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Technical Writing Sample. The change in viscosity as a function of temperature for a selection of fluids is investigated. The liquids investigated are motor oil, water, and corn syrup. Viscosity is measured through the use of a newly constructed falling-ball viscometer. Our experimental results are compared with the predictions of several models, including the Reynolds, Arrhenius, Seeton, and Walther functions, and a newer one proposed by Hussain, Biswas, and Athre [1]. This will allow for a determination of the most accurate viscosity model.
Citation preview
Fourth Lab Experiment Final Proposal
Experimental Validation of a Relatively New
Temperature-Viscosity Relation
Brad Gassner
October 16, 2015
Synopsis
The change in viscosity as a function of temperature for a selection of fluids is investigated. The
liquids investigated are motor oil, water, and corn syrup. Viscosity is measured through the use
of a newly constructed falling-ball viscometer. Our experimental results are compared with the
predictions of several models, including the Reynolds, Arrhenius, Seeton, and Walther
functions, and a newer one proposed by Hussain, Biswas, and Athre [1]. This will allow for a
determination of the most accurate viscosity model.
Theory
The falling ball viscometer utilizes a sphere which is dropped through a tall cylinder of the test
fluid. This concept is shown in Figure 1.
Figure 1: Sphere drop through liquid [2]
The measurements are performed only after the ball reaches its terminal velocity. At this point,
the sum of the weight, drag force, and buoyant force is zero.
(1)
The third term in the above relation houses the drag force expression. Using Stokes’ law [3], the
drag force is proportional to velocity and the viscosity of the fluid can be expressed as
(2)
where γ is the specific weight, d is the diameter of the sphere, and ut is the terminal velocity.
The subscripts s and f represent the sphere and fluid, respectively [4]. A simple extension of this
equation gives us a relation expressed as a function of the falling length and the time taken to
traverse that length as
(3)
This determination of the viscosity coefficient will be repeated for many different temperatures
and plotted with results predicted by the following existing models:
● Reynolds
(4)
● Arrhenius
(5)
● Seeton
(6)
● Walther
(7)
● Hussain, Biswas, and Athre
(8)
Typically, at temperatures less than 100 degrees F and above 210 degrees F, many of these
models fit poorly. The appropriateness of the newly proposed curve fit outside of these bounds
shall be discussed.
Figure 1: A Typical Viscosity vs. Temperature Relationship [5]
Experimental Procedure
A tall glass cylinder is measured and graduated to a length of 0.25 meters (approximately 10
inches). The liquid specimen is added to the cylinder and heated to 25 degrees C
(approximately 75 degrees F). The spherical viscometer is dropped into the top of the cylinder.
Upon reaching the first graduation from the top of the device, two stopwatches are started.
Timing continues until the ball falls below the bottom graduation. The stopwatches are paused
and their displays are recorded. These two data points are to be averaged. The liquid is heated
by ten degrees and the measurement is repeated. This procedure is repeated up to and
including 125 degrees C (260 degrees F) while being stirred simultaneously. Three liquids to be
tested are motor oil, water, and corn syrup.
Once the raw data is collected, the experimental viscosity of each of the liquids will be
calculated for each temperature using equation 3. The viscosity is then plotted against
temperature. The highest and lowest temperature data points will be used to determine
unknown coefficients in the other models. This data will then be plotted against our experimental
graph. By plotting the models against each other, we will be able to determine which model is
the most accurate for each of the liquids that were tested.
Preliminary Budget
Table 1: Bill of Necessary Supplies
Item Source Cost Number
Stopwatch phone application $0.00 2
Glass vase
Walmart1 $35.95 1
Stirring rod group member $0.00 1
Magnet Walmart2 $2.25 1
12 inch string Walmart3 $3.39 1
½ inch ball bearing ME Shop $0.00 1
Stove group member’s apartment
$0.00 1
Thermometer group member $0.00 1
Ruler group member $0.00 1
20 oz Motor Oil Walmart4 $4.97 1
20 oz Water tap $0.00 1
20 oz Corn Syrup Walmart5 $4.00 1
Poster Display Printing Office $25.00 1
TOTAL $75.566
1http://www.walmart.com/ip/Entrada-Glass-
Vase/34395219?action=product_interest&action_type=title&item_id=34395219&placement_id=irs-2-
m3&strategy=PWVAV&visitor_id&category=&client_guid=89a31515-a36a-4a17-a620-
bced1f4e77cb&customer_id_enc&config_id=2&parent_item_id=34395205&parent_anchor_item_id=34395205&guid=e77dece3-
0baa-4034-9bac-74d5b9a6bb26&bucket_id=irsbucketdefault&beacon_version=1.0.1&findingMethod=p13n 2http://www.walmart.com/ip/Craft-and-Hobby-Ceramic-Disk-Disc-Magnets-1-2-Inch-Diameter-10/30108837 3http://www.walmart.com/ip/Silk-Fabric-String-2mm-Ivory-White-42-Inch-Strand-1/30757958 4http://www.walmart.com/ip/Pennzoil-SuperTech-Full-Synthetic-5W30-Motor-Oil-1-Quart/16474420 5http://www.walmart.com/ip/Great-Value-Light-Corn-Syrup-16-Oz/10315278 6Exclusive of shipping costs
References
1. Hussain, A., S. Biswas, and K. Athre. "A New Viscosity-Temperature Relationship for
Liquid Lubricants." Wear, vol. 156, no. 1, 15 July 1992, pp. 1–18, 15 July 1992. [Online].
Available:http://www.sciencedirect.com/science/article/pii/0043164892901404
2. Shearer, Scott A., and Hudson, Jeremy R. Fluid Mechanics: Stokes’ Law and Viscosity.
On line. Measurement Laboratory. [Online]. Available:
http://isites.harvard.edu/fs/docs/icb.topic1032465.files/Final%20Projects/Fluids%20Drag/
stokes%20lab.pdf
3. W. Contributors. (2015, October) Stokes’ law. On line. Wikipedia. [Online]. Available:
https://en.wikipedia.org/wiki/Stokes%27_law
4. Yuan, Ping, and Lin, Ben-Yuan. (2008, October) Measurement of Viscosity in a Vertical
Falling Ball Viscometer. On line. American Laboratory. [Online]. Available:
http://www.americanlaboratory.com/913-Technical-Articles/778-Measurement-of-
Viscosity-in-a-Vertical-Falling-Ball-Viscometer/
5. Mitsuru, Abe Yikinobu, Fukaya, and Hiroyiki, Ohno. “Extraction of Polysaccharides from
Bran with Phosphonate or Phosphinate-derived Ionic Liquids under Short Mixing Time
and Low Temperature." Green Chemistry, vol. 12, no. 7, pp.1274-1280, 1 July 2010.
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