PHYSICS INVESTIGATORY PROJECT Fluid Mechanics: Viscosity of Engine Oils
By Arpit Joshi
INDEX Introduction Aim Apparatus Theory Procedure Observations Calculations Conclusion Bibliography
INTRODUCTION Consider the following situation: You are driving your diesel car on the road to shimla and it is very cold outside. Suddenly your car breaks down and you open the bonnet to see what is wrong. You notice that grime has accumulated in your engine and the motor oil is to be replaced for the car to start. You only have the following oils: 1) 2) 3) 4)
MAK Gold 40(for bikes) Servo 4T (for bikes) HP Milcy Turbo (for trucks) Castrol Active (for trucks)
Of the given choices, you must use your knowledge of viscosity and fluid mechanics to choose the oil most suited for your car.
AIM To compare the viscosity of different engine oils at a given temperature and thereby determine the most effective one for a diesel car.
APPARATUS 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 oils
THEORY Why is engine oil used and how does it work? Engine oil is used for lubricating various internal combustion engines. The main function is to reduce wear and tear of moving parts. Thus, the oil creates a layer that helps them move smoothly. It also cleans, inhibits corrosion, improves sealing, and cools the engine by carrying away the heat from the moving parts.
How is engine oil rated? Engine oils can be made of single polymers or multiple polymers and are rated accordingly. These differ in their viscosity and hence, differ in their uses. The SAE gives a single grade to
engine oils. However, multi grade oils are more popular. Multi grade oils are rated in the form xWy. ‘W’ is the winter rating which shows that the oil has been tested for cold conditions. ‘x’ tells us which single grade polymer the oil behaves like under cold conditions. The lower the number, the less viscous the oil and better the performance in low temperatures. ‘y’ tells the single grade polymer as much as which the oil thins at high temperature. The rating is primarily based on the viscosity of engine oils. Hence, it is evident that viscosity is the single most important characteristic deciding the efficiency of these oils.
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, it opposes the motion between its different layers.
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. Thus, a backward dragging force F acts tangentially to every layer. Thus, the force becomes: F= ἠA(v/x) Where, v=Speed of the layer A=Area of the layer x=Seperation between the layer. In this equation, the constant of proportionality (ἠ) is called the coefficient of viscosity.
Stokes Law It was shown by stokes law that if a small sphere of radius ‘r’ be moving with a terminal velocity ‘v’ through an infinite homogenous and incompressible fluid of coefficient of viscosity ‘ἠ’, it experiences a force F given by:
F=6πἠrv Terminal velocity is known as the maximum velocity acquired by the body falling in a viscous medium.
PROCEDURE 1. 850ml 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 marker. 3. Two loops of string were tied around the lower part of the glass tube, 50 cm apart. One at 65cm and the other at 15cm. 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 and was stopped when it reached the second. 7. Three reading were taken for each engine oil and their observations were noted.
OBSERVATIONS Radius of carbon steel ball = 1.905 (r) Density of carbon steel ball = 549.45 kg/m3 (ρ) Density of all oils = 0.84 g/m3 = 840 kg/m3 (ρ) Ambient temperature = 25 (degree Celsius) Time taken in different oils OIL NAME TIME(seconds AVERAGE ) TIME T1 T2 T3
MAK Gold 40
3.5 1 Servo 4T 3.0 1 HP Milcy 2.8 Turbo 6 Castrol Active 3.1
3.3 5 3.0 6 2.6 6 3.0 1
3.4 1 3.0 3 2.7 1 3.0 8
3.42 3.03 2.74 3.06
Terminal Velocity in different oils OIL NAME TERMINAL VELOCITY(m/s) MAK Gold 40 0.146 Servo 4T 0.165 HP Milcy Turbo 0.182 Castrol Active 0.137
CALCULATIONS 6πἠrv = (4/3) π r3 (ρ-σ) g
ἠ = [2 r2 (ρ-σ) g]/9v MAK Gold 40 ἠ = [2*(1.9x10-3)2 * (549.45-0.84) * 9.8] / (9*0.146) ἠ = 0.029541 kg/ms Servo 4T ἠ = [2*(1.9x10-3)2 * (549.45-0.84) * 9.8] / (9*0.165) ἠ = 0.02614 kg/ms HP Milcy Turbo ἠ = [2*(1.9x10-3)2 * (549.45-0.84) * 9.8] / (9*0.182) ἠ = 0.023698 kg/ms Castrol Active ἠ = [2*(1.9x10-3)2 * (549.45-0.84) * 9.8] / (9*0.137) ἠ = 0.031482 kg/ms These 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 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 decrease with increase in temperature. Therefore, we must also look at the coefficient of thermal expansion of engine oils in order to calculate the new density and in turn, the kinematic viscosity. Volumetric Expansion ∆V=α∆T V=Volume
α=Coefficient of thermal expansion T = temperature Change in density ρ1=ρ0 / [1+ α(t1-t0)] Kinematic Viscosity v=µ/ρ v=kinematic viscosity µ=absolute/dynamic viscosity ρ=density Viscosity Index VI=(L-U) / (L-H) * 10 U=Kinematic viscosity L and H=kinematic viscosity of the reference oils
Volume Flowrate = F = P1-P2/R = π (Pressure difference)(radius)4 / 8(viscosity)(length) Resistance to flow = R = 8ἠL/πr4 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 µ(T)= µ0exp(-bT) In order to calculate the the kinematic viscosity ratio, we can use this formula and then divide by the respective densities.
Dynamic viscosity is the coefficient of viscosity of a liquid which we have calculated. OIL NAME MAK Gold 40
COEFFICIEN T OF VISCOSITY 0.029541
Servo 0.02614 4T HP 0.023698 Milcy Turbo Castrol 0.031482 Active
DENSIT Y 820
KINEMATIC VISCOSITY (m2/s) 0.000359
KINEMATIC VISCOSITY (cSt) 359
840
0.000311
311
820
0.000289
289
840
0.000374
374
Calculating the kinematic viscosity at 1000C: µ(T)= µ0 * e-bt µ0= µ(T) / e-bt µ(100)=( µ(T) / e-bt ) * e-b(373) ( Used to calculate ‘b’ in the equation ) e-b(373) / e-bt=K V(T) / V(100) = [µ0 * e-bt / ρ(t)] / [ { µ0*e-b(373) }/ {ρ(t)/1+α(100-T)}]
Thus, V(100) / V(T)=[ e-b(373) / e-bt ] * [1+ α(100-T)]
CONCLUSION V(100) / V(T)=[ e-b(373) / e-bt ] * [1+ α(100-T)] This Equaiton puts all the values of kinematic viscosity of the oils in the SAE 40 range. In order to compensate for the grime buildup and the face that the engine may have to start in colder weather, the least vicous oil should be used. With a dynamic viscosity of 0.023698 kg/m3 and a kinematic viscosity of 289 cSt, HP Milcy Turbo is the ideal engine oil.
BIBLIOGRAPHY www.machinerylubrication.com www.kittiwake.com www.carbibles.com www.racq.com.au www.redlineoil.com www.upmpg.com www.oilwinlube.com www.kewengineering.co.uk www.howstuffworks.com www.synlube.com/viscosity.html www.engineeringtoolbox.com www.en.wikipedia.org/wiki/Motor_oil