density is shown in Eqn. 1 where m, is mass and V, is volume.
𝒎
𝝆=
(𝟏)
𝑽
𝝆
𝑺𝑮 =
(𝟐)
𝝆𝑯𝟐𝑶 @ 𝟑𝟗.𝟐 ℉
Hydrometers function on Archimedes principle, which is the buoyant force on an object in a liquid or gas, is equal to
the weight of the fluid that is displaced. This means that an object will sink until it displaces its own weight. 1
Hydrometers date back to 400 B.C. in Greece. Later in Europe in the 19 th century, Antoine Baumé invented the
Baumé hydrometer.2 This scale is often used in chemical industry. It is not a measurement of temperature even
though the measurement is in degrees (°Be). The Baumé scale has two different scales. The “light” scale is used
when SG < 1, this means the liquid is lighter than water. The “heavy” scale is for liquids that are heavier than water
when SG > 1. The equation to convert from SG < 1 to °Be, is shown in Eqn. 3 and the equation to convert from SG
> 1 to °Be, is shown in Eqn. 4.1
°𝑩𝒆 =
𝟏𝟒𝟎 − 𝑺𝑮 × 𝟏𝟑𝟎
𝑺𝑮
°𝑩𝒆 =
𝟏𝟒𝟓 (𝑺𝑮 − 𝟏)
𝑺𝑮
(𝟑)
(𝟒)
Another hydrometer scale is called the Balling/Plato scale. Karl Balling, Simon Ack, and Fritz Plato developed it in
the 1840s. This hydrometer is used to measure the density of beer. The density is in terms of the percentage of
sucrose by weight. The following is an example of this: The measurement “12° Balling-Plato has the same density
as a water-sucrose solution containing 12% sucrose by weight.”3 The Twaddell scale (°Tw), another hydrometer
scale, was developed by William Twaddell in the 19th century in England. This hydrometer was used in tanning
solutions in the leather industry. This scale is only used for liquids with SG > 1. Eqn. 5 shows how °Tw is
calculated.4
°𝑻𝒘 = 𝟐𝟎𝟎 (
𝝆@ 𝟔𝟎 ℉
− 𝟏)
𝝆𝑯𝟐𝑶 @ 𝟔𝟎 ℉
(𝟓)
VI. Procedure
1.
The temperature of water was measured.
2.
A hydrometer was place in the first beaker to measure the specific gravity (SG) of ethylene glycol.
4
3.
The measurement and scale were recorded.
4.
The hydrometer was then rinsed off.
5.
Steps 2-4 were repeated for each beaker.
VII. Data
After completing step 1 in the procedure, the temperature was recorded to be 22 °C in the water. Table 1 shows the
information recorded in step 3 in the procedure. The hydrometer range corresponds to the scale that was used. The
0.65 to 1 hydrometer range indicates the light scale, and the 1 to 2 hydrometer range indicates the heavy scale.
Table 1. Data Recorded During Experiment
Fluid
Ethylene Glycol
Water
Mixture
Glycerin
Red Gage Oil
Hydrometer Reading (SG)
1.110
1.000
1.085
1.255
0.825
Hydrometer Scale
Heavy
Heavy
Heavy
Heavy
Light
Hydrometer Range (SG)
1 to 2
1 to 2
1 to 2
1 to 2
0.65 to 1
VIII. Results/Calculations
Table 2. shows the experimental data including the measured SG, the calculated Baumé scale and the calculated
densities. The calculations for °Be and the densities are shown in Table 4.
Table 2. Experimental Data
Fluid
SG
°Be
Density (kg/m^3)
Density (slugs/ft^3)
Ethylene Glycol
1.110
14.4 (heavy)
1109
2.151
Water
1.000
0
998.8
1.938
Mixture
1.085
11.4 (heavy)
1084
2.103
Glycerin
1.255
29.5 (heavy)
1253
2.432
Red Gage Oil
0.825
39.7 (light)
824.0
1.599
Table 3. shows the theoretical data including SG, the Baumé scale, and density at 60 °F. These values were found at
websites indicated in the table. The values for °Be were calculated as shown in Table 4. The water/ethylene glycol
mixture is not shown because the theoretical data for this fluid is unknown.
Table 3. Theoretical Data
Fluid
SG
°Be
Ethylene Glycol
Water
Glycerin
Red Gage Oil
1.1255
1.0005
1.2605
0.8267
29 (heavy)
0
29.9 (heavy)
39.5 (light)
Density (kg/m^3)
Density (slugs/ft^3)
10976
998.8
12596
825.0
2.129
1.9388
2.443
1.601
The Baumé scale calculations were done using Eqns. 3 and 4. The densities were calculated using Eqn. 2 in the
following form:
5
𝝆 = 𝑺𝑮 × 𝝆𝑯𝟐𝑶 @ 𝟔𝟎 ℉
The calculations were completed using the corresponding SG values in Tables 2 and 3. The results to these
calculations are shown in the corresponding columns in Tables 2 and 3. The red gage oil theoretical density
calculations are shown below.
𝝆𝒓𝒆𝒅 𝒈𝒂𝒈𝒆 𝒐𝒊𝒍 = 𝟎. 𝟖𝟐𝟔 × 𝟗𝟗𝟖. 𝟖
𝝆𝒓𝒆𝒅 𝒈𝒂𝒈𝒆 𝒐𝒊𝒍 = 𝟎. 𝟖𝟐𝟓 × 𝟏. 𝟗𝟑𝟖
𝒌𝒈
𝒎𝟑
𝒔𝒍𝒖𝒈𝒔
𝒇𝒕
𝟑
= 𝟖𝟐𝟓. 𝟎
= 𝟏. 𝟔𝟎𝟏
𝒌𝒈
𝒎𝟑
𝒔𝒍𝒖𝒈𝒔
𝒇𝒕𝟑
Table 4. Baumé Scale and Density Calculations
Fluid
°Be (experimental)
Density (kg/m3)
Density (slugs/ft3)
°Be (theoretical)
Ethylene
Glycol
Mixture
145 (1.11 − 1)
1.11
145 (1.085 − 1)
1.085
145 (1.255 − 1)
1.255
140 − 0.825 × 130
0.825
𝑘𝑔
𝑚3
𝑘𝑔
1.085 × 998.8 3
𝑚
𝑘𝑔
1.255 × 998.8 3
𝑚
𝑘𝑔
0.825 × 998.8 3
𝑚
𝑠𝑙𝑢𝑔𝑠
𝑓𝑡 3
𝑠𝑙𝑢𝑔𝑠
1.085 × 1.938
𝑓𝑡 3
𝑠𝑙𝑢𝑔𝑠
1.255 × 1.938
𝑓𝑡 3
𝑠𝑙𝑢𝑔𝑠
0.825 × 1.938
𝑓𝑡 3
145 (1.125 − 1)
1.125
Glycerin
Red Gage Oil
1.11 × 998.8
1.11 × 1.938
–
145 (1.26 − 1)
1.26
140 − 0.826 × 130
0.826
Eqn. 6 shows how to calculate the experimental percent discrepancy.
𝑬𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑫𝒊𝒔𝒄𝒓𝒆𝒑𝒂𝒏𝒄𝒚 =
|𝑺𝑮𝒕𝒉𝒆𝒐 − 𝑺𝑮𝒆𝒙𝒑 |
× 𝟏𝟎𝟎%
𝑺𝑮𝒕𝒉𝒆𝒐
(𝟔)
Table 5 shows the calculations done for each liquid. The SG values were taken from Tables 2 and 3. Table 5 does
not include water because the experimental and theoretical calculations were the same, so the percent error would be
0%.
Table 5. Experimental Percent Discrepancy Calculations
Fluid
Experimental Percent Discrepancy
Ethylene Glycol
|1.125 − 1.11|
× 100% = 1.33%
1.125
|1.26 − 1.255|
× 100% = 0.40%
1.26
|0.826 − 0.825|
× 100% = 0.12%
0.826
Glycerin
Red Gage Oil
Specific weight, γ, is the weight per unit volume, which is shown in Eqn. 7. The letter g denotes the acceleration due
to gravity, which is equal to 9.81 m/s2 or 32.2 ft/s2.
𝜸 = 𝝆𝒈
(𝟕)
Eqn. 8 shows the relationship between units used to calculate specific weight.
𝒌𝒈
𝑵
= 𝟑
𝟐
𝟐
𝒎 𝒔
𝒎
(𝟖)
6
Eqns. 9 and 10 show conversion factors used in calculating specific weight.
𝒌𝒈
𝟎. 𝟎𝟎𝟏 𝒌𝑵
𝒌𝑵
×
= 𝟑
𝒎𝟐 𝒔 𝟐
𝑵
𝒎
𝒔𝒍𝒖𝒈𝒔 𝒍𝒃𝒇 𝒔𝟐
=
𝒇𝒕𝟑
𝒇𝒕𝟒
(𝟗)
(𝟏𝟎)
The values of density from Tables 2 and 3 are used to calculate specific weight as shown in Tables 6 and 7.
Table 6. Calculation of Specific Weight for Experimental Data
Experimental
γ (kN/m3)
Fluid
Ethylene
1109
Glycol
Water
998.8
Mixture
1084
Glycerin
Red Gage Oil
1253
824
γ (lbf/ft3)
𝑘𝑔
𝑚 0.001 𝑘𝑁
× 9.81 2 ×
3
𝑚
𝑠
𝑁
𝑘𝑁
= 10.88 3
𝑚
𝑘𝑔
𝑚 0.001 𝑘𝑁
× 9.81 2 ×
𝑚3
𝑠
𝑁
𝑘𝑁
= 9.798 3
𝑚
𝑘𝑔
𝑚 0.001 𝑘𝑁
× 9.81 2 ×
𝑚3
𝑠
𝑁
𝑘𝑁
= 10.63 3
𝑚
𝑘𝑔
𝑚 0.001 𝑘𝑁
× 9.81 2 ×
3
𝑚
𝑠
𝑁
𝑘𝑁
= 12.29 3
𝑚
𝑘𝑔
𝑚 0.001 𝑘𝑁
𝑘𝑁
× 9.81 2 ×
= 8.083 3
3
𝑚
𝑠
𝑁
𝑚
2.151
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
4
𝑓𝑡
𝑠
= 69.26
1.938
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
4
𝑓𝑡
𝑠
= 62.40
2.103
𝑙𝑏𝑓
𝑓𝑡 3
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
𝑓𝑡 4
𝑠
= 78.31
1.599
𝑙𝑏𝑓
𝑓𝑡 3
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
4
𝑓𝑡
𝑠
= 67.72
2.432
𝑙𝑏𝑓
𝑓𝑡 3
𝑙𝑏𝑓
𝑓𝑡 3
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
𝑓𝑡 4
𝑠
= 51.49
𝑙𝑏𝑓
𝑓𝑡 3
Table 7. Calculation of Specific Weight for Theoretical Data
Theoretical
γ (kN/m3)
Fluid
Ethylene
Glycol
1097
𝑘𝑔
𝑚 0.001 𝑘𝑁
× 9.81 2 ×
𝑚3
𝑠
𝑁
𝑘𝑁
= 10.76 3
𝑚
γ (lbf/ft3)
2.129
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
𝑓𝑡 4
𝑠
= 68.55
𝑙𝑏𝑓
𝑓𝑡 3
7
Water
998.8
Glycerin
Red Gage Oil
1259
825
𝑘𝑔
𝑚 0.001 𝑘𝑁
× 9.81 2 ×
𝑚3
𝑠
𝑁
𝑘𝑁
= 9.798 3
𝑚
1.938
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
4
𝑓𝑡
𝑠
= 62.40
𝑘𝑔
𝑚 0.001 𝑘𝑁
× 9.81 2 ×
3
𝑚
𝑠
𝑁
𝑘𝑁
= 12.35 3
𝑚
2.443
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
𝑓𝑡 4
𝑠
= 78.66
𝑘𝑔
𝑚 0.001 𝑘𝑁
𝑘𝑁
× 9.81 2 ×
= 8.093 3
3
𝑚
𝑠
𝑁
𝑚
1.601
𝑙𝑏𝑓
𝑓𝑡 3
𝑙𝑏𝑓
𝑓𝑡 3
𝑙𝑏𝑓 𝑠 2
𝑓𝑡
× 32.2 2
𝑓𝑡 4
𝑠
= 51.55
𝑙𝑏𝑓
𝑓𝑡 3
The percent concentration of ethylene glycol in the water/ethylene glycol mixture is calculated using Eqn. 11. The
calculation for this is shown bellow Eqn. 11.
𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑪𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏 =
𝑺𝑮𝒎𝒊𝒙𝒕𝒖𝒓𝒆 − 𝑺𝑮𝒘𝒂𝒕𝒆𝒓
× 𝟏𝟎𝟎%
𝑺𝑮𝒆𝒕𝒉𝒚𝒍𝒆𝒏𝒆 𝒈𝒍𝒚𝒄𝒐𝒍 − 𝑺𝑮𝒘𝒂𝒕𝒆𝒓
(𝟏𝟏)
𝟏. 𝟎𝟖𝟓 − 𝟏
× 𝟏𝟎𝟎% = 𝟕𝟕. 𝟐𝟕%
𝟏. 𝟏𝟏 − 𝟏
IX. Conclusion
During the experiment, a Baumé hydrometer was used to record the specific gravity of various liquids. This data
was then used to calculate °Be, density, percent discrepancy, and specific weight of each liquid. The theoretical
densities were found on websites, but the °Be, percent discrepancy, and specific weight were calculated. It was
found that ethylene glycol had the largest percent error of 1.3%, and the red gage oil had the smallest percent error
of 0.12%. These errors could be due to reading the measurement inaccurately. The water/ethylene glycol mixture
was found to have an ethylene glycol concentration of 77.27%. I learned about different scales of hydrometers, and I
also learned how to calculate °Be, density, percent discrepancy, specific weight, and percent concentration.
X. Discussion Questions
1) Define specific weight and specific gravity (include dimensions and units).
Specific weight, γ, is the weight per unit volume, which has dimensions
𝑀
𝑇 2 𝐿2
and units
𝑙𝑏
𝑓𝑡 3
or
𝑁
𝑚3
.
Specific gravity (SG) is the ratio of the density (ρ) of a fluid to the density of water at a given temperature. Since SG
is a ratio of densities, it does not have units.9
8
2) Which specific gravity measured had the greatest percent error? Would this error be a problem in engineering
practice?
According to Table 5, the specific gravity measured with the greatest percent error is ethylene glycol with a percent
discrepancy of 1.33%. This is a small error, so it would not be a problem in engineering practice.
3) Name three other hydrometer scales used in various industries and discuss how the scales are used.
In Europe in the 19th century, Antoine Baumé invented the Baumé hydrometer. *2 This scale is often used in chemical
industry. It is not a measurement of temperature even though the measurement is in degrees (°Be). The Baumé scale
has two different scales. The “light” scale is used when SG < 1, this means the liquid is lighter than water. The
“heavy” scale is for liquids that are heavier than water when SG > 1.
The Balling/Plato scale, is another hydrometer scale. Karl Balling, Simon Ack, and Fritz Plato developed it in the
1840s. This hydrometer is used to measure the density of beer. The density is in terms of the percentage of sucrose
by weight. The following is an example of this: The measurement “12° Balling-Plato has the same density as a
water-sucrose solution containing 12% sucrose by weight.”*3
The Twaddell scale (°Tw), another hydrometer scale, was developed by William Twaddell in the 19 th century in
England. This hydrometer was used in tanning solutions in the leather industry. This scale is only used for liquids
with SG > 1.
4) What is the specific weight (lbf/gal) for a fluid with SG of 0.826? Assume a temperature of 39.2 °F and gravity to
be 32.2 ft/s2.
The specific weight is calculated using Eqns. 2 and 7.
𝜸 = 𝝆𝒈
𝝆 = 𝑺𝑮 × 𝝆𝑯𝟐𝑶 @ 𝟑𝟗.𝟐 ℉
𝝆 = 𝟎. 𝟖𝟐𝟔 × 𝟏. 𝟗𝟒
𝟏 𝒔𝒍𝒖𝒈 =
𝒍𝒃𝒇 𝒔𝟐
𝒇𝒕
𝝆 = 𝟏. 𝟔𝟎𝟐𝟒𝟒
𝜸 = 𝟏. 𝟔𝟎𝟐𝟒𝟒
𝒔𝒍𝒖𝒈𝒔
𝒇𝒕𝟑
𝒍𝒃𝒇 𝒔𝟐
𝒇𝒕𝟒
𝒍𝒃𝒇 𝒔𝟐
𝒇𝒕
𝟏 𝒇𝒕𝟑
×
𝟑𝟐.
𝟐
×
𝒇𝒕𝟒
𝒔𝟐
𝟕. 𝟒𝟖𝟎𝟓𝟐 𝒈𝒂𝒍
𝜸 = 𝟒. 𝟓𝟕
𝒍𝒃𝒇
𝒈𝒂𝒍
The specific weight of a fluid with SG of 0.826 is 4.57 lbf/gal as shown in the calculations above.
5) When using a hydrometer for precise measurements, the reference of water is taken to be at 4 °C (39.2 °F), but in
engineering practice the reference of water is taken to be 15.6 °C (60 °F). Why use 60 °F instead of 39.2 °F? What is
the percent difference?
9
If the hydrometer is calibrated on a different temperature basis the measurement could be off by 0.001, which is a
percent difference of 0.1%.10
10
XI. References
1Mechanical
Engineering Department, “ME317L Fluid Mechanics Lab 1- Hydrometers,” Lab manual, University of New Mexico,
2014, Print.
2Mitchell, J., “The History of the Hydrometer,” eHow, URL: http://www.ehow.com/about_5438638_history-hydrometer.html
[cited 29 August 2014].
3“Balling (Plato) Hydrometers,” Nova-Tech International, URL: http://www.novatech-usa.com/Products/Balling-PlatoHydrometers [cited 30 August 2014].
4“Twaddell Number,” Sizes, URL: http://sizes.com/units/hydrometer_twaddell.htm [cited 30 August 2014].
5“Liquids and Fluids – Specific Gravities – SG,” The Engineering Toolbox, URL: http://www.engineeringtoolbox.com/specificgravity-liquid-fluids-d_294.html [cited 30 August 2014].
6“Liquids – Densities,” The Engineering Toolbox, URL: http://www.engineeringtoolbox.com/liquids-densities-d_743.html [cited
30 August 2014].
7“Red Gage Fluid – Safety Data Sheet,” Environmental Monitoring Systems, URL:
http://www.emssales.net/uploads/red_gage_fluid.pdf [cited 30 August 2014].
8“Water – Density and Specific Weight,” The Engineering Toolbox, URL: http://www.engineeringtoolbox.com/water-densityspecific-weight-d_595.html [cited 30 August 2014].
9Munson, B., and Young, D., Fundamentals of Fluid Mechanics, 7th ed., John Wiley & Sons, New Jersey, 20212, Chap. 1.
10“60°/60°F Hydrometer Instructions 3-0011,” LaMotte, URL:
http://galvbay.org/docs/WMT%20web%20files/Hydrometer%20Instruction%20Manual.pdf [cited 30 August 2014].
11