Division of Engineering Assessed In-depth Report 2 EH0SCA: Foundation Science A Experiment to find the Viscosity of Oil To be submitted one week from the date of the laboratory session To be completed by student| Student Name| | | Student ID| | | Date of experiment| | | Date submitted| | | Office use only| Grade awarded| | | Penalty| | | Final grade| | | Markers Signature| | Summary The purpose of this experiment is to use Stockes law to obtain the viscosity of an oil sample.

During the experiment, there are a number of knowledge are associated with the final results such as Stockes law F = 6?? rv. According to this equation, calculate the viscosity of an oil sample is simple when ? = g(? s-? f)D218??. Therefore, it is essential to find out the value of terminal speed u? = Lt and measure the diameter of balls as well as utilizing ? s=m43? (D2)3 to calculate ? s. In addition, learning how to use the equipments also is contained such as micrometer and electronic weighing instrument during the experiment. However, there exist some errors associated many factors.

For example, the measurements about the diameter and mass of ten balls are not accurate and when reading the data on the electronic weighing instrument and tubes is incorrect so that it influences the final result. Thus, in order to improve the result, it is necessary to read the data as accurately as possible and improve the accuracy of the electronic weighing instrument and other equipments. Although the final result is not prefect but it also assumes that Stockes’ flow exists. Content Summary………………………………………………………………………………. Page2 1. Objective……………………………………………………………………………….

Page 5 2. Theory……………………………………………………………………………………Page 5 3. Apparatus…………………………………………………………………………….. Page 6 4. Procedure…………………………………………………………………………….. Page 6 5. Results and Calculations………………………………………………………. Page 8 6. Discussion ………………………………………………………………………….. Page 11 7. Conclusion …………………………………………………………………………. Page 11 8. Reference ……………………………………………………………………………. Page 13 Figures and Tables Figure 3. 1 the equipments in the experiment …………………………………7 Figure4. 1 the graph to show procedure 5……………………………………….. 7 Table 5. 1 The known data…………………………………………………………………. 8

Table5. 2The measured data (A)……………….. ……………………………………… 8 Table 5. 3The measured data(B)…………………………………………………………9 Table5. 5 The calculated data…………………………………………….. ………………9 1. Objective The purpose of this experiment is to use Stockes law to obtain the viscosity of an oil sample. 2. Theory Real fluids have viscosity. Consequently, the boundary layer fluid in contact with a stationary wall or surface is nearly at rest, whereas flow speeds in the center of a pipe or channel. Flow is typically laminar at low speeds; at higher speeds, flow tends to become turbulent.

One more useful relation in viscous fluid flow is the expression for the magnitude F of force exerted on a sphere of radius r that moves with speed v through a fluid with viscosity ?. When v is small enough that there is no turbulence, the relationship is simple: F = 6?? rv This relation is called Stokes’s law. A sphere falling in a viscous fluid reaches a terminal speed u? for which the total force, including the weight of the sphere and the viscous retarding force, is zero, and the sphere no longer accelerates (neglect the effect of buoyancy of the sphere in the fluid).

Let ? be the density of the sphere; then the weight of the sphere is 43? r3? g. When the sphere reaches terminal speed, the total force on it is zero: 6?? ru? – 43? r3? g = 0 Or u? = 29(r2g? /? ) Theory shows that a sphere falling in a liquid, at very low speed and therefore very low Reynolds number is subjected to Stokes’ flow. In this type of flow the sphere reaches a terminal or constant velocity where the acceleration is zero and all of the forces acting on the sphere are in equilibrium. These forces are the weight, the buoyancy and the drag.

Balancing these and solving the equation for the viscosity gives the following relationships: First of substitute the relationships of f, G, F into the equation G = F + f f = 6?? ru? G = 43? r3? sg F = 43? r3? fg So 43? r3? sg = 43? r3? fg + 6?? ru? After simplifying the equation, then the result can be shown in this form: ? = 43? g(? s-? f)r36? u? r Then ? = 2(? s-? f)gr29 u? and r= D /2 So ? = g(? s-? f)D218 u? = g(? s-? f)D218 u? When ? s is the density of sphere and ? s = m/V = m43? r3 ? f is the density of the oil and ? f = 1. 613g/cm3 (20°C, 1atm) u? equals to L/t (L is the distance and t is the amount of time that the sphere falls). D presents the diameter of balls which equals to 2r. In addition, in order to find out the uncertainties, there are some formulas are utilized in the final calculation: The uncertainty in the velocity ? u? : (? u? u? )2=(? DD)2+(? tt)2 The uncertainty in the relative density ?? r(? s-? f): (?? r)2=(?? s)2+(?? f)2 The uncertainty in the calculated viscosity ?? : (??? )2=(2? DD)2+(?? r? r)2+(? u? u? )2 3. Apparatus Oil (density: 880. 10 kg/m3) Metal balls Micrometer Tubes Stopwatch Electronic weighing instrument

Figure 3. 1 the equipments in the experiment 4. Procedure 1. Ten of the aluminium balls provided were chosen, the average diameter with the micrometer was measured and the table provided overleaf was filled. 2. The mass of each ball in the ten balls was measured, then the error was determined and the table was completed. 3. The question that which is the most accurate method of determining the average density and a better way were discussed. 4. Then two easily determined marks were picked and the distance between the two marks was measured and recorded. 5. The aluminium balls was dropped one by one at the top of the tube.

The stopwatch was used and the time taken for the ball to fall between two marks was recorded on the tube wall. Repeat this for all ten balls. Figure 4. 1 the graph to show this procedure 6. The velocity for each ball was calculated and the uncertainty was calculated in the velocity using: (? u? u? )2=(? DD)2+(? tt)2 7. The viscosity ? was found from the derivation of the mean terminal velocityu? , indicated by experimental data for the oil. 8. The uncertainty in the relative density (? s-? f) is given by: (?? r)2=(?? s)2+(?? f)2 9. The uncertainty in the calculated viscosity is given by: (??? )2=(2?

DD)2+(?? r? r)2+(? u? u? )2 10. The possible improvements to the procedure to minimize the total error of the experiment was discussed. 11. Stockes’ flow exists was assumed by this theory. It was checked, the Reynolds number was verified is less than 1 as follows: Re=? f?? D? 12. Make comments on the experiment. 5. Results and Calculations Part1: Table 5. 1 The known data The density of the oil (? f)| 1261. 3kg/m3(20°C, 1atm)| Table5. 2The measured data (A) The distance between marks(L)| 0. 6m| Table 5. 3 The measured data (B) | Diameter(D)| error| Mass (M)| error| Time (t)| UnitThe ball | m| m| g| g| s| | 3. 700? 10-3| +7. 9? 10-5| 0. 26| +0. 05| 6. 19| 2| 3. 614? 10-3| -7? 10-6| 0. 26| +0. 05| 6. 35| 3| 3. 600? 10-3| -2. 1? 10-5| 0. 25| -0. 05| 6. 13| 4| 3. 670? 10-3| +4. 9? 10-5| 0. 26| +0. 05| 6. 25| 5| 3. 575? 10-3| -4. 6? 10-5| 0. 25| -0. 05| 6. 31| 6| 3. 598? 10-3| -2. 3? 10-5| 0. 26| +0. 05| 6. 28| 7| 3. 610? 10-3| -1. 1? 10-5| 0. 25| -0. 05| 5. 97| 8| 3. 624? 10-3| +3? 10-6| 0. 25| -0. 05| 6. 25| 9| 3. 604? 10-3| -1. 7? 10-5| 0. 26| +0. 05| 6. 19| 10| 3. 610? 10-3| -1. 1? 10-5| 0. 25| -0. 05| 6. 34| Average| (D)0. 003621m| | 0. 255| | (t) 6. 23s| Standard Deviation| (? D)3. 681? 10-5| | | | (? )0. 11394| Table 5. 4The calculated data The balls| ? s (kg/m3)| u? (m/s)| ? | ? r| ? f| 1| 9808. 2| 0. 0646| 0. 987| 8546. 9| | 2| 10525. 2| 0. 0630| 1. 047| 9263. 9| | 3| 10238. 9| 0. 0653| 0. 972| 8977. 6| | 4| 10050. 7| 0. 0640| 1. 008| 8789. 4| | 5| 10455. 2| 0. 0634| 1. 01| 9193. 9| | 6| 10666. 2| 0. 0637| 1. 042| 9404. 9| | 7| 10154. 1| 0. 0670| 0. 943| 8892. 8| | 8| 10036. 8| 0. 0640| 0. 981| 8775. 5| | 9| 10577. 8| 0. 0646| 1. 023| 9316. 5| | 10| 10154. 1| 0. 0631| 1. 001| 8892. 8| | Average| (? s)10266. 7| (u? )0. 064265| (? )1. 0014| (? r)9005. 4| | Standard Deviation| (?? s)277. 809| (? u? 0. 0011993| (?? )0. 048| (?? r)277. 81| (?? f)2. 39673? 10-13| Example Calculations: The density of the ball: ? s=mV=m43? (D2)3 for example: ? s=0. 00002643? (3. 7? 10-32)3=9808. 2kg/m3 The velocity of the ball: u? = Lt for example: u? = 0. 4m? 6. 19= 0. 06462m/s The viscosity: ? = g(? s-? f)D218?? for example: ? =9. 8? (9808. 2-1261. 30)? (3. 7? 10-3)218? 0. 06462=0. 987 The average data: x=i=1nxin for example: D=i=110Di10=0. 003621m The standard deviation: ? x=1ni=1n(xi-x)2 (except calculating? u? , ?? rand ?? ) for example: ? D=110i=110(xi-0. 003621)2=3. 681? 10-5m The uncertainty in the velocity ? u? (? u? u? )2=(? DD)2+(? tt)2 for example: (? u? 0. 06427)2=(3. 681? 10-50. 003621)2+(0. 113946. 23)2 ? u? =1. 3448? 10-3 The uncertainty in the relative density ?? r:(? s-? f) is given by (?? r)2=(?? s)2+(?? f)2 for example: (?? r)2=(277. 81)2+(2. 39673? 10-13)2 ?? r=277. 81 The uncertainty in the calculated viscosity ?? is given by (??? )2=(2? DD)2+(?? r? r)2+(? u? u? )2 for example: (?? 1. 0014)2=(2? 3. 681? 10-50. 003621)2+(277. 89005. 4)2+(0. 00119930. 064265)2 ?? =0. 048 Result: ?=1. 0014±0. 048 Part2: The theory also assumes that Stokes’ flow exists.

To check it, verify that the experiment number is less than 1 as follows: Calculate with the data above: = 0. 2930 <1 Therefore the answer is true. 6. Discussion The purpose of this experiment is to use Stockes law to obtain the viscosity of an oil sample. It is clearly provided the viscosity of an oil sample and the uncertainty ?? in the calculated viscosity in Table 5. 4. However, before finding the result, it is essential to calculate and measure ? u? , ?? r, ?? s, ? Dand other useful values. Therefore, there exists an error. Maybe it associated with the measurement of the diameter was 10 times larger than that of the other terms.

This means that if improve the accuracy of the diameter measurements, then the total error of the result will be less. Furthermore, the measurements about the diameter and mass of ten balls are not accurate and when reading the data on the electronic weighing instrument and tubes is incorrect so that it influences the final result. Thus, in order to improve the result, it is necessary to read the data as accurately as possible and improve the accuracy of the electronic weighing instrument and other equipments. Moreover, the most accurate method of determining the verage density maybe is to measure the mass of balls one by one, however ensure the accuracy of the electronic weighing instrument is essential. In addition, the result also assumes that Stockes’ flow exists. 7. Conclusion The objective of this experiment is to use Stockes law to obtain the viscosity of an oil sample. The viscosity of an oil sample and the uncertainty ?? in the calculated viscosity in Table 5. 4 can be shown clearly. During the experiment, there are a number of knowledge are associated with the final results such as Stockes law and the method to calculate standard deviation.

In addition, learning how to use the equipments also is contained such as micrometer and electronic weighing instrument. Although the final result is not prefect but it also assumes that Stockes’ flow exists. There are a number of factors associated with the errors such as the equipments are not accurate enough and reading the wrong data during the experiment. To improve those errors, it is necessary to read the data as accurately as possible and improve the accuracy of the equipments.