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In Figure 13, the temperatures of the different sensors are plotted.
The coldest temperatures were seen at the base of the tank close to the canister. Water sinks near the center and then flows across the bottom of the tank. As such, the sensors at this location will record very cold temperatures. The water along the base but closer to the edge of the tank will be slightly warmer as the cold water interacts with surrounding water, and warms. As water reaches the edge of the tank, it is warmer than the water closer to the tank, and it gets pushed upward. As such the sensors at the outer edge of the tank record the warmest temperatures. Lastly, water will move toward the center of the tank and then sink again, repeating the cycle. As it reaches the ice, the water will sink and cool. The sensors along the canister do not record temperatures as cold as along the base because the water cools significantly before reaching the base of the tank.
Angular Velocity
Below (Figure 15) is the trajectory of paper dots that were placed into the rotating tank. The bottom right side of the figure lacks tracks because the sensors were there preventing the particle tracker from seeing the paper dots.
Although none of the tracks made a full circle, it is clear by comparing the radii in each track that the majority of the particles are spiraling inward. Figure 16 shows the angular velocities (in centimeters/second) associated with the inward particle tracks in Figure 15.
The figure reveals a general trend of increasing angular velocity with decreasing radius. Some negative velocities can be seen for the particles that are toward the edge of the tank, and this is because of the slow speed with which they were traveling. When there is little motion of particles, the tracker may locate the particle a pixel or two off in the wrong direction, thus leading to negative velocities. If this experiment were performed in a bigger tank, or if there was a more accurate way to track the particles, negative velocities as observed in this experiment would likely be less common.
Thermal Wind Calculation
The velocity data above can be compared with the thermal wind velocity prediction. Thermal wind relates wind speeds to temperature gradients. The most reliable place to measure a temperature gradient is along the base of the tank. The equation for thermal wind is:
∂u/∂z=gα/2Ω ∂T/∂r,
for which α (the coefficient of thermal expansion) is 2.17*10-4 assuming that the average water temperature along the base of the tank is 21°C, g is 9.81 m/s2, and Ω is .101 rad/sec. The difference in temperature between the two sensors along the base was usually 2°, the distance apart was 8cm, and the depth of the water was 9cm. By plugging these values into the thermal wind equation, the predicted difference in speed between the surface and base of the water is 2.37cm/s. Because the temperature gradient chosen was between the two base sensors, this prediction is for the particle speed between those sensors (between 9 and 17 cm radius). The surface particle speeds observed were much smaller than 2.37cm/s, meaning that there was likely a significant clockwise flow at the base of the tank