Fnding the Fluid Resistance on a Ball Bearing Falling Through Glycerine
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Fnding the Fluid Resistance on a Ball Bearing Falling Through Glycerine
Planning Aim In this experiment I want to investigate the terminal velocity of the ball bearings that are falling through glycerine and the viscosity of the liquid. Prediction I predict that the as the balls fall through glycerine, their acceleration will decrease until they will reach their terminal velocity, (due to fluid resistance) and after that they will travel with a constant velocity, because the opposing forces balance. The bigger the ball, the longer time it needs to reach its terminal velocity, so it will take less time to fall through the fluid than a small ball. I measured the density of glycerine with a gravity hydrometer and using Stokes' law I want to find out the viscosity of glycerine. According to Stokes' law, 'when a sphere is falling under streamlined conditions, terminal velocity has the following formula: (Ïs  Ï1)g Vt = 2r2 9Î· In this formula 'Ïs, Ï1 and Î· are the density of solid, the density of liquid and viscosity of liquid, respectively'. Another way to calculate, also shown by Stokes, is to find the frictional force which equals: F = 6Î aÎ·v, where a (cm) is the radius of the sphere, Î· is the coefficient of viscosity (poises) and v (cm/s) is the velocity. 'When the sphere reaches a constant velocity then F balances the weight of the sphere less the upthrust of the liquid on it.' Ïƒ mg( 1 Ï ) = 6Î aÎ·v , where Ï is the density of steel and Ïƒ is the density of glycerine. Speed is the distance travelled on time taken. Velocity is the speed of an object in a specific direction. The viscosity of a fluid is its resistance to flow; the easier the fluid flows, the lower is its viscosity. "Archimede's Principle says that the upthrust is always equal to the weight of fluid displaced. A body in water experience an upthrust equal to the weight of the water it displaces. If the upthurst equals the weight of the body, the object does not sink." The hydrometer uses this principle to measure the density of a liquid, which is given 'by the level of the liquid on the float', then the density is read off the scale. To find out the density of glycerine I used a hydrometer and I wrote down the value. I found the density of steel on National Physics Laboratory web site address; steel density = 8.0 gcm3 I also base my experiment on Newton's third law of motion: 'to every action there is an equal and opposite reaction'. Ball bearings that fall through a fluid accelerate initially due to the force of gravity, but as the balls fall the fluid resistance increases until it balances the gravitational force. When the resultant forces are balanced, the balls fall at their terminal velocity. Terminal velocity is reached when a 'falling object stops accelerating and continue to fall at a constant speed, due to balance between gravity on air resistance' (in my experiment fluid resistance). When this happens the resultant force is equal to zero, because the opposing forces are balanced. The terminal velocity depends on the size of the fluid resistance force, the shape of the object and its mass. I used ball bearings because due to their shape the fluid resistance is smaller than it would be with some other shape. After that I have to calculate the viscosity of glycerine. Apparatus  five steel balls of different sizes  glass cylinder with glycerine  ruler  two strong magnets  stop watch  micrometer  scale  thermometer  gravity hydrometer The apparatus is shown in the diagram below. Method I set out the apparatus as shown in the diagram. In a glass cylinder of 1000cm3 I put glycerine from bottom to top. With the ruler I measured the distance that the balls have to travel through glycerine and kept it constant for all my measurements. I used the micrometer to measure the diameter of the balls and the scale to measure the mass of the balls. With the thermometer I found out the temperature of the glycerine, because at different temperature the density may vary, and after that I used the hydrometer to measure the density of glycerine. Then I started to let the balls fall through glycerine, one by one, measuring and recording the time needed to reach the bottom, using a stop watch. After every measurement I recovered the ball with the two strong magnets. To make my experiment a fair test I kept constant the distance the balls travelled through glycerine, the volume of glycerine and its temperature, so the density should remain the same and the material the balls were made of and I repeated each experiment six times. I changed only the size of the balls  diameter and mass. For my experiment I chose glycerine because it's ser than water, so the balls will fall slower, due to increased fluid resistance and I can record the time more accurate. The table shows the standard values for viscosity of aqueous glycerine at different temperatures and concentrations. Viscosity of Aqueous Glycerine Solutions in Centipoises/mPa s Glycerine percent weight Temperature (Â°C) 0 10 20 30 40 50 60 70 80 90 100 0(1) 1.792 1.308 1.005 0.8007 0.6560 0.5494 0.4688 0.4061 0.3565 0.3165 0.2838 10 2.44 1.74 1.31 1.03 0.826 0.680 0.575 0.500    20 3.44 2.41 1.76 1.35 1.07 0.879 0.731 0.635    30 5.14 3.49 2.50 1.87 1.46 1.16 0.956 0.816 0.690   40 8.25 5.37 3.72 2.72 2.07 1.62 1.30 1.09 0.918 0.763 0.668 50 14.6 9.01 6.00 4.21 3.10 2.37 1.86 1.53 1.25 1.05 0.910 60 29.9 17.4 10.8 7.19 5.08 3.76 2.85 2.29 1.84 1.52 1.28 65 45.7 25.3 15.2 9.85 6.80 4.89 3.66 2.91 2.28 1.86 1.55 67 55.5 29.9 17.7 11.3 7.73 5.50 4.09 3.23 2.50 2.03 1.68 70 76 38.8 22.5 14.1 9.40 6.61 4.86 3.78 2.90 2.34 1.93 75 132 65.2 35.5 21.2 13.6 9.25 6.61 5.01 3.80 3.00 2.43 80 255 116 60.1 33.9 20.8 13.6 9.42 6.94 5.13 4.03 3.18 85 540 223 109 58 33.5 21.2 14.2 10.0 7.28 5.52 4.24 (1) Viscosity of water taken from "Properties of Ordinary WaterSubstance." N.E. Dorsey, p. 184. New York (1940) Risk assessment The apparatus is relatively safe, the only thing that I have to be careful about is not to touch my face or eyes while I am working with glycerine, because I can have an allergic reaction and also to clean the ball bearings after use. Obtaining evidence I recorded my results in the following table: Ball no. Diameter (mm) Mass (g) Time(s) Mean of the times (s) 1st 2nd 3rd 4th 5th 6th 1 7.88 2.10 1.22 1.25 1.29 1.17 1.24 1.24 1.235 2 8.85 3 1.04 1.18 1.08 1.18 1.16 1.07 1.118 3 15.80 16.41 0.73 0.76 0.67 0.64 0.62 0.65 0.678 4 17.89 23.79 0.68 0.54 0.67 0.57 0.56 0.57 0.598 5 23.85 56.41 0.53 0.51 0.51 0.47 0.45 0.49 0.493 Distance = 42 cm Fluid temp. = 26 ËšC Density of glycerine = 1.246 kg/l From the evidence collected I can calculate the average speed the balls travelled through glycerine. distance travelled (in cm) Average speed (in cm/s) = time taken (in seconds) Ball 1: Average speed = 42 Ã· 1.235 = 34.008 cm/s (to 3dp) Ball 2: Average speed = 42 Ã· 1.118 = 37.567 cm/s (to 3dp) Ball 3: Average speed = 42 Ã· 0.678 = 61.946 cm/s (to 3dp) Ball 4: Average speed = 42 Ã· 0.598 = 70.234 cm/s (to 3dp) Ball 5: Average speed = 42 Ã· 0.493 = 85.192 cm/s (to 3dp) Using Stokes formula I can find the viscosity of glycerine. F = 6Î aÎ·v Ïƒ mg( 1 Ï ) = 6Î aÎ·v In my experiment m (mass) and a (radius of the sphere) have 5 different values, because I used 5 different balls, so I will calculate the value for each ball. For g (the gravitational acceleration), Ï( the density of steel) and Ïƒ (the density of glycerine) I have only one value, because these are constant. Î is also a constant and I'll use the value Î = 3.142 I will name the masses m1, m2â€¦.m5 for different balls; ball 1, ball 2â€¦ball 5, respectively. The same kind of notation I'll use for radius  radius = diameter Ã· 2 In this case I have the following calculations: Ï = 8.0 gcm3 Î = 3.142 Ïƒ = 1.246 kg/l = 1.246 Ã— 103 g/ cm3 g = 9.8 m/s2 For ball 1: m1 = 2.10g v1 = 34.008 cm/s a1 = 3.94 mm = 0.394 cm = 3.94 Ã— 101cm 2.10 Ã— 9.8 ( 1 1.246 Ã—103 Ã· 8.0) = 6 Ã— 3.142 Ã— 3.94 Ã— 101 Ã— Î· Ã— 34.008 â†’ 2.10 Ã— 9.8 ( 1  1.557 Ã—102) = Î· Ã— 2.526 Ã— 102 2.10 Ã— 9.8 Ã— 1.547 Ã— 102 Î· = 2.526Ã— 102 Î· = 31.837 Ã· 2.526 â†’ Î· = 12.603 centipoise/mPa s (to 3dp) For ball 2: m2 = 3g v2 = 37.567 cm/s a2 = 4.425 mm = 4.425 Ã— 101cm 3 Ã— 9.8 ( 1 1.246 Ã—103 Ã· 8.0) = 6 Ã— 3.142 Ã— 4.425 Ã— 101Ã— Î· Ã— 37.567 3 Ã— 9.8 Ã— 1.547 Ã— 102 Î· = 3.133 Ã— 102 â†’ Î· = 14.517 centipoise/mPa s (to 3dp) For ball 3: m3 = 16.41g v3 = 61.946 cm/s a3 = 7.90 mm = 7.90 Ã— 101cm 16.41 Ã— 9.8 ( 1 1.246 Ã—103 Ã· 8.0) = 6 Ã— 3.142 Ã— 7.9 Ã— 101Ã— Î· Ã— 61.946 16.41 Ã— 9.8 Ã— 1.547 Ã— 102 Î· = 9.225 Ã— 102 â†’ Î· = 26.968 centipoise/mPa s (to 3dp) For ball 4: m4 = 23.79g v4 = 70.234 cm/s a4 = 8.945 mm = 8.945 Ã— 101cm 23.79 Ã— 9.8 ( 1 1.246 Ã—103 Ã· 8.0) = 6 Ã— 3.142 Ã— 8.945 Ã— 101Ã— Î· Ã— 70.234 23.79 Ã— 9.8 Ã— 1.547 Ã— 102 Î· = 1.184Ã— 103 â†’ Î· = 30.462 centipoise/mPa s (to 3dp) For ball 5 m5 = 56.41g v5 = 85.192 cm/s a5 = 11.925 mm = 1.192 cm 56.41 Ã— 9.8 ( 1 1.246 Ã—103 Ã· 8.0) = 6 Ã— 3.142 Ã— 1.192 Ã— Î· Ã— 85.192 56.41 Ã— 9.8 Ã— 1.547 Ã— 102 Î· = 1.914 Ã— 103 â†’ Î· = 44.481 centipoise/mPa s (to 3dp) Ball no. Diameter (mm) Mass (g) Viscosity (centipoise/mPa s) 1 7.88 2.10 12.603 2 8.85 3 14.517 3 15.80 16.41 26.968 4 17.89 23.79 30.462 5 23.85 56.41 44.481 [IMAGE] [IMAGE] [IMAGE] Analysis As we can see in the graph 1 and 2 the time needed for the smaller balls to travel the same distance is longer than the time needed for the bigger ball to travel the distance. All the values fit to the trend, showing that the smaller the ball, the larger the time needed to reach the bottom of the cylinder  the graphs have a descending trend line. So far my prediction is confirmed. After I calculated the viscosity for the different balls and calculate my results with the predicted values for glycerine viscosity I realised that I should have taken the temperature of the glycerine after every experiment and I should have asked what is the concentration of the glycerine solution. Although the initial temperature of the glycerine was 26ËšC, my values tell me that the temperature must have risen, considering the fact that the concentration of the solution remained constant. From my result and the table of 'Viscosity of Aqueous Glycerine Solution' I think that the concentration of the solution was about 70% and the temperature dropped from 26ËšC to about 10ËšC, although I have no evidence that this happened. Another mistake I've made in my experiment is that I didn't record the time needed for the balls to travel a smaller distance to be able to calculate terminal velocity. Evaluation My measurement are reliable and my calculations are also correct, but I am not sure that I reached the purpose of the experiment because I neglected some of the factors and didn't realize that I am suppose to take some extra measurements. Considering the facts written above I can't draw a firm conclusion about my experiment. The only thing that I can confirm is that average speed of a ball falling through a fluid increases directly proportional with the mass of the ball. I think that if I had more time to do my experiment, and I was more enlightened about the implication of the title of the experiment, my results could be much better. If I will do my experiment again I will place a change the distance the balls will travel through glycerine, using two pieces of rubber tied out to the cylinder, outside  one at the top and one at the bottom and move the top one 5cm down for each measurement. After that record the time needed to travel smaller distances. All this will help me calculate the terminal velocity. I will also try to find out more information about viscosity and search for more detailed values of glycerine viscosity at intermediate temperatures, because the values I have are for every 10ËšC. I will also record the temperature of the glycerine solution after each experiment. References: AQA GCSE, Physics Specification B, 2004 Key Science, Physics  Jim Breithaupt, 1997 Stanley Thornes (Publishers) Ltd Advanced Level, Physics  Nekon & Parker, 2001 Heinemann Advanced Practical Physics  Leslie Beckett, 1982 John Murray (Publishers) Ltd http://www.neolytica.co.uk/glycerine/resources/table18.htm http://www.npl.co.uk/mass/research.html How to Cite this Page
MLA Citation:
"Fnding the Fluid Resistance on a Ball Bearing Falling Through Glycerine." 123HelpMe.com. 20 Apr 2014 <http://www.123HelpMe.com/view.asp?id=121652>. 
