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Impact of Temperature on Viscosity of Liquid

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INTRODUCTION  

Hydrodynamics, as defined by the Merriam Webster Dictionary, is the 'branch of physics that deals with the motion of fluids, and the forces acting on solid bodies immersed in fluids and in motion relative to them' (2017). The study of fluids originated in Ancient Greece, was coupled with the works of Persian philosophers in Medieval times, and eventually, with many contributions made by scientists such as Archimedes, Leonardo Da Vinci and Isaac Newton, was developed into the branch of fluid dynamics that exists today (WiseGeek, 2017).

Any substance can be classed as a fluidif it 'changes shape uniformly in response to external forces'. Many characteristics of such a substance include; pressure, temperature, mass, density and viscosity (Washington.edu, 2017). The term 'viscosity' is defined as 'a fluid's resistance to flow in relation to its inner molecular structure', and is largely affected by temperature (Viscopedia, 2017). As the temperature of a fluid increases, so does the thermal/kinetic energy of its liquid molecules, which results in increased amounts of movement as the particles begin to move faster. Due to this increased amount of movement, the attractive binding energy of the fluid is reduced, consequently decreasing the fluid's resistance to flow (Azom, 2013). This principle is demonstrated in the following theoretical figures, which depict the relationship between the temperatures and viscosities of various fluids:      

From using the known viscosities of fluids at various temperatures, and developing functions that model these relationships in programs such as Microsoft Excel or on a graphics calculator, the approximate viscosity of a liquid at any temperature can be found by substituting values for temperature into the relevant formula. An example of this process is seen below:

As seen in Figure 1, the equation that models the relationship between temperature and viscosity of water is y = 1.5396e-0.018x. If the temperature of the water was 4ᵒC….

y = 1.5396e-0.018x

y = 1.5396e-0.018 x 4

y = 1.433 mPas

Therefore, the viscosity of the water at 4áµ’C is 1.433 mPas.

Viscosity is also what causes an object to slow as it travels through a fluid, and is one component in the phenomenon of drag force, 'the retarding force that acts opposite to the direction of motion of a body or object'. The drag force of any object is dependent on the viscosity of the fluid it travels through, velocity of the object, reference area of the object, and the drag coefficient.

The following formula can be used to calculate the total drag force acting upon an object (Wikipedia, 2017):

Where: = Drag force (N), = Mass density of fluid (mPas), = Flow speed of object relative to fluid (ms-1), = Drag coefficient (no units), A = Reference area (m2)

A worked example of this calculation with assumed and exact values is modelled below:

Assume that for a flat surfaced mass travelling through water at 4ᵒC….

mPas

= 0.3ms-1

0.82

A = 2.5 x 10-4

The values are then substituted into the drag force formula……

Therefore the drag force of the mass travelling through water at 4áµ’C is approximately 4.6125 x 10-5N.

One component of this force, as represented by in the drag force equation, is a drag coefficient (The Free Dictionary, 2017). As stated in 'The Physics of Sailing' by Ryan M. Wilson (2010), 'intuitively, the drag should depend linearly on the density of the fluid in which the body is immersed (because force depends linearly on mass) and linearly on the area of the body that is exposed to the flow because the volume of fluid that must be displaced as the body moves through it is proportional to this area'. A range of calculated drag coefficients for various shapes can be seen in Figure 3. It can therefore be concluded that the lower the drag coefficient of an object, the lower the amount of drag force that occurs as it travels through a fluid (Brock University, 2017).

As seen in Figure 2, the drag coefficient of an object is reliant on its shape. It can be concluded that a mass with a flat reference area will travel almost two times slower than that with a spherical reference area. A conical reference area will cause an object to fall slightly slower than a spherical mass, but faster than one with a flat reference area. Theoretically, as deducted from Figure 2, it is concluded that a mass with a spherical reference area will travel faster than one with either a conical and flat surfaced reference area, the latter of these theoretically having the slowest time of fall through a liquid out of the three.

Although many different fields of study incorporate knowledge of drag forces and viscosity, arguably one of the most important applications is found within the engineering of ships and the design of the hulls, specifically in relation to sailing competitions such as the America's Cup. As one of the largest sailing races in the world, this competition has strict guidelines for ship design, consequently meaning that vessel engineers must 'find the best combinations (of measurements) to create the fastest ship possible' (Krepal, 2014). When building, engineers must be familiar with the environmental sailing conditions of the race in order to build the most suitable hull with the least amount of drag - this is determined in regards to the temperature of the sea and its viscosity. As calculating viscosity is a complex procedure, ship engineers often refer to data such as seen in Figure 2 to determine aspects of ship design.

Image result for america's cup boats

In regards to the speed of the ship, it can be concluded from previous knowledge on drag force that the lower the drag coefficient of a vessel, the easier it is for it to break through the water, overcoming shear force and resulting in a faster travelling time (Krepal, 2014). When unknown, the drag force formula can be rearranged to find the drag coefficient; however, often these values are computed from graphical designs of the ship as the phenomenon of drag force is dependent on many variables. Testing on model ships is also performed to determine how vessels will travel under different conditions (Mecaflux, 2013).

HYPOTHESIS

Based on the previous research, the hypothesis for this experiment is that:

'If a body is falling in a liquid, then i) the lower the viscosity of the liquid, which decreases as temperature increases, the faster will be the rate of fall of the object, and ii) the lower the drag coefficient of the body, the smaller its drag force will be, as the velocity of an object as it travels through a fluid is inversely proportional to the amount of resistance it encounters.

METHOD

The supplies needed - 1L glass measuring cylinder, 2L water, 2kg honey, 2L canola oil, 3 x 53g cylindrical masses with different reference areas of the same 0.9cm radius (flat, spherical, streamlined/conical), a Thermomix, thermometer, a logbook and pencil, and a video recording device. All measurements and data were to be collected and stored in a logbook and on the video recording device. A risk assessment form was completed before the commencement of the experiment, in order to recognise any potential hazards regarding the equipment that was to be used. It was identified that any device used to heat up the liquids, and the hot liquids themselves, had potential to burn the person completing the experiment, and it was possible for the glass cylinder to topple over and shatter as it was filled with each liquid. Covered shoes were worn during the experimental procedures to protect the feet from any falling objects and glass, and care was taken when using heating devices and handling hot liquids.

As the hypothesis was written in two parts, there were two variables that remained constant depending on the experimental procedure (independent variables) - the first was the temperature/viscosity of each liquid, and the second was the reference area of the masses travelling through each. The dependent variable in both was the velocity of the object.

The equipment was set up for the experiment as depicted in Figure 6. 1L of each liquid was placed in the fridge and cooled to 5áµ’C. 1L of the first liquid, water, was heated in the Thermomix to 37áµ’C and then poured into the glass cylinder. The flat ended mass was dropped from the 1L mark, and its fall was timed and recorded on the video recording device. The object was then extracted from the bottom of the cylinder, and this process was repeated two more times. The flat ended mass was then removed, and the same procedure was performed again for both the spherical and conical shaped masses. After these tests were completed, the water was poured back into the Thermomix and was heated to 50áµ’C. Once at temperature, the water was again poured into the cylinder, and the previously stated processes were repeated for each mass. After these tests were completed, the water was poured into the Thermomix. The chilled water from the fridge was then taken out, checked with a thermometer to be at 4áµ’C, and poured into the cylinder for testing. The previously stated processes for each mass were repeated. After all of the masses had been dropped into the water at all three temperatures, the water was disposed of, and the experimental space cleaned up to prepare for the next round of testing. All results were recorded into various tables in the logbook, and later graphed for analysis.

The second liquid, canola oil, was heated in the Thermomix to 35áµ’C and then poured into the glass cylinder. The previously stated procedures were repeated. All results were recorded into a table, and later graphed for analysis.

The third liquid, honey, was heated in the Thermomix to 35áµ’C and then poured into the glass cylinder. The previously stated procedure was repeated. All results were recorded into a table, and later graphed for analysis.

In this experiment, it is noted that apart from that which were independent and dependant, all other variables were controlled, consequently meaning that every aspect of the testing remained consistent. These controlled variables included the positioning of the glass cylinder and video recording device, the dropping point of the masses, the weight of the small masses used, the radius of the masses, the distance each mass fell, the type of oil and honey used, etc. By controlling all other variables, the results recorded from the testing become more accurate.

RESULTS

(HYPOTHESIS - PART 1)

CALCULATED VALUES FOR VISCOSITY

By using the formulas generated from the Excel graphs in Figure 1, which model the relationships between the viscosity and temperature of each liquid, and substituting in the experimental temperatures for 'x' (4, 37 and 50), the empirical viscosities of each fluid at different temperatures were calculated. The tables and graphs of these results follow, with all calculations performed recorded in the logbooks.

WATER

Temperature (áµ’C)

Viscosity (mPas)

4

1.433

37

0.791

50

0.626

y = 1.5396e-0.018x

CANOLA OIL

y = 186.16e-0.049x

Temperature (áµ’C)

Viscosity (mPas)

4

153.026

37

30.375

50

16.064

HONEY

y = 138468e-0.117x

Temperature (áµ’C)

Viscosity (mPas)

4

86716.073

37

1825.108

50

398.774

Water

Flat Surfaced Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Time of Fall (s)

4

0.41

0.62

0.81

0.61

37

0.62

0.50

0.50

0.54

50

0.66

0.60

0.69

0.65

Spherical Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Time of Fall (s)

4

0.91

0.68

0.37

0.65

37

0.53

0.59

0.55

0.56

50

0.43

0.62

0.60

0.55

Conical Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Time of Fall (s)

4

0.40

0.57

0.54

0.50

37

0.78

0.50

0.62

0.63

50

0.59

0.50

0.43

0.51

Canola Oil

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Time of Fall (s)

4

0.60

0.55

0.65

0.60

37

0.62

0.69

0.58

0.63

50

0.49

0.52

0.46

0.49

Flat Surfaced Mass

Spherical Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Rate of Fall (s)

4

0.63

0.59

0.69

0.636667

37

0.56

0.56

0.53

0.55

50

0.45

0.46

0.42

0.443333

Conical Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Rate of Fall (s)

4

0.67

0.53

0.43

0.543333

37

0.46

0.49

0.38

0.443333

50

0.36

0.45

0.39

0.4

Honey

Flat Surfaced Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Rate of Fall (s)

4

2040

2257.2

2008.2

2101.8

37

498.6

489

508.2

498.6

50

84

91.2

95.4

90.2

Spherical Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Rate of Fall (s)

4

1428

1537.2

1362.6

1442.6

37

362.4

370.2

389.4

374

50

72

70.8

73.8

72.2

Conical Mass

Temperature of Fluid (áµ’C)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average Rate of Fall (s)

4

1188

1135.2

1305

1209.4

37

307.2

305.4

320.4

311

50

66.6

65.4

67.2

66.4

HYPOTHESIS - PART 2

CALCULATED DRAG FORCES

Worked Example:

Flat surfaced mass travelling through water at 4°C

mPas

= 0.2916 ms-1

0.82

A = 2.545 x 10-4

The values are then substituted into the drag force formula……

WATER:

TEMPERATURE (°C)

DRAG FORCE (Nx10-5)

Flat

4

4.3600

37

3.0830

50

1.6840

Spherical

4

3.9480

37

2.9358

50

2.4084

Conical

4

132.3700

37

46.0270

50

55.5820

CANOLA OIL:

TEMPERATURE (°C)

DRAG FORCE (Nx10-5)

Flat

4

483.020

37

86.971

50

76.033

Spherical

4

434.850

37

116.860

50

96.567

Conical

4

12120.000

37

3620.000

50

2320.000

HONEY:

TEMPERATURE (°C)

DRAG FORCE (Nx10-5)

Flat

4

0.0223060

37

0.0083423

50

0.0556950

Spherical

4

0.0485340

37

0.0151850

50

0.0890290

Conical

4

1.3691000

37

0.4357500

50

2.0887000

DISCUSSION & CONCLUSION

HYPOTHESIS - PART 1

It is clearly seen from analysing the relevant results that there is a common pattern throughout - as the temperature of a fluid increases, its viscosity decreases, and the average time of fall for each mass decreases. This is seen visually in the generally decreasing gradients of the trendlines through Figures 6 to 23, which represent how as each liquid gets hotter, the viscosity level decreases and the mass travelling through moves faster. There are a few anomalous results throughout, however these will be explored in further detail in the evaluation. It is observed that for both the water and canola oil experiments, the relationship between the temperature of the fluid and the time of fall is linear, whereas for the honey it is clearly exponential. This is possibly due to the fact that as the first two liquids are not severely dense to begin with, the little change in viscosity that occurs as the temperature increases is fairly constant, as the increments of time are short. However, as the honey is a more viscous liquid, the relationship between temperature and time of fall is more distinct and dramatic as the fluid gets hotter, particularly due to the longer time period for the travel of the mass, which results in a defined curve as a trendline. These relationships agree with the theoretical data presented in Figure 1, and also show that the two variables of temperature and time of fall are not directly proportional to one another.

It is seen from analysing the results that the first part of the hypothesis, 'if a body is falling in a liquid, then i) the lower the viscosity of the liquid, which decreases as its temperature increases, the faster will be the rate of fall of the object', is supported.

HYPOTHESIS - PART 2.

As stated in the background research, the drag coefficient of an object is reliant on its shape and affects the drag force acting upon a mass, as seen through the data from the second phase of the experiment - this is found in Figures 24-29. Theoretically, as deducted from Figure 2, it was concluded that a mass with a spherical reference area would travel faster than one with either a conical and flat surfaced reference area, the latter of these theoretically having the slowest time of fall through a liquid out of the three.

It is observed that there is no mass that consistently achieves the lowest amount of drag throughout the tests - the calculated empirical values of this resistance are very close for the spherical and flat surfaced masses in each situation. For example, as seen when analysing the canola oil results, at 4áµ’C, the flat surfaced mass has a higher drag force than the spherical one. However, at 37áµ’C the spherical mass has a higher drag force than that of the flat surfaced mass. Although such discrepancies occur for these masses throughout the data, when comparing the trendlines of all graphs it is seen that the functions that represent the relationship between temperature and drag force for the spherical mass are consistently the smallest of the three - these also represent how as a liquid gets hotter, the drag force acting on the object decreases. Therefore, it is concluded that the mass with the lowest drag coefficient, the spherical object, encounters the smallest amount of drag force. However, in contrast to the theoretical data, the functions that model the same relationship for the conical mass are the greatest of the three, whereas in theory the flat ended mass would have experienced this For example, when analysing the data from the water experiments, this relationship follow for each mass:

FLAT ENDED MASS: y = 4.9866e-0.019x

SPHERICAL MASS: y = 4.1585e-0.01x

CONICAL MASS: y = 133.55e-0.021x

Where: x = Temperature of Fluid (°C), y = Drag Force (Nx10-5 )

The function for the spherical mass models the smallest amount of drag force in regards to temperature, which is to be expected, however in comparison the conical mass function models a much greater amount of drag force than that of the flat ended mass - in theory these positions were reversed. This is most likely a result of the fact that the conical mass had the most surface area in contact with the liquid as it fell, consequently meaning that such a large value substituted into the formula would affect the calculated values for drag force.

From analysing the honey experimental results, it is noted that the trend line is polynomial instead of exponential, as this function is a better representation of the relevant data. Additionally, the graphs depict that instead of a consistent decrease in drag force as the temperature increases, the resistance exerted on each mass decreases from 0 to 20 degrees, but between 20 to 30 degrees increases. This is likely a result of the high viscosity level of the honey and its sugar content, which may alter the time taken for the mass to fall through the fluid when heated to particular increments of time, and consequently affect the calculated drag force. Additionally, it is observed that the calculated drag forces for the honey experiments are much smaller than the of the others. Because the viscosity of the honey is so great, and the velocity of the mass travelling through is so small, that the two values, when substituted into the drag force equation, essentially cancel one another out. Therefore, this results in drag force values that are less than that of water and canola oil. It is still concluded however that the masses encounter the least amount of resistance in water, and further research would need to be conducted in order to challenge this.

It is noted that all functions begin when x = 4, as any value less than this may alter the composition of the fluid from a liquid to a solid, such as the freezing of water at 0áµ’C, which therefore nullifies the experimental procedures.

It is seen from analysing the results that the second part of the hypothesis, 'the lower the drag coefficient of the body, the smaller its drag force will be, as the velocity of an object as it travels through a fluid is inversely proportional to the amount of resistance it encounters', is both supported and challenged.

EVALUATION

It is observed that there are many anomalous results found in the results of each experiment, and that there are differences between the outcomes of the theoretical and empirical data. These discrepancies may be caused by multiple reasons, the first of which is parallax vision.

Parallax vision is defined as 'the way an object's position or direction seems to change depending on viewing angle' (What.Is.com, 2016). Depending on the position of the camera in each experiment, this phenomenon could affect the results recorded for the time of fall of the masses through the liquid, depending on whether the video recording device was knocked over and consequently had new vantage points every time it was adjusted. This error could be overcome in the future by using a fixed camera or device, theoretically preventing any accidental bumping from occurring and therefore increasing the accuracy of the testing. Also, anomalies can be found through Figures 8, 12 and 14, which all include an increasing linear trendlines instead of decreasing - when the temperature of a fluid increases, the mass falling through should in reality travel faster. This discrepancy is likely due to the large margin for error in the timing of the fall and interpreting the videos, as three masses for one temperature of a liquid were all tested in the same video file. A way to prevent these discrepancies in the future would be to have a second person timing the fall from the exact points the mass was released and stopped, to eliminate the need to find the points in the video where the mass was released or stopped, or by using machines and technology to automate the procedures to record exact values.

In relation to this, the place where the mass was dropped from may have changed throughout the testing due to human error, which would also have affected the results recorded. This provides an explanation as to how some average times of fall in Figures 7-23 do not follow the general decreasing trend as temperature increases. A solution for this would be to use a robot to release the masses into the cylinder at the same point every time, which would decrease the inaccuracy in the results recorded. Also, the temperature of each fluid is unlikely to have stayed unchanging over the three trials for each mass, as over time each liquid would have cooled and affected the viscosity and time of fall of the objects. One way to prevent this in the future would be to drop the masses into a heated container, possibly over a stove top or Bunsen burner, which would keep the liquid at one constant temperature for the entirety of the experiment. Additionally, every time the conical mass hit the bottom of the glass cylinder its apex blunted due to the impact. This would have affected the relevant data recorded, but could be remedied in future by using masses of a more sturdier material.

From evaluating the possible errors that may have occurred from this experiment, it can be seen that the hypothesis needs to be modified to state that 'the smaller the reference area and lower the drag coefficient of an object, the faster its rate of fall and smaller its drag force will be'.


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