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.