SHORT INTRO

An experiment was conducted to find the viscosity of oil by

using the relationship between diameter and terminal velocity of a sphere. This

was done by dropping balls of different materials and masses and recording the

time taken to fall a certain distance. The results I obtained were INSERT

RESULT HERE. The oil that was used is called SAE30 and has a real value of

INSERT RESULT HERE, this is quite different to the values that were calculated

with a percentage error of INSERT RESULT HERE.

INTRODUCTION

The main application for this experiment is to find the

viscosity of an oil with unknown viscosity, this can give applications such as

being able to predict how the oil will behave, and can also help in

transportation and production of the oil as well. However, the viscosity

calculated only applies to one temperature as viscosity varies greatly with

temperature.

The oil used was SAE 30 which

according to the manufacturers website has a dynamic viscosity of 0.2393 at a temperature of 20oC, the website that I

am using did not have any errors associated with it. According to the website

they use a rotational viscometer. This involves rotating a probe in a sample of

the liquid and the force required is used to calculate the viscosity. Another

value for SAE from a different source is 0.310 and

again does not come with errors. This is quite different to the other supposed

value, this could be due to the fact the website states three different methods

used; capillary tube viscometer, Saybolt viscometer, and a rotational viscometer.

A saybolt viscometer calculates viscosity by heating the oil until it fills a

container of known volume, and a capillary tube viscometer measures the time

taken for a known value of oil to flow through a capillary with known diameter

and

length.

The

method that I used involved dropping a spherical ball into a cylinder of the

oil and calculating the terminal velocity which I then, using stokes law and

other equations allowed me to calculate the viscosity of the oil. To have an

accurate answer two different types of materials were used, this way the

viscosity of the oil should be the same in both cases and it would give further

credibility to our answer. However, the values I obtained varied by nearly

double, which then led me to believe that a mistake was made during the

experiment most likely when dropping the WHICHEVER HAD THE MOST DIFFERENCE as

this was nearly double the reported value of the viscosity for the oil.

THEORY

The experiment that I did finds the value for the dynamic

viscosity of an unknown oil. This is mainly done by using stokes law where is viscous drag force and is the viscosity of the fluid:

In the case of our experiment the total acceleration needs

to be zero as the sphere will be travelling at terminal velocity. This can be

done by formulating an equation using newtons second law and making the

resultant force equal to its weight minus the buoyancy force .

In order for the acceleration to be zero the resultant force

must equal as this means that the ball will be travelling

at terminal velocity. Now with equation one and two can be substituted

together.

The buoyancy force in the case of the sphere is equal to with being the buoyancy of the liquid. The buoyancy

force can now be substituted into the equation and can be changed into as this will allow for easier simplifying

later with being the density of the sphere and as the volume of the ball. Now substituting

both of these into the equation and simplifying you get the equation:

Elimanting some variables and swapping for the equation can be simplified to make it

equal to the terminal velocity in terms of the diameter of the sphere dropped

in the liquid.

This now means that the visocosity of the oil can be

calculated after plotting a graph of terminal velocity against diameter

squared, this then means, if the other variables are known, the viscosity of

the oil can be found.

For this model there are several assumptions, one of the

main ones being that the sphere is actually travelling at terminal velocity

when it passes the two markings as this is the mian theory for the experiment,

another being the temperature doesn’t change during the experiment as this

would cause the value for viscosity to change because it is very temperature

dependent. This also applies to measuring the density of the oil because if

this is measured at a different time to the experiment the temperature could

have a difference that affects the final value.

METHOD

As shown in the theory section of this report the

measurements required are terminal velocity, the density of the sphere and the

oil, and the diameter of the spheres that have been dropped. The main set up

for the experiment is to find the terminal velocity of the spheres and the

values can be obtained with little equipment such as a scale and a micrometer.

Figure 1: Basic diagram of the experiment.

A cylinder filled with the oil and with three lines at equal distance apart

from each other and a stopwatch to record the time for the sphere to travel

these distances

To collect all the data several other measurements are

required which involve equipment not shown in Figure 1. These include using a

density bottle to find the density of the oil and using a micrometer to find

the diameters of the spheres, then a scale to find the density of each sphere.

Once these measurements had been collected I could use the setup in Figure 1.

This involved dropping the ball and recording the time taken to drop from the

first line to the second, then separately record the time taken to drop from

the second line to the third line. These two times are then averaged to get the

value for the time taken to drop a known distance. This was then repeated for

spheres of different diameters made of steel and nylon so that a graph could be

plotted.

PARAGRAPH ON ERRORS

ANALYSIS AND RESULTS

In this section I will be looking at my results and

comparing them to the real values as provided by the manufacturers and other third-party

companies. I will also be commenting on the validity of the experiment and the

analysis methods used to obtain values for the viscosity. As said in a previous

method the raw data was measured using a stopwatch and this was then used to

find a value for terminal velocity, as this allowed the viscosity to be found

more easily. Figures 1 and 2 are both shown below with them representing

terminal velocity against diameter squared with Figure 1 showing the results

for steel balls and figure 2 for nylon balls. For both Figure 2 and 3 have data

that very closely resemble their respective linear fit which also means the

error bars are easily in the best fit line.

Figure 2: Graph

showing terminal velocity against diameter squared with a least squares fit

shown. This graph is showing the results for when steel was the material of

the spheres.

Figure 3: Graph

showing terminal velocity against diameter squared with a least squares fit

shown. This graph is showing the results for when nylon was the material of

the spheres.