Phy 202
Your 'flow experiment' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Your initial message (if any): **
I think there were some timing errors that i didn't catch initially so they show up in the data. I am sure this probably threw off a few results so please correct any errors you see in reasoning based on these errors.
** Is flow rate increasing, decreasing, etc.? **
I would expect the rate of flow to decrease as the water flows from the cylinder. My assessment is based on the conversion of PE to KE. The water at the top of the cyliner has a higher PE than that at the bottom of the cylinder. The equation for KE= 1/2*m*v^2. Since the mass of each segment of water should be close to equal, velocity must be increasing to cause this increased KE. This means that the rate of flow would decrease as the water level decreases.
** Is the velocity of the water surface increasing, decreasing, etc.? **
I would expect the velocity of the buoy to decrease as the mass of the water below decreases and the decreased mass causes decreased water pressure pushing water out of the hole.
** How would the velocity of the water surface, the velocity of the exiting water, the diameter of the cylinder and the diameter of the hole be interrelated? **
You could use the diameter of the cylinder to find cross sectional area of the water. We can then use this to find the volume of the water if given length. We can then find the mass of the water since we know the density of water and mass=density/volume. Once we know the mass, we can calculate the KE of the water which is KE=.5(mass)(velocity^2). This would allow us to find the velocity of the water. The velocity of the exiting water could be used by finding KE by using the cross sectional area of the hole to find mass and then using the velocity of the exiting water to find KE. We can then relate the KE of the system back to the PE of the system and use this to find the velocity of the water's surface somehow.
** Explain how we know that a change in velocity implies the action of a force: **
The increase in velocity stems from a sudden increase in pressure on the water as it leaves the cylinder. Much like in the circulatory system, when an object goes from an area with a large cross-sectional area (like the cylinder) to an area of low cross-sectional area (such as the hole) there is an increase in pressure. This increase in pressure is an increase in force which causes and increased velocity. Another comparison could be putting a finger over the end of a hose, causing it to spray at a higher velocity. This is because the area gets smaller and the pressure increases.
** Does the depth seem to be changing at a regular rate, at a faster and faster rate, or at a slower and slower rate **
The depth seems to be changing at a regular rate, however i noticed that the first cylinder is a bit smaller in the pictures than the other, so the pictures are not to perfect scale. It would be good if we could see the actual ml marks on the side of the cylinder.
** What do you think a graph of depth vs. time would look like? **
I would assume based on the pictures that the graph would be linear, meaning the depth would decrease at a constant rate. The depth would go on the y axis and time would go on the x axis. The slope would be negative.
** Does the horizontal distance (the distance to the right, ignoring the up and down distance) traveled by the stream increase or decrease as time goes on? **
The horizontal distance that the stream travels decreases as time goes on.
** Does this distance change at an increasing, decreasing or steady rate? **
I feel that velocity will decrease at a steady rate, therefore distance should also decrease at a steady rate.
** What do you think a graph of this horizontal distance vs. time would look like? **
I feel that a graph of horizontal distance vs. time would have a negative slope. Horizontal distance would be on the y axis and time would be on the x axis. The decreasing slope would be linear showing that the relationship is constant.
** The contents of TIMER program as you submitted them: **
1 279.207 279.207
2 281.5938 2.386719
3 284.0234 2.429688
4 286.5 2.476563
5 288.5938 2.09375
6 291.7227 3.128906
7 294.3633 2.640625
8 297.5156 3.152344
9 301.207 3.691406
10 305.3633 4.15625
11 310.8906 5.527344
12 322.125 11.23438
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
0.9
2.9
4.8
6.7
8.6
10.5
12.3
14.1
15.8
17.5
19.1
20.8
** Your table for depth (in cm) vs clock time (in seconds) **
42.93, 0.9
31.7, 2.9
26.17, 4.8
22.01, 6.7
18.32, 8.6
15.17, 10.5
12.53, 12.3
9.40, 14.1
7.30, 15.8
4.82, 17.5
2.39, 19.1
0, 20.8
** Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? **
The depth is changing at a slower and slower rate.
** Your description of your depth vs. t graph: **
The graph is labeled with depth in mL on the vertical axis and time in seconds on the horizontal axis. As time increases, the depth of the water will slowly reach 0, but at a decreasing rate. There is no y intercept or minimum or maximum for this graph. There is a negative slope. The slope increases as the time increases becomming less and less negative.
** Your explanation and list of average average velocities: **
ave velocity='dx/'dt
time interval= average velocity
31.7-42.93= -.17cm/sec
26.17-31.7= -.34 cm/sec
22.01-26.17= -1.59cm/sec
18.32-22.01= -1.58 cm/sec
16.17-18.32= -.60cm/sec
12.53-15.17= -.68 cm/sec
9.4-12.53= -.57 cm/sec
7.3-9.4= -0.81 cm/sec
4.82-7.30= -.68 cm/sec
2.39-4.82= -.63 cm/sec
0-2.39= -.71cm/sec
I found the average velocities of these intervals by taking the positional change over the time change.
** The midpoints of your time intervals and how you obtained them: **
I found the midpoints by finding the average of the extremes of each time interval. I added the two numbers together and divided by two.
** Your table of average velocity of water surface vs. clock time: **
37.32, -.17cm/sec
28.94, -.34 cm/sec
24.04, -1.59cm/sec
20.16, -1.58 cm/sec
16.75, -.60cm/sec
13.85, -.68 cm/sec
10.97, -.57 cm/sec
8.35, -0.81 cm/sec
6.06, -.68 cm/sec
3.61, -.63 cm/sec
1.195, -.71cm/sec
** Your description of your graph of average velocity vs clock time: **
My graph seems to be linear with a negative slope. I had two extreme values which I am attributing to human error and disregarded when determining my trend. It appears that the graph would have a y intercept of 0 at about7.8. I feel that my data may have skewed my result.
** Your explanation of how acceleration values were obtained: **
-.02 cm/sec/sec
-.26 cm/sec/sec
.003 cm/sec/sec
.29 cm/sec/sec
-.03 cm/sec/sec
.03 cm/sec/sec
-.09 cm/sec/sec
.05 cm/sec/sec
.02 cm/sec/sec
.03 cm/sec/sec
** Your acceleration vs clock time table: **
37.32, -.02 cm/sec/sec
28.94, -.26 cm/sec/sec
24.04, .003 cm/sec/sec
20.16, .29 cm/sec/sec
16.75, -.03 cm/sec/sec
13.85, .03 cm/sec/sec
10.97, -.09 cm/sec/sec
8.35, .05 cm/sec/sec
6.06, .02 cm/sec/sec
3.61, .03 cm/sec/sec
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
My data is inconclusive on the first question. I could say based on my data that the acceleration is constant, but there were definitely some errors that point in other directions. Also this doesn't seem to make sense based on logic.
** **
2 hrs
Acceleration should be constant. The reasons for this are related to the energy analysis you mentioned at the beginning, but the reasoning itself is beyond the scope of this course.
The accelerations are determined from the original data by taking difference quotients, which is done twice. This magnifies the inevitable uncertainties in the data and makes it difficult to tell whether the acceleration of the system is indeed constant.