This document summarizes a physics investigatory project on measuring the viscosity of different engine oils. It finds that HP Milcy Turbo oil has the lowest viscosity, measured as 0.023698 kg/m3, and would be most suitable for a diesel car traveling to high altitudes where lower temperatures require less viscous oil. The project involved measuring the terminal velocity of a steel ball falling through samples of various oils using Stokes' Law calculations to determine each oil's viscosity coefficient. While all oils fell under the SAE 40 rating, HP Milcy Turbo was determined to flow most easily at cooler temperatures based on its dynamic viscosity.

1. GHAZIABD
PHYSICS INVESTIGATORY PROJECT
TOPIC VISCOSITY OF ENGINE OIL
CLASS 11 SECTION B

2. This is to certify that MAYANK
SINGH is student of class XI B has
successfully completed the
research on the below mentioned
project under the guidance of
physics teacher during year 2017-
2018 in partial fulfillment of
chemistry practical examination of
central board of secondary
education(CBSE)
Physics teacher

3. I would like to express my special
thanks to our school “RYAN
INTERNATIONAL SCHOOL", principal
ma’am, to the management team of
our school who gave me the golden
opportunity to do this wonderful
project on the topic “viscosity of
engine oil "which also helped me in
doing lot of research I came to know
about so many new things.
Secondly I would also like to thank
my parents and friends who helped
me a lot in finishing this project
within limited time.

4. INDEX
 Aim
 Apparatus
 Theory
 Procedure
 Observation
 Calculation
 Result
 Conclusion

5. To compare the viscosity of different
engine oils at given temperature
there by determine the most
effective one for a diesel car.
AIM

6. APPARTUS
1.Meter high, 5cm broad
cylindrical glass tube.
2.Meter scale alongside
tube.
3.High density carbon
steel balls.
4.Screw gauge
5.Stop watch
6.String
7.Assorted engine oil

7. THEORY
Why is engine oil used and how does it work?
Motor oil or engine oil is used for lubrication of various
internal combustion engines.
The main function is to reduce wear on moving parts.
How it is rated:
Engine oils can be made of singular polymers (single
grade) or multiple polymers (multi grade) and are rated
accordingly. These differ in their viscosity, and therefore,
in their uses. The SAE gives a single grade to engine oils.
However, single grade oils cannot withstand the variety
of conditions vehicles today are put through. Therefore,
multi grade oils are more popular. These behave as
differently rated single grade oils under different
temperature conditions. Under cold conditions, the oil is
thin enough to grease the engine and allow for proper
ignition and running. Under high engine temperatures,
the oil only thins to a particular extent so as to keep the
engine sufficiently lubricated.

8. What is viscosity?
It is the property of a fluid by virtue of which an
internal resistance comes into play when the fluid is
in motion, and opposes the motion between its
different layers. In a vehicle engine, viscosity
determines how easily the motor oil flows to
different parts of the engine.
Coefficient of viscosity
When liquid flows over a flat surface, the liquid
layer in contact with the fixed surface does not
move. Higher layers move forward with increasing
velocity. Due to relative motion, a backward
dragging force F acts tangentially to every layer. This
force is proportional to the speed (v) of the layer,
the area (A) of the layer and inversely proportional
to their separation (x). Combining these factors we
have the following:
F = ηA (v/x)

9. Stokes Law
It was shown by Stokes Law that if a small sphere of
radius r be moving with a terminal v through an
infinite homogeneous and incompressible fluid of
coefficient of viscosity η, it experiences a force F
given by,
F = 6πηrv (This relation is known as Stokes Law)
Terminal Velocity
This is the maximum velocity acquired by the body
falling freely in a viscous medium. Consider a small
sphere of radius (r) and density (ρ) falling freely in
a viscous medium (coefficient of viscosity η and
density σ).
Total downward force = Weight of sphere – up-
thrust F = (4/3) π r3 (ρ – σ) g
This is equal to the upward force of viscosity
= 6πηrv ∴ 6πηrv = (4/3) π r3 (ρ – σ) g

10. 1. 850 ml of the oil was weighed and the density
was found out
2. The jar was cleaned and filled with the motor
oil up to a 97 cm (850 ml) marker.
3. Two loops of string were tied around the
lower part of the glass tube, 50 cm apart: one
at 65 cm and the other at 15 cm.
4. A high density carbon steel shot was
measured and weighed to determine its
density
5. The carbon steel shot was dropped into the
liquid
6. The timer was started when the shot reached
the first string (at terminal velocity) and
stopped when it reached the second one.
7. Three readings were taken for each engine oil
and the observations were noted.

11. Radius of carbon steel ball = 1.905mm (r)
Density of carbon steel ball = 549.45 kg/m3 (ρ)
Density of all oils = 0.84 g/cm3 = 840 kg/m3 (σ)
Ambient temperature = 25oc
Oil
name
TIME(SECONDS) AVERAGE
TIMET1 T2 T3
MAK
gold40
3.51 3.35 3.41 3.42
Servo 4t 3.01 3.06 3.03 3.03
HP Milcy
turbo
2.86 2.66 2.71 2.74
Castrol
active
3.1 3.01 3.08 3.06
Time taken in different oils

12. Terminal velocity in different oils
OIL NAME TRMINAL
VELOCITY
MAK Gold40 0.146
Servo4T 0.165
HP Milcy Turbo 0.182
Castrol active 0.137
Terminal velocity = 0.5m/average
time

13. 6πηrv = (4/3) π r3 (ρ – σ) g
η = [2r2 (ρ – σ) g ] / 9 v
MAK Gold 40
η = [2 * (1.9x10-3)2 * (549.45 - 0.84) * 9.8] / (9 * 0.146)
η = 0.029541 kg/ms
Servo 4T
η = [2 * (1.9x10-3)2 * (549.45 - 0.84) * 9.8] / (9 * 0.165)
η = 0.02614 kg/ms
HP Milcy Turbo
η = [2 * (1.9x10-3)2 * (549.45 - 0.84) * 9.8] / (9 * 0.182)
η = 0.023698 kg/ms
Castrol Active
η = [2 * (1.9x10-3)2 * (549.45 - 0.84) * 9.8] / (9 * 0.137)
η = 0.031482 kg/ms

14. There are a wide range of factors that must be taken
into consideration to choose the right engine oil.
Engine oil ratings are based on the viscosity of the oil,
but these ratings aren’t exactly accurate. Each of
these oils falls under a SAE 40 rating, but they have
different viscosities.
The rating of engine oils therefore is based on a factor
known as kinematic viscosity. Kinematic viscosity in
turn is the ratio between dynamic viscosity (absolute
viscosity) and the density of the liquid. These values
are then divided into ranges and then SAE ratings.
The kinematic viscosity however will not be constant
at a given temperature. The density of liquids
decreases with increase in temperature. This is
because when temperature rises so does volume.
When volume rises the density decreases.
Therefore we must also look at the coefficient of
thermal expansion of engine oils in order to calculate
the new density and in turn, kinematic viscosity.

15. The Coefficient of Thermal Expansion of light diesel oil is
0.00085.
Assuming this value to be equal to the coefficient of thermal
expansion of our engine oils, we have postulated that we can
calculate the kinematic viscosity at any given temperature.
Assuming the exponential model for calculation of absolute
viscosity to hold true under our conditions
In order to calculate the kinematic viscosity ratio at a given
temperature we can use this equation, divided by the respective
densities.
Dynamic viscosity is the coefficient of viscosity of a liquid which
we have calculated
Oil Name Coefficient of
Viscosity
Density Kinematic
Viscosity
(m2/s)
Kinematic
Viscosity
(cSt)
MAK Gold
40
0.029541 820 0.000359 359
Servo 4T 0.02614 840 0.000311 311
HP Milcy
Turbo
0.023698 820 0.000289 289
Castrol
Active
0.031482 840 0.000374 374

16. Volumetric Expansion
ΔV = α ΔT
(V-Volume, α-Coefficient of Thermal
Expansion, T-Temperature)
Change in Density
ρ1 = ρ0 / [1 + α ( t1 - t0 )]
(ρ – Density, α- Coefficient of Thermal
Expansion, t-Temperature)
Kinematic Viscosity
ν = μ / ρ
(ν = kinematic viscosity, μ = absolute or
dynamic viscosity, ρ = density)
Viscosity Index
VI = (L - U)/ (L - H) * 10
(U - kinematic viscosity, L and H –
kinematic viscosity of the reference
oils)

17. Calculating the kinematic viscosity at 1000 C :
μ(T)= μ0 * e-bT
μ0 = μ(T) / e-bT
μ(100) = (μ(T) / e-bT) * e-b(373)
(Used to calculate the value of the constant ‘b’ in the
equation)
e-b(373) / e-bT = k (constant at a given
temperature T)
V(T) / V(100) = [μ0 * e-bT / ρ(t) ] / [ {μ0 * e-b(373)} /
{ρ(t) / 1 + α ( 100 – T ) } ]
(Cancelling μ0 and ρ(T) from the equation)
V(T) / V(100) = [1 / k * {1 + α ( 100 – T ) } ]
V(100) / V(T) = k * [1 + α ( 100 – T ) ]
or
V(100) / V(T) = [e-b(373) / e-bT ] * [1 + α ( 100 – T ) ]
(This is a hypothesised relation which may or may not
hold true for all values that are entered into it.)

18. CONCLUSION
V(100) / V(T) = [e-b(373) / e-bT ] * [1 +
α ( 100 – T ) ]
This equation puts all the values of
kinematic viscosity of the oils in the
SAE 40 Range. Therefore any of the oils
may be used as SAE 40 is suitable for
prolonged use in cars.
But in order to compensate for the
grime build-up and the fact that the
engine may have to start in colder
weather as it is specified that the car is
on its way to a hill station, the least
viscous oil should be used. This oil will
ensure it doesn’t get too thick at lower
temperatures and will still flow.

19. RESULT
With a dynamic
viscosity of 0.023698
Kg/m3 and a kinematic
viscosity of 289 cSt, HP
Milcy Turbo is the ideal
engine oil.

20. 1.Help from internet
• www.sciencefare.com
• www.mycbseguide.com
2. Help from books
• Reference from physics NCERT
3. Help from teachers