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SHORT INTROAn experiment was conducted to find the viscosity of oil byusing the relationship between diameter and terminal velocity of a sphere. Thiswas done by dropping balls of different materials and masses and recording thetime taken to fall a certain distance.

The results I obtained were INSERTRESULT HERE. The oil that was used is called SAE30 and has a real value ofINSERT RESULT HERE, this is quite different to the values that were calculatedwith a percentage error of INSERT RESULT HERE. INTRODUCTIONThe main application for this experiment is to find theviscosity of an oil with unknown viscosity, this can give applications such asbeing able to predict how the oil will behave, and can also help intransportation and production of the oil as well. However, the viscositycalculated only applies to one temperature as viscosity varies greatly withtemperature. The oil used was SAE 30 whichaccording to the manufacturers website has a dynamic viscosity of 0.

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2393 at a temperature of 20oC, the website that Iam using did not have any errors associated with it. According to the websitethey use a rotational viscometer. This involves rotating a probe in a sample ofthe liquid and the force required is used to calculate the viscosity. Anothervalue for SAE from a different source is 0.310 andagain does not come with errors. This is quite different to the other supposedvalue, this could be due to the fact the website states three different methodsused; capillary tube viscometer, Saybolt viscometer, and a rotational viscometer.A saybolt viscometer calculates viscosity by heating the oil until it fills acontainer of known volume, and a capillary tube viscometer measures the timetaken for a known value of oil to flow through a capillary with known diameterand length. Themethod that I used involved dropping a spherical ball into a cylinder of theoil and calculating the terminal velocity which I then, using stokes law andother equations allowed me to calculate the viscosity of the oil.

To have anaccurate answer two different types of materials were used, this way theviscosity of the oil should be the same in both cases and it would give furthercredibility to our answer. However, the values I obtained varied by nearlydouble, which then led me to believe that a mistake was made during theexperiment most likely when dropping the WHICHEVER HAD THE MOST DIFFERENCE asthis was nearly double the reported value of the viscosity for the oil. THEORYThe experiment that I did finds the value for the dynamicviscosity 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 needsto be zero as the sphere will be travelling at terminal velocity. This can bedone by formulating an equation using newtons second law and making theresultant force equal to its weight minus the buoyancy force .In order for the acceleration to be zero the resultant forcemust equal  as this means that the ball will be travellingat terminal velocity. Now with  equation one and two can be substitutedtogether.The buoyancy force in the case of the sphere is equal to  with  being the buoyancy of the liquid.

The buoyancyforce  can now be substituted into the equation and  can be changed into  as this will allow for easier simplifyinglater with  being the density of the sphere and  as the volume of the ball. Now substitutingboth of these into the equation and simplifying you get the equation:Elimanting some variables and swapping  for  the equation can be simplified to make itequal to the terminal velocity in terms of the diameter of the sphere droppedin the liquid.This now means that the visocosity of the oil can becalculated after plotting a graph of terminal velocity against diametersquared, this then means, if the other variables are known, the viscosity ofthe oil can be found. For this model there are several assumptions, one of themain ones being that the sphere is actually travelling at terminal velocitywhen 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 thiswould cause the value for viscosity to change because it is very temperaturedependent. This also applies to measuring the density of the oil because ifthis is measured at a different time to the experiment the temperature couldhave a difference that affects the final value.

METHODAs shown in the theory section of this report themeasurements required are terminal velocity, the density of the sphere and theoil, and the diameter of the spheres that have been dropped. The main set upfor the experiment is to find the terminal velocity of the spheres and thevalues 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 arerequired which involve equipment not shown in Figure 1.

These include using adensity bottle to find the density of the oil and using a micrometer to findthe 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 thefirst line to the second, then separately record the time taken to drop fromthe second line to the third line. These two times are then averaged to get thevalue for the time taken to drop a known distance. This was then repeated forspheres of different diameters made of steel and nylon so that a graph could beplotted.

PARAGRAPH ON ERRORS ANALYSIS AND RESULTSIn this section I will be looking at my results andcomparing them to the real values as provided by the manufacturers and other third-partycompanies. I will also be commenting on the validity of the experiment and theanalysis methods used to obtain values for the viscosity. As said in a previousmethod the raw data was measured using a stopwatch and this was then used tofind a value for terminal velocity, as this allowed the viscosity to be foundmore easily. Figures 1 and 2 are both shown below with them representingterminal velocity against diameter squared with Figure 1 showing the resultsfor steel balls and figure 2 for nylon balls. For both Figure 2 and 3 have datathat very closely resemble their respective linear fit which also means theerror 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.

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