# Viscosity of Fluids

Viscosity of Fluids Background Theory ===== Viscosity is the resistance of a fluid to flow. This resistance can be to a solid trying to pass through a liquid or against the liquid itself whilst trying to move past stationary objects. Viscosity can also act on fluids of differing viscosities between one another. All fluids, exhibit viscosity to some degree. Viscosity may be thought of as fluid friction, just as the friction between two solids resists the motion of one over the other, it is also possible to cause an acceleration of one fluid relative to the other. Viscosity resists the motion of a solid through a fluid but also makes it possible for a propeller or other device to accelerate the solid through the fluid. George Gabriel Stokes developed a way to measure the viscosity of fluids by studying the force exerted on a spherical object moving through a fluid. This force is known as the viscous drag. This force, in relationship to the terminal velocity of the sphere, gives the coefficient of viscosity (viscosity) of the fluid using stokes law

Where: F is the overall force r is the radius of the sphere Î? is the viscosity of the fluid v is the terminal velocity of the sphere The viscosity is calculated by rearranging the above equation to: Î? = F 6 Ï? r v Along with the viscous drag, another force is acting in the fluid. This is known as the upthrust. It affects an object in liquid due to the object displacing some of the liquid. The weight of the object should cause it to sink but if the upthrust of the liquid is equal to or higher than the force of the weight, the object will sit either partially immersed or float completely in the fluid. An object, when dropped into a liquid, will first accelerate due to the downward force of its weight, then as the viscous drag force increases due to the increase in the objects speed the downward force will decrease and the acceleration will stop. This is the objects terminal velocity and it will continue at this velocity unless another force acts upon the object i.e. the upward force of the bottom of the container. What effects viscosity? ======= Temperature: As temperature increases the viscosity of a fluid decreases (gets runnier or easier for an object to pass through the liquid). Density: The denser the fluid the more viscous it will be. Concentration: If water were to be added, the fluid would become closer to the viscosity of water. Friction: This is caused by the surface properties of the object passing through the fluid. Gravity: Although gravity on Earth is 9.8ms-2 if the experiment were to be carried out else where i.e. on the moon, the same viscosity would not be calculated. Investigation ===== I am going to investigate the effect of temperature on the viscosity of honey. To do this I will use a falling ball viscometer. Before I carry out my experiment to determine the viscosity of honey at specific temperatures I need to consider the following variables: 1) Sphere radius: I will use the same ball bearing during this experiment so that it has the same mass and volume which I will measure, allowing me to calculate its density. 2) Temperature: An increase in temperature decreases the viscosity of a fluid and therefore decreases the friction opposing the motion of the ball bearings. In this investigation I will vary the temperature of the honey to see how it affects the viscosity. 3) Gravitational field: The ball bearings fall through the honey due to the attraction created by the gravitational field from the Earth. In this investigation, this can be considered constant at 9.8ms-2. 4) Distance: In order to make accurate measurements on the terminal velocity of the ball bearings the distance over which their speed is measured must be kept constant. Prediction == Using the information I have gathered and explained above, I would expect to see certain general trends when looking at the results of my experiments: 1) I would expect to see that if I increased the temperature of the fluid then the viscosity of the liquid would decrease. 2) If the concentration of the fluid were increased then the viscosity of the liquid would also increase. 3) The terminal velocity reached by the object passing through the liquid will decrease as the viscosity of the fluid increases. Apparatus ===== 1 measuring cylinder Thermometer 750cm3 honey Stopwatch Ruler Magnets Ball bearing 5 beakers Balance Method == 1) Firstly weigh the ball bearing and measuring cylinder; accurately measure the diameter of the ball bearing and note down the measurements. 2) Place 150cm3 of honey in each of the 5 beakers and place them in water baths of different temperatures 25ËšC, 30ËšC, 35ËšC, 40ËšC and 45ËšC. 3) When the honey has reached the correct temperature, fill the cylinder to the top with honey and weigh it again. 4) Set up the apparatus as shown in diagram above. 5) Hold the ball bearing just above the surface of the honey. 6) Release the ball bearing and start the stopwatch simultaneously. 7) Record the time it takes for the ball bearing to fall every 10cm. 8) Use the magnet on the outside of the cylinder to remove the ball bearing from the honey. 9) Repeat the experiment 3 times for each temperature so that an accurate average can be determined. 10) Using the equations below calculate the viscosity for each temperature. Results === Table showing the time taken for the ball bearing to travel 10cm while falling through honey. These results are cumulative. Temperature displacement Experiment 1 Experiment 2 Experiment 3 Average result (ËšC) (seconds) (seconds) (seconds) (seconds) 25 0 ? 10 cm 11.81 10.58 9.37 10.5 10 ? 15cm 23.26 16.35 14.22 17.94 15 ? 20cm 26.63 24.05 21.07 23.92 30 0 ? 10cm 7.81 6.31 5.47 6.53 10 ? 15cm 12.23 10.48 9.56 10.76 15 ? 20cm 17.16 15.09 12.83 15.02 35 0 ? 10cm 4.68 4.37 5.52 4.85 10 ? 20cm 9.14 8.68 9.49 9.1 40 0 ? 10cm 2.05 2.16 2.26 2.16 10 ? 20cm 5.77 5.95 5.5 5.74 45 0 ? 10cm 2.18 2.09 1.81 2.03 10 ? 20cm 4.73 4.61 4.82 4.72 As I am going to determine the viscosity of the honey at specific temperatures, I will need to consider the following equations Upthrust is : 4 Ï? r3 Ï(fluid) g 3 Viscous drag is : 6 Ï? r Î? v Weight of ball is : 4 Ï? r3 Ï(solid) g 3 Where: Ï is density The magnitudes of the above forces are related as shown below: 4 Ï? r3 Ï(fluid) g + 6 Ï? r Î? v = 4 Ï? r3 Ï(solid) g 3 3 As I will be calculating the viscosity I will need to rearrange the equation to: 6 Ï? r Î? v = 4 Ï? r3Ï(solid) g ? 4 Ï? r3Ï(fluid) g 3 3 Î? = (4/3 Ï? r3 Ï(solid)) g ? (4/3 Ï? r3 Ï(fluid)) g 6 Ï? r v Using the measurements taken I can determine: Density (Ï) = mass volume Density of ball bearing (solid) = 0.0165kg = 7891kg/m3 4/3 Ï? (0.00553)m3 Density of honey (fluid) = 189.6g X 1000 = 1264kg/m3 150cm3 Terminal velocity(v) = displacement Time Temperature (ËšC) Terminal velocity (m/s) 25 0.0059 30 0.01 35 0.023 40 0.028 45 0.037 With the results of my experiment and the measurements for density and terminal velocity I know that: Upthrust is : 4 Ï? r3 Ï(fluid) g = 8.63 X 10-3 3 Weight of ball is : 4 Ï? r3 Ï(solid) g = 0.054 3 Using these values I can calculate the viscosity of the honey at each temperature. Viscosity Î? = (4/3 Ï? r3 Ï(solid)) g ? (4/3 Ï? 3r Ï(fluid)) g 6 Ï? r v Temperature (ËšC) Viscosity (poises) 25 74.13 30 43.63 35 19.06 40 15.64 45 11.82 Analysis The experiment conducted above was successful in proving my predictions. I knew from my background theory that generally a fluid will decrease in viscosity if the temperature of that fluid is increased. My results show that at 25ËšC that the viscosity was 74.13 but when the temperature was increased to 45ËšC the viscosity dropped to 11.82. When looking at these results on the graph, it shows that the temperature is not proportional to the viscosity. The graph also shows that with temperatures above 35ËšC the decrease in viscosity is significantly less than for the temperatures below it. I believe that if I had conducted the experiment at 20ËšC the viscosity of the honey would be approximately 101 and with a temperature of 50ËšC the viscosity would be approximately 9.5. The results collated from the experiment at each temperature were all within 2.44 seconds of each other except for the readings at 25ËšC, which had a variation of 5.56 seconds at 15 ? 20cm. This shows that my results are accurate with this one exception. This could cause an error with the calculations and show an untrue picture of viscosity at 25ËšC. However when looking at the results on the graph this inaccuracy does not seem particularly obvious. The terminal velocity increases as the temperature increases (and therefore as the viscosity decreases), at 25Ëšthe Vt is 0.0059m/s whereas at 45ËšC the Vt is 0.037m/s. There were many difficulties that arose whilst conducting this experiment: ============== 1) It is very difficult to release the ball bearing and start the stopwatch at exactly the same time; this meant that although this would happen consistently with every experiment, it might have caused some inaccuracies with the final calculations. 2) The temperature of the fluid was taken at the beginning but could have decreased after each set of results were taken, therefore if I were to conduct this experiment again I would take the temperature before each set of results so that a greater degree of accuracy could be obtained. 3) After the first experiment the ball bearing was still covered in honey, if I were to repeat this experiment I would wash the ball bearing each time it was used so that its current surface properties would not affect the results by its change in friction altering the acceleration. 4) The measuring cylinder was quite narrow and this may have affected the ball bearings decent due to the friction from the sides of the tube. I would use a wider tube to counteract this affect. Conclusion == The experiment conducted above was accurate overall, leading to a clear set of results that proved my prediction. If I were to repeat this experiment I would consider the above points and put each of the ideas into practice to ensure a completely accurate experiment. I would also like to compare these results with other fluids so that a clearer picture can be gained as to the effect of temperature on viscosities of other liquids compared to properties such as density and concentrations. References == Salters Horners ?Advanced Physics? Nelkon and Parker: Advanced Physics"

Viscosity of Fluids
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