## The calculation of all tests

The viscosity5 of a fluid is the dominant factor in assessing the drag of a fluid. This value refers to the amount of internal friction, or resistance to flow, possessed by a fluid. Viscosity in fluids is due to a number of reasons. Certain physical properties of the fluid, for instance, strong intermolecular bonds, such as hydrogen bonding and other electrostatic bonds, will pull the molecules together and make it much harder for the fluid to “flow” and stretch around objects. Since the fluid is made up of particles, the size of these particles will also have an effect on the viscosity.

For example, a liquid with significantly smaller particles will be more concentrated and therefore the particles will be more in contact with each other than if they were larger, causing more friction and therefore more viscosity. One of the equations used to describe the effect of viscosity as a retardant force was derived by Stokes. His equation dealt solely with a laminar flow involving an extremely low Reynolds number and the fall of a sphere with a small radius through a viscous fluid.

As I mentioned before, the viscosity of a fluid is also dependent on its temperature above all other factors. This is illustrated when syrup is heated; it becomes thinner and pours easily; and in cool climates motor oil thickens and can affect the performance of an automobile. This dependency on temperature is related as well to the intermolecular forces6. As the temperature decreases in a fluid, the average velocity of the particles within it will decrease as well, due to the Kinetic Theory7.

Since the particles will now be moving slower, they will spend more time in close contact and therefore the intermolecular bonds will be stronger. If the temperature increases, the velocity will increase as well, causing the bond forces to weaken, as the particles are further apart from each other and less affected by their neighbours force. The exact numerical correlation between temperature and viscosity is quite difficult to identify, since the relationship fluctuates greatly when the phase of the fluid changes, since the viscosity of a gas acts in the opposite.

To be precise, in a gas, the opposite of this relationship is true: as the temperature increases, the viscosity increase because the particles are hitting each other more, and vice-versa. The apparatus consisted of the plastic cylinder held in an upright position. The level was used to ensure that the tube was parallel to the earth’s gravity. The meter stick was attached to the cylinder in order to measure the descent of the ball. The video camera was placed on the tripod and set i?? 1m away from the tube, so that it was possible to zoom in and include only the tube and the ruler on the side in the frame.

The tripod also gave the ability to scroll up and down. This setup is illustrated in Figure 2. The tube was filled to within 3cm from the top with glycerine. In order to use many of the equations I mentioned in the theory, I needed to first discover or solve for constants such as the density of the ball and the glycerine, and the viscosity of the glycerine at room temperature. For each test, the descent of the ball through the glycerine was captured on video film, which was then transferred to the computer for direct measurement on the monitor.

To do this, I connected my camera via Firewire to Adobe Premiere and uploaded all the video. It was recorded at 29. 97 frames per second or fps. From this I could measure the rate of change of distance of the ball: its velocity. I did this using the programs QuickTime and Excel. I opened the video in QuickTime, and using Adobe After Effects9, added in a “time code” (elapsed frames) on the bottom right corner in order to make time measurements easier (Figure 4).

I then used a ruler with a right angle to measure the distance travelled by the ball by placing it up against my monitor and through the center of the ball. I recorded the absolute distance traveled for each 1/29. 97th of a second for the first several seconds of each fall. When the change in distance began to be fairly constant, I started measuring at intervals of 2 seconds, 15 seconds and finally 30 seconds. As you can imagine, the spreadsheet that was created is huge and it is not possible to present the complete data in this paper.

The result of trial 5 appeared to be way out side of the standard deviation, so it was left out of the average vt. By dividing the standard deviation by the mean and multiplying it by 100, I calculated the percent of variation of my results, which was 7. 36%. Measurement of vt at varying temperatures The same methodology was used to capture the data from the second part of the experiment, the variation of temperature. These values were much more numerous as the ball fell much slower and therefore there was more data. They are displayed in Appendix C. Several problems arose during the variation of temperatures.

As the glycerine was poured into the tube, a large number of air bubbles were formed. Since the fluid was so viscous, the bubbles floated up very slowly and I did not have the time to let them disperse completely, as the glycerine was heating up and I wanted to have some results at a very cold temperature. While I noticed in the video that the ball did not hit any extremely large bubbles, this may have introduced considerable error. As the experiment proceeded, it appeared that the temperature of the glycerine varied between the two points of temperature measurement, at 5cm and 15cm.

Luckily, there seemed to be consistency between the variations, which turned out to be a difference of 1i?? C in each case. Since the temperature was constantly decreasing, the vt changed as the ball entered a new temperature range. When deciding how to average the velocities, I arbitrarily chose two points that seemed to display a fairly constant velocity, between 3. 5cm and 13cm that were very close to the points at which the two temperatures were measured, and used the values between these points to average the velocities. The two points between which averages were calculated remained constant for the calculation of all tests.