Extended essay

Subject: Physics
Research question: How does the viscosity of used and
new engine oils change with temperature?

Written by: Marie JOUIN during the year 2022

Word count: 4000

Page number: 40

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Table of contents:

A. Introduction and literature review…………………………………………………….…3

A1. Essay overview………..………………………………………………………..4

A2. Background research…………………………….…………………………….3

A3. Developing an hypothesis based on literature review…………...…………6

A4. Derivation of formula.……………………………………………………..……7

B. The experiment……………………………………………………………..…..………12

B1. Oils used …………………………………………………………………….15

B2. Method ………….……………………………………………………………18

B3. Variables …………………………………………………………………….23

B4. Safety…………………………………………………………………………23

C. Analysis …………………………………………………………………………………24

C1. Results ………………………………………………………………..……24

C2. Error analysis ………………………………………………………………29

C3. Relationship …………………………………………………………………30

D. Conclusion ……………………………………………………………………………32

E. Evaluation……………………………………………………………………………32

E1. Strengths and weaknesses……………………………………….33

E2. Improvements ………………………………………………………33

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 Question statement: How does the viscosity of used and new engine oils change

with temperature?

The dynamic viscosity of two engine oil is found, each used and unused. The

viscosity is found at 8 different temperatures to see how viscosity varies with

temperature for each of the oils.

A. Introduction to viscosity

A1. Essay overview

Fluid dynamics is a complex area of physics. Yet, it is an important part of physics as

it has numerous applications. For instance, engine oils used to lubricate engines and

reduce mechanical wear have a property called viscosity, which describes the

resistance to flow. Viscosity will determine how well the engine is protected from

mechanical wear, and it is interesting to see how temperature affects the viscosity of

oils.

This essay will attempt at answering the question “How does the viscosity of used

and new engine oils change with temperature”. The main objective is to model the

change in viscosity of the oils with temperatures, and comparing used and new oils

in relation to the change in viscosity with temperature. Motor oils are so widely used

that understanding how their most important property, viscosity, changes with use

and temperature could lead to better oils being produced and less oil wastage.

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 A2. Background research

Viscosity is a physical property of fluids that describes their resistance to a change in

shape, or movement of neighbouring particles relative to another. (Britannica, 2022).

Lubricants with a high viscosity are the ones who offer the most resistance to motion,

whereas ones with a low viscosity offer a lower resistance.

Motor lubricants, or engine oils, are fluids that are used to reduce the mechanical

wear between the different moving parts of the engine. If two surfaces are rubbing

against each other, an oil film between them will reduce friction and therefore

improve performance and efficiency. This is shown in Figure 1 below. The layer of oil

creates a film that prevents the two engine parts from rubbing together.

Figure 1: Layer of oil between two surfaces

Viscosity is therefore extremely important in engine protection. How it reacts to

temperature determines how well it will protect the engine. Indeed, when engines

heat up, the oil contained in them rises in temperature as well. As they heat up, the

4
fluids have a lower viscosity. An increase in temperature causes the molecules to

move faster and hence increase their kinetic energy. The attractive binding energy is

reduced and therefore the viscosity is reduced.

Viscosity is such an important property of lubricants that the lubricant chosen for an

engine will depend on its grade. Lubricants can be classified into two categories

named monograde and multigrade. This depends on how significantly their viscosity

changes with temperature or not. The classification we use has been created by the

Society of Automotive Engineers (SAE). The oil grade is noted in the format

“XW-YY”. The X number rates the oil’s flow at 0 degrees Fahrenheit (-17.8 degrees

Celsius), and the “W” written next to it stands for winter. The lower the number “X” is,

the less the oil thickens in the cold, so the less the viscosity increases. For instance,

a 5W-30 viscosity engine oil thickens less in the cold than a 10W-30, but more than a

0W-30. In a colder climate an engine would benefit more from the 0W or 5W grade,

as they remain fluid and watery instead of viscous. High viscosity in motors

increases the fluid friction, resulting in reduced energy efficiency, higher operating

temperatures, and hard starting. This is why motors of formula ones or planes need

time to heat up before performing at high regimes. (www.farmoyl.com, n.d.)

The numbers YY indicate the oil's viscosity measured at 100 degrees Celsius. This

number represents the oil's resistance to thinning, so decreased viscosity at high

temperatures. For example, 10W-30 oil will thin out at higher temperatures faster

than 10W-40 will.

Understanding the viscosities of the oils, and how they vary with temperature is

therefore crucial for thermic engines.

5
Oils are also defined by their viscosity index, an arbitrary number assigned as a

measure of the constancy of the viscosity of a lubricating oil with change of

temperature with higher numbers indicating viscosities that change little with

temperature. (Merriam-webster.com, 2020)

A3. Developing a hypothesis based on literature review

In (Chandra, 2006) and in (Raţiu et al., 2020), it is shown that, for used oils, the

viscosity decreases with temperature, also following an exponential graph.

Comparison of the dynamic viscosities of the oils in the two studies shows that used

oils tend to have a lower viscosity than unused ones. This is also seen in (Buchar,

Hlaváč and Čupera, 2012), where comparison of used and unused oils has shown

that the used ones have a lower dynamic viscosity, due to sulfation, oxidation and

nitration.

Oil is a complex substance which consists mainly of atoms of carbon, hydrogen,

oxygen. Oils in motors undergo three main reactions while they are being used in

engines: oxidation, nitration and sulfation.

Oxidation is very common in engines. Oxygen from the atmosphere reacts with the

hydrocarbons in the lubricant to form carboxylic acids. These acids increase the

viscosity of the oil due to acid dissociation. (Zeng et al., 2012)

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Nitration is a reaction of concern in engine oils. Heat from the engine causes

atmospheric nitrogen (𝑁2) and oxygen (𝑂2) to react, forming nitrous oxides (𝑁𝑂𝑥). By

interacting with the lubricant, these oxides either create organic nitrates or are picked

up as either soluble or insoluble nitrous compounds. This elevated nitration of the oil

will increase viscosity due to oil thickening and acidity.

Sulfation is the reaction between oxygen, heat, water and sulphur. The sulphur

comes from the fuel or for the oil. They create sulphurous compounds including

sulphur based acids. Sulfation reactions occur when these acids react with the

additives in the oil or the lubricant. They cause increased viscosity.

My hypothesis is therefore the following: the oils viscosity will decrease with

increasing temperature, and used oils will have a lower viscosity than the new ones.

A4. Derivation of formula

In order to relate terminal velocity to viscosity, we need to take a step-by-step

approach. First, let us examine the forces acting on a falling sphere.

Weight (Force of gravity)

All bodies on earth experience gravity, a force that attracts them to the centre of the

Earth.

Weight = Mass × acceleration due to gravity (𝑔)

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Mass of sphere = volume × density (ρ)

4 3
= 3
π𝑟 × ρ (equation 1)

Where:

ρ: density

𝑟: radius of sphere

Therefore the weight of the sphere can be equal to

4 3
𝑊= 3
π𝑟 × ρ × 𝑔 (equation 2)

Figure 2: Weight of sphere

Buoyancy

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Archimedes’ principle states that “any object, wholly or partially immersed in a fluid,

is buoyed up by a force equal to the weight of the fluid displaced by the object”.

(Britannica, 2022)

The force of buoyancy opposes the downward direction of motion. When immersed

in a liquid, the difference in pressure between the bottom and top surface causes the

object to experience buoyancy, a force opposing gravity and equivalent to the weight

of the displaced fluid.

Figure 3: Sphere experiencing buoyant force

𝐹 𝑏𝑢𝑜𝑦
= 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑

= 𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑
× 𝑔 (equation 3)

𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑
= 𝑉 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑
× ρ 𝑙𝑖𝑞𝑢𝑖𝑑
(equation 4)

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Since we know that the volume of fluid displaced will be equal to the volume of the

ball:

𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑
= 𝑉 𝑏𝑎𝑙𝑙
× ρ 𝑙𝑖𝑞𝑢𝑖𝑑
(equation 5)

4 3
𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑
= 3
π𝑟 × ρ 𝑙𝑖𝑞𝑢𝑖𝑑
(equation 6)

If we insert Equation 6 into Equation 3, we get an equation for the force of buoyancy

experienced by our sphere in the oil.

4 3
𝐹 𝑏𝑢𝑜𝑦
= 3
π𝑟 × ρ × 𝑔 (equation 7)

Turbulence

In fluid mechanics, we distinguish two types of flows: turbulent and laminar.

In a laminar flow, all particles move in straight lines and in the same direction.

​Velocity, pressure, and other flow properties stay constant.

When the velocity exceeds a certain value, the flow becomes turbulent. Flow

properties start to vary, and the velocity vector might be altered.

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 Figure 4: Laminar versus turbulent flow.

Reynolds number indicates whether a fluid is laminar or turbulent. (Nuclear Power,

n.d.). For our experiment, we need to make sure the flow is laminar, as turbulence

will add uncertainty. In addition, turbulence is random, and cannot be easily

calculated. Hence the need to keep the flow laminar, and Reynold’s number smaller

than one. This will be done by using a sphere of a small size.

2𝑟 × 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × ρ
𝑅𝑒𝑦𝑛𝑜𝑙𝑑𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 = η
𝑙𝑖𝑞𝑢𝑖𝑑
(equation 8)

Where

r: Radius of sphere

η: Viscosity

Viscosity

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Viscosity in a fluid is due to the friction of the neighbouring particles that are moving

at different velocities. Stoke’s law allows us to express the drag force resisting the

fall of small spherical particles through a fluid medium using a mathematical

equation. (Britannica, 2018)

In Stoke's law, the drag force 𝐹 acting upward in resistance to the fall is equal to

6π𝑟η𝑣, in which 𝑟 is the radius of the sphere, η is the viscosity of the liquid, and 𝑣 is

the velocity of fall. (Britannica.com, 2000)

Stoke’s law states that:

𝐹 𝑣𝑖𝑠𝑐
= 𝑆𝐴 𝑓𝑎𝑐𝑡𝑜𝑟
× 𝑟η𝑣 (equation 9)

Where

SA factor: Surface area factor (6 π) for spheres

𝑟: Radius of sphere

η: viscosity

For our sphere:

𝐹 𝑣𝑖𝑠𝑐
= 6π × 𝑟 × η𝑣 (equation 10)

To use Stoke’s law to find the viscosity of the liquid, 𝑣 needs to be constant, meaning

that the terminal velocity of the falling spheres is what has to be measured in order to

calculate viscosity.

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Interactions of these forces

Figure 5: Forces acting on a sphere as it falls through a viscous liquid

When the ball has reached terminal velocity, acceleration is constant so we can

equate the upward and downward forces.

This leaves us with the following equation:

𝐹 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦
+ 𝐹 𝑏𝑢𝑜𝑦
= 𝐹 𝑤𝑒𝑖𝑔ℎ𝑡
(equation 11)

Rearrange to get

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 𝐹 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦
= 𝐹 𝑤𝑒𝑖𝑔ℎ𝑡
− 𝐹 𝑏𝑢𝑜𝑦
(equation 12)

Previously, we had found 𝐹 𝑤𝑒𝑖𝑔ℎ𝑡

and 𝐹 𝑏𝑢𝑜𝑦
. We can therefore substitute the

expressions in Equation 12. This gives us:

4 3 4 3
𝐹 𝑣𝑖𝑠𝑐
= ( 3 π𝑟 × ρ 𝑏𝑎𝑙𝑙
× 𝑔) − ( 3 π𝑟 × ρ 𝑙𝑖𝑞𝑢𝑖𝑑
× 𝑔) (equation 13)

Simplify to get

4 3
𝐹 𝑣𝑖𝑠𝑐
= 3
π𝑟 × 𝑔 × (ρ 𝑏𝑎𝑙𝑙
− ρ 𝑙𝑖𝑞𝑢𝑖𝑑
) (equation 14)

If we equate the two equations we derived for 𝐹 𝑣𝑖𝑠𝑐

, we get the following

expression:

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 10 = 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 14

4 3
6π × 𝑟 × η𝑣 = 3
π𝑟 × 𝑔 × (ρ 𝑏𝑎𝑙𝑙
− ρ )
𝑙𝑖𝑞𝑢𝑖𝑑

Rearrange to obtain

2
2𝑟 ×𝑔×(ρ −ρ )
η= 𝑏𝑎𝑙𝑙
9𝑣
𝑙𝑖𝑞𝑢𝑖𝑑
(equation 15)

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Where:

𝑟: Radius of sphere

𝑔: Acceleration due to gravity

ρ : Density of the steel ball

𝑏𝑎𝑙𝑙

ρ 𝑙𝑖𝑞𝑢𝑖𝑑
: Density of the liquid, therefore, density of the oil used

𝑣: Terminal velocity of the ball

B. The experiment

B1. Oils used

As stated earlier, the goal of this EE is to understand the relationship between the

viscosity of oil and its temperature. Additionally, my interest was to compare how the

viscosity of new and used motor oils vary with temperature. Indeed, motor oils have

to be changed after a certain time as they degrade in engines.

Finding used oils is challenging. Indeed, engine oils are made of 75%-95% base oil,

a mineral oil that comes directly from a refinery. These base oils are hydrocarbons.

Hydrocarbons can be harmful for the environment, therefore most mechanics drain

the oils into a special cuve. Finding mechanics who agreed to collect the oils was

therefore a challenge in this EE. Lockdowns because of Covid and the difficulty of

finding used oils are the reasons why only two types of oils are studied in this essay.

Nevertheless, the two oils studied are interesting, as they are used in two types of

engines. The first one is “TOTAL QUARTZ 5000 SN'' , referred to as 15W-40 in this

15
essay. The oil is used in diesel, 4 stroke engines. The second oil studied is the

“Engen Super Outboard TC-W3”, referred to as TC-W3. This two-stroke oil lubricates

the engine parts as it passes through the engine, and is then burned along with the

fuel.

The differences between two-stroke and four-stroke engines, and the differences in

the properties of the oils used in them are beyond the scope of this paper.

Lubricants are made mainly of base oil, and the rest of their composition is additives.

Additives are added to improve the performance of the oil. They include anti-wear

additives, corrosion inhibitors to protect the engine and antioxidants which improve

the useful life of the lubricant. The useful life is the time for which the lubricant can

be used before being changed. Engine lubricants also have additives which improve

their viscosity variation, with temperature and these are called viscosity modifiers.

Indeed, the viscosity of the lubricant is its most important property. Dynamic viscosity

is measured in millipascals second (mPA s), and describes the resistance to shear

stress. This is the viscosity that is going to be measured in this experiment.

Scientists usually use a quantity known as kinematic viscosity, which is dynamic

viscosity divided by fluid density. However, the reason why we are using dynamic

viscosity and not kinematic viscosity is to reduce the possibility of error in the

experiment by adding a new value which will add uncertainty.

Another reason why we use dynamic viscosity is because we assume the oils to be

Newtonian Fluids, meaning that they follow Newton’s law of viscosity. Dynamic

16
viscosity being the coefficient of viscosity as defined in Newton’s law of viscosity, we

need to assume the oils are Newtonian fluids to measure it. Newton’s law of viscosity

states that “the ratio of shear stress to shear rate is a constant, for a given

temperature and pressure, and is defined as the viscosity or coefficient of viscosity”,

as he defines the relationship between the shear stress and shear rate of a fluid

subjected to mechanical stress. Newtonian fluids obey this law, hence we can

calculate their dynamic viscosity. (George and Qureshi, 2013)

Thermic engines operate at very high temperatures, usually ranging from 50°C to

1000°C. At high temperatures, due to chemical and physical reactions, oils tend to

have a lower viscosity. Before being commercialised, oils undergo a series of tests to

see if they can still assure their lubricating properties at higher or lower

temperatures.

The table below summarises the properties of both oils used, and this information

was retrieved from official data sheets published by their producers.

Property 15w40 TC-W3

Kinematic Viscosity at 40°C 90.48 𝑚𝑚 𝑠

2 −1
42 𝑚𝑚 𝑠
2 −1

Kinematic Viscosity at 13.59 𝑚𝑚 𝑠

2 −1
7,1 𝑚𝑚 𝑠
2 −1
100°C

Viscosity grade 15W-40 TC-W3

Viscosity index 152 130

Table 1: Oils properties, extracted from data sheets

17
 B2. Method

The objective of the experiment is to measure the terminal velocity of a steel ball as

it falls through oil, to calculate the viscosity of this one. Equation 15 will be used, and

−1 −2
will give the viscosity in newton-second per square metre (𝑁𝑠 𝑚 ), which is

equivalent to Pascals per second (Pa/s).

First of all, the density of the ball has to be found. The mass of a ball is measured

using a scale. Then the radius of the ball is measured with a micrometre screw

gauge, and we can find its volume. It is measured at different places on each ball to

4 3
ensure that they are spherical. Volume of a sphere being equal to 3
π𝑟 where 𝑟 is

the radius of the sphere. Ten spheres were used to gain time, as trials could be done

one after the other without having to retrieve the ball from the bottom of the cylinder.

Therefore, the radiuses of the 10 steel balls were used, and were all identical. Then,

by dividing the mass of the ball by its volume, the density of the ball is found. The

second step is to find the density of the oil. To do so, the mass of the empty

graduated cylinder is found. Then, the mass of the graduated cylinder is measured

3
with 100 𝑐𝑚 of oil in it. The mass of the fluid is found by subtracting the mass of the

empty cylinder from the mass of the cylinder with the fluid. Density being mass

divided by volume, it is easily calculated.

To find the viscosity of the ball, a tall cylinder of glass is filled with the oil to be tested.

The cylinder used measured 150 𝑐𝑚. A first mark was put 25 𝑐𝑚 above the bottom of

the cylinder, and then two other marks were put at points of difference 25 𝑐𝑚, as

shown on the diagram below.

18
 Figure 6: Tall cylinder

The ball is then dropped in the cylinder, and recorded on a phone camera. If the time

it takes to travel in the first 25 𝑐𝑚 is the same as the time it takes to travel through

the second 25 𝑐𝑚 area, it means the ball has reached terminal velocity. Then, the

distance travelled at terminal velocity, 50 𝑐𝑚, is divided by the time, and from there

we can find the velocity of the ball.

For temperatures above room temperature, the oil to be tested is heated up using a

magnetic stirrer. This device was chosen over traditional bunsen burners to avoid

putting the oils next to a flame. The oil is heated up in a beaker, before being poured

in a measuring cylinder, to ensure an even heating of the oil, and also for practicality

reasons. Then, as the oil cools down, readings are taken at each 5°C change, until

the oil reaches room temperature, 25°C.

19
For temperatures below room temperature, the oils are placed in a refrigerator until

they reach 10°C. They are taken out, poured in a measuring cylinder, and readings

are taken each 5°C change, until the oil heats up to room temperature.

When manipulating oil at high temperature, safety needs to be assured. As the oil

heats up, it becomes relatively dangerous. This is why the range of temperatures in

experiments did not exceed 50°C.

The diagrams below show the experiment set-up.

Figure 7: Heating the oils

20
Figure 8: Cylinder

21
 Image 1: Measuring cylinder

In addition, the table below shows the uncertainty of the measuring materials used.

Material Uncertainty

Digital scale ± 0.05 g

Ruler ±0.01 cm

Phone (stopwatch) ± 0.01 s

Micrometre screw gauge ±0.001 cm

Table 2: Materials used

22
 B3. Variables

Dependent variable: Terminal velocity

Independent variable: Temperature

Variable Way of control Reason for control

Length between the two Make the three marks with a Marks should not fade away.
marks permanent marker, and
each 25cm from each other.

Ball used Use the same type of ball Balls with different masses
throughout the experiment. and shapes fall into oil at
different speeds as they
have different Reynold
numbers.

Temperature of oil when Thermometer stays in the We do not want the oil
viscosity is measured measuring cylinder to temperature to vary while
detect any changes, and taking readings.
experiment is done with
windows closed and fans
off. The experiment is also
done quickly.

Amount of oil used The ball’s velocity is always

measured between the two
marks and the cylinder is
filled up to 125cm.

Friction The ball is dropped in the Avoid friction with the walls
middle of the cylinder. of the cylinder.
Table 3: Control variables

B4. Safety

Protective gloves and a lab coat have to be worn to protect skin from the oil. Inhaling

motor oils might lead to dizziness (UK Health and Safety Executive, 2011).

23
Therefore, a mask has to be worn and it is advised to work with safety goggles as

well.

As for the experiment, to ensure the stability of the retort clamp that was used to hold

the cylinder up, as seen in Image 1, a brick was placed at the back of it to make sure

the cylinder does not fall.

Moreover, oils can damage the environment. After the experiment, the oils were

given back to mechanics, who dispose of special curves where they safely collect

the oils.

24
 C. Analysis

C1. Results

State of oil Temperature °C ±0.5 Viscosity (𝑁𝑠

−1
𝑚 )
−2

±14.5%

New 50 1.256
45 1.412
40 1.545
35 1.688
30 1.732
25 2.315
20 2.774
15 2.999
10 3.210
Used 50 1.154
45 1.338
40 1.494
35 1.590
30 1.692
25 2.360
20 3.521
15 3.673
10 3.834
Table 4: Viscosity at different temperatures for TC-W3

25
 State of oil Temperature °C ±0.5 Viscosity (𝑁𝑠
−1
𝑚 )
−2

±14.5%

New 50 1.560
45 1.767
40 1.984
35 2.351
30 2.514
25 4.266
20 4.816
15 5.551
10 8.171
Used 50 1.464
45 1.576
40 1.841
35 2.235
30 2.500
25 3.578
20 4.160
15 5.459
10 6.007
Table 5: Viscosity at different temperatures for 15W-40

This information was compiled in the graphs below for more clarity. As predicted, the

best fit for all the lines was exponential.

26
Graph 1: Viscosity at different temperatures for TC-W3 oil (boat)

Graph 2: Viscosity at different temperatures for 15W-40 oil (car)

27
Graph 3: Viscosity at different temperatures for all oils

28
 C2. Error analysis

Calculating uncertainty in viscosity:

To find uncertainty in viscosity, the uncertainty in time is first found.

% 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = (𝐻𝑖𝑔ℎ𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 − 𝐿𝑜𝑤𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒) / 𝑀𝑒𝑎𝑛 × 100

From this, we can find the average percentage uncertainty in the velocity.

The table with the exact values can be found in the appendix, but the average

absolute uncertainty in time was 4.76% (see page 38). It was calculated using

formula:

% 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = (𝐻𝑖𝑔ℎ𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 − 𝐿𝑜𝑤𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒) / 𝑀𝑒𝑎𝑛 × 100

Uncertainty in the distance travelled, 25cm is ±0.01cm, which gives 0.04%.

%𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 / 𝑣𝑎𝑙𝑢𝑒 × 100

= 0. 01/25 × 100 = 0. 04%

Therefore, uncertainty in velocity is:

= %𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + %𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝑡𝑖𝑚𝑒

= 0. 04 + 4. 76 = 5%

29
Uncertainty in the density of the liquid is equal to

% 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 / 𝑣𝑎𝑙𝑢𝑒 × 100

𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝑚𝑎𝑠𝑠 + 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝑣𝑜𝑙𝑢𝑚𝑒

= 1. 3% + 1. 2%

This equals 2.5% .

Uncertainty in the density of the steel balls is found using the same formula as

above, this equals to 1%. This is lower than the uncertainty for liquid as a micrometre

screw gauge was used, giving more precise results.

Uncertainty in the radius of the sphere, 𝑟, equals to 0.5%.

From equation 15, we know that the absolute uncertainty in the viscosity of the oil

will be:

∆η = 2∆𝑟 + ∆ρ 𝑏𝑎𝑙𝑙
+ ∆ρ 𝑙𝑖𝑞𝑢𝑖𝑑
+ ∆𝑣

2
2𝑟 ×𝑔×(ρ −ρ )
η= 𝑏𝑎𝑙𝑙
9𝑣
𝑙𝑖𝑞𝑢𝑖𝑑
(Equation 15)

∆η = 2(0. 5) + 1 + 2. 5 + 2(5) = 14. 5%

Therefore, the percentage uncertainty for the viscosities of the oils is 14.5%. This is

a relatively high percentage, but can be explained by the fact that we used an

alternative way of measuring viscosity as I did not have access to a viscometer.

30
 C3. Relationship

The graphs all follow an exponential relationship. The graphs all show that, as

temperature increases, viscosity decreases, confirming the hypothesis. What is

interesting to note is that, if the viscosity of the unused car oil is smaller than the new

one, following the hypothesis, it is not the same for the boat oil. Indeed, the viscosity

of the used oil is greater than the viscosity of the new one at low temperatures,

before converging to a value.

To understand why this does not follow my hypothesis, it is important to understand

where my used oils come from. The used TC-W3 oil comes from a boat, and has

100 hours of use, which is the maximum amount of hours this oil can be used in the

engine. The car oil was removed after a specific number of kilometres, but not hours,

being in a four-stroke engine. Car manufacturers, when recommending oil changes,

tend to be less precise than boat manufacturers.

With more research, it is understandable why the results did not follow the

hypothesis. The best way of explaining it is through the following graph, which shows

why oils have to be changed. It explains that ideally oil will be changed when the

maximum useful life has been attained (condition-based) rather than by a schedule

where the oil may be still fit for purpose or even beyond its use-by-date. When the

viscosity increases too much at room temperature, it means it needs to be

changed. This increased viscosity is linked to the oxidation of the oil. These

31
chemical changes come from the reactions discussed in part A3, and therefore

explain why the boat oil does not follow the hypothesis: it needed to be changed,

unlike the car oil.

Graph 4: The Life Cycle of Oil (www.kewengineering.co.uk, n.d.)

D. Conclusion

From this EE, the following conclusions can be made:

- The viscosity of motor oils decreases with increasing temperature following an

exponential relationship.

- Used motor oils will have a greater viscosity than new ones only if they have

reached their maximum useful life.

32
 E. Evaluation

Calculating the viscosity of an oil using a falling sphere is a simple experiment that

can easily be done in schools. In this section, I will discuss the strengths and

weaknesses of this experiment as well as how to improve it.

E1. Strengths and weaknesses

The first advantage of this experiment is its simplicity. It only requires a little amount

of materials, and is relatively quick to conduct. Due to new technologies, taking

precise measurements is possible, allowing us to work with small amounts of oil, and

little filming time.

However, working with motor oils leads to a few disadvantages. First of all, it is quite

hard to find used motor oils, as most mechanics, when changing car oil, will put it in

a specific cuve. Finding and retrieving used oils is therefore a long process, which

takes a lot of persuading. Secondly, it is dangerous to work with high temperatures,

due to the risks of burning and impossible to use a bunsen burner due to the risks

with putting oil close to a flame.

In addition, even if falling spheres is the most accurate way I have of finding

viscosities, the accuracy is still quite poor compared to a viscometer.

E2. Improvements

33
If ever this experiment were to be done again, here are some improvements that

could be made:

- Use of a more accurate means of measuring viscosity, such as a viscometer

would have increased the accuracy of the experiment and ensured more

reliable results.

- Have knowledge of the number of hours both the oils have been in the motor,

or in the case of the car oil, how many kilometres it had been used for. This

information would have allowed me to confirm my conclusion concerning the

age of the oils.

- Use a more accurate means of measuring the temperature, such as a digital

thermometer would ensure more accurate results.

Extensions:

This investigation highlights how the time the oil was in the engine affects its

properties. Indeed, oils and the additives in it undergo chemical reactions that

change its viscosity. More investigation in comparing how time of use affects

viscosity, and how additives can be used to improve the time oil can be used in the

engine could lead to better oils being produced and less oil wastage.

34
Appendix

Engen Super Outboard TC-W3

State of oil Temperatu Time in s / Trials ±0.001

re
1 2 3 4 5

New 50 0.161 0.183 0.179 0.161 0.182

45 0.210 0.223 0.194 0.187 0.190
40 0.231 0.223 0.210 0.237 0.220
35 0.230 0.252 0.240 0.241 0.230
30 0.245 0.266 0.251 0.259 0.249
25 0.341 0.333 0.380 0.357 0.360
20 0.546 0.529 0.531 0.515 0.521
15 0.561 0.544 0.558 0.563 0.530
10 0.535 0.601 0.551 0.611 0.579

Used 50 0.190 0.177 0.188 0.192 0.196

45 0.224 0.196 0.218 0.210 0.212
40 0.246 0.236 0.245 0.220 0.213
35 0.245 0.258 0.242 0.261 0.261
30 0.260 0.270 0.270 0.250 0.250
25 0.314 0.326 0.377 0.352 0.369
20 0.410 0.400 0.423 0.435 0.414

15 0.444 0.430 0.459 0.468 0.450

10 0.490 0.512 0.489 0.459 0.460

Table 5: Time taken for sphere to fall at different temperatures in Engen Super

Outboard TC-W3 oil

35
TOTAL QUARTZ 5000 SN

State of oil Temperatu Time in s / Trials ±0.001

re °C
1 2 3 4 5

New 50 0.233 0.217 0.221 0.221 0.207

45 0.223 0.235 0.247 0.248 0.230
40 0.285 0.270 0.278 0.289 0.260
35 0.355 0.341 0.310 0.342 0.330
30 0.371 0.385 0.378 0.364 0.379
25 0.541 0.535 0.571 0.517 0.522
20 0.611 0.645 0.626 0.631 0.610
15 0.800 0.801 0.836 0.812 0.849
10 0.912 0.892 0.909 0.886 0.910

Used 50 0.215 0.236 0.251 0.230 0.239

45 0.251 0.261 0.283 0.270 0.261
40 0.295 0.289 0.301 0.312 0.292
35 0.344 0.355 0.355 0.362 0.349
30 0.381 0.370 0.381 0.360 0.395
25 0.651 0.625 0.641 0.656 0.629
20 0.729 0.690 0.745 0.720 0.731
15 0.819 0.821 0.857 0.840 0.830
10 1.241 1.230 1.225 1.227 1.210
Table 6: Time taken for sphere to fall at different temperatures in TOTAL QUARTZ

5000 SN

Oil used TC-W3 15W-40

State of oil Temperature °C Percentage Percentage

uncertainty in the uncertainty %
time of fall %

New 50 6.35 5.91

45 8.96 5.28

36
 40 6.02 5.25
35 4.61 6.70
30 4.13 2.80
25 6.63 5.03
20 2.93 2.80
15 2.99 2.99
10 6.60 1.44
Used 50 5.04 7.69
45 6.60 6.03
40 7.11 3.86
35 3.75 2.55
30 3.85 4.64
25 9.06 2.42
20 4.20 3.80
15 4.22 2.28
10 5.50 1.26
Table 7: Percentage uncertainty

Mean of uncertainty in time: 4.76%

Density of sphere 482.96 𝑔𝑐𝑚

−3

Density of used TOTAL QUARTZ 5000 SN 0.8524 𝑔𝑐𝑚

−3

Density of new TOTAL QUARTZ 5000 SN 0.8208 𝑔𝑐𝑚

−3

Density of used Engen Super Outboard 0.6723 𝑔𝑐𝑚

−3
TC-W3

Density of new Engen Super Outboard 0.8464 𝑔𝑐𝑚

−3
TC-W3

Distance travelled by sphere 25 cm

Table 8: Key values for calculation

37
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40