CELERE+Final+Report



Looking at each frame from the video, we used Paint to find six points of data for each frame—where the silicon liquid level touches the tube on the left and right and the liquid level in the middle of the tube for each of the two tubes (the control and the variable). Each point has two coordinates, which we then combined to find an R value (  ), or the distance from (0,0) on the screen. Knowing that the frame rate for these videos is 59 frames per second, we then converted the frame number into seconds. We also know that the straight tube is 17 mm x 184 mm, and could then convert pixels to millimeters. The change in mm over the change in time is velocity. We then created multiple plots showing the progression of the silicon liquid through the tube over time, as well as different velocities. These graphs were fitted with lines of best-fit and are analyzed below. In all trials, the graphs of X coordinates versus time were all fit with a linear trend line; and it is interesting to note that the data tapers off towards the end, as though approaching a horizontal asymptote.
 * Method of Analysis **



 Example of the points collected on each frame (6 points in red).

This trial featured a curved path and a straight path. Just by watching the video, it seems as if the silicon liquid travels at similar horizontal velocities through both paths. In other words, the silicon liquid seems to be traveling at a constant and equal rate in each tube. The difference between the times that the silicon liquid reaches the end of the tubes is barely noticeable, though there is a difference. The silicon liquid seems to reach the end of the curved tube first, which contradicts our expectations.
 * Dry A - **[]

 Looking at the graphs of the R Velocities versus Time, we can see that the velocities are largely linear and approach zero, indicating that the silicon liquid level in the tubes approach the top more slowly as time passes.

 In both tubes, the velocity of the silicon liquid level in the middle of the tube is noticeably smaller than either of the side velocities, showing that the silicon liquid creeps up the side of the tube faster than the middle is forced upwards due to capillary action.

 In the curved tube, the acceleration of the right side of the liquid (derivative of velocity equations) was also distinctly larger than the acceleration of the left side, which accounts for why the liquid reached the same points normal to the sides of the tube at the same time. This is attributed to the normal force in the tubes.

 The overall velocities for the curved tube are distinctly larger than the velocities in the straight tube, which supports the video that shows the silicon liquid reaching the end of the curved tube first. A possible reason for this effect is the normal force created as a result of the curved tube.

Example of data sheet and plotted data for Dry A trial, right point of control. This trial included a curved path and a straight path, and the tubes had already been dropped once. This second trial’s purpose was to see if the silicon liquid from the previous trial would affect the silicon liquid’s cohesion to the rest of the silicon liquid and the adhesion to the side of the tubes. The distance travelled by silicon liquid through the center of each tube was the same, so the two droplets of silicon liquid should have reached the end of the paths at approximately the same time. But, since one path was curved, the capillary force may have been slightly different which would change the normal force, which would cause friction to change. In the video, the silicon liquid droplet in the curved tube reaches the end just moments before the droplet in the straight tube, once again contradicting our predictions.
 * Wet A - **[]

Just as in the dry trial, the overall velocities for the curved tube are higher than the ones for the straight tube, indicating that the silicon liquid level accelerated more in the curved tube.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;"> The effects of a slick surface as opposed to the dry surface in trial Dry A do not seem significant, and the graphs of the wet trial match the graphs of the dry trial very closely.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;"> The R Velocity data points follow a clearer linear trend in the curved tube than in the straight tube, where the data points are more scattered and random. This visual observation is supported by the R2 values on each graph, which show the correlation of the data points to the trend line. This shows that the velocity in the curved tube is more linear (and the acceleration is more constant). <span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">Example of data sheet and plotted graphs for midpoint of variable in Wet A trial.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">For the B trials, we paid less attention to the y values of the data points because they did not significantly affect the data. <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">In this trial, the right tube had its right side indented with hemispheres, and the left side was straight, while the left tube was the control: a right cylinder. The right tube at its narrowest point was as wide as the left tube; therefore we concluded that the left tube’s silicon liquid level would increase faster than that of the right tube. While this hypothesis was experimentally verified with a significant distance, the right tube’s left (straight) side became submerged faster than the right indented side(but slower than the left tube) because of the silicon liquid’s capillary action on the sides of the tube: the adhesive forces on the left side pulled the silicon liquid up, while the forces on the right side pulled the edge anywhere in an 180 degree angle, corresponding to the section of the hemisphere that it currently touched.
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Dry B - **[]

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">The graphs of the X velocities on the variable tube’s right side seem to resemble sinusoidal functions, which may result from the indentations in the position graphs. These indentations cause the position graphs to appear as slanted sinusoidal functions with extremely small periods and amplitudes. A peak in each “bump” of the position function occurs quite regularly (every 3-4 time intervals), and the velocity graph increases during that period. At the peak, the velocity seems to “reset,” dropping down to a negative velocity and starting to climb back up until the next bump. These bumps correspond to the wedges between the semicircles, showing how the wedge affects velocity.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;"> Looking once again at the overall velocities and accelerations of the liquid, the equations show that the straight tube has greater velocities and accelerations. This supports the observation that the liquid level both flowed faster and increased faster in the straight tube than in the wedged tube. It was also obvious that the wedges slowed down the liquid’s flow.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;"> The presence of gas bubbles is notable, but such small bubbles have little to no effect on the liquid’s flow rate.



<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">This trial featured two tubes: one straight tube with no special changes that acts as the control and one straight tube with circular bumps of equal radii on one side. During the drop, the silicon liquid level in the control tube ascended at a generally constant rate. The silicon liquid level in the experimental tube also ascended at a constant rate, but it ascended more slowly than that in the control tube. The silicon liquid level on straight side on the experimental tube ascended close to but still slightly behind the level in the control, but the level on the bumpy side of the experimental lagged behind by a large amount. Bubbles were produced on the bumpy side as the silicon liquid level passed each of the indentions.
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Wet B - **[]

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Just as in the dry trial, the liquid on the bumpy side has a much smaller velocity and acceleration at every point along the tube than either the smooth side of the same tube or either side of the straight tube.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;"> The overall plots of the data match the plots of the dry trial, however the accelerations for the sides seem larger in the wet trial, but the midpoints have smaller accelerations. This shows the effect of capillary action and cohesion as the sides of the tubes were already slick from the previous trial.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 1.5;">Equations of best-fit lines for Wet B and Dry B trials.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">All data can be seen here: