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):
Is flow rate increasing, decreasing, etc.?
I believe that the rate of flow would decrease over time because the pressure at which the rate is dependent will change as the amount of fluid over the exit of the graduated cylinder becomes less and less.
Is the velocity of the water surface increasing, decreasing, etc.?
Since the rate at which the water is leaving the graduated cylinder is slowing I beleive that the velocity of the water surface would slow as well.
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?
If the hole had a larger diameter than the velocity of the water surface would increase as would the velocity of the exiting water. If the cylinder had a larger diameter I would expect the velocity of the water surface would decrease. You could probably create a ratio of the diameter of the hole over the diameter of the cylinder and multiply this by the velocity of the exiting water and this might give you the velocity of the water surface. This is what I believe not necessarily true.
Explain how we know that a change in velocity implies the action of a force:
To see that the change in velocity implies a force we can look at the eqution: F = m*a . This equation reads Force = mass * acceleration. We know that there is an acceleration and this could be figured out. We also know that the mass of the water above the exit hole is present. When you multiply these two you are given the force that is acting upon this system.
The force that is accelerating the water, I believe, is due to gravity and the weight of the water that is over the exit hole at any given time.
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 of seems to be changing at a slower and slower rate. I determine this by looking at the difference in the water level. In the pictures it seems as though the amounts are cut in half at regular intervals (as stated above) thus the rate is slower and slower each time. If the rate were constant from the first picture than the second picture would show an empty or almost empty cylinder. Also, if it were faster than the second picture woul dhave to show an empty cylinder.
What do you think a graph of depth vs. time would look like?
I believe that the graph of depth vs. time would show a line that has a negative slope and is decreasing at a decreasing rate because the first point would be at (0, 20?), the twenty possibly being the maximum depth of the water. At each second you would cut the depth in half so the next point would be (1, 10) and so on.
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 distance at which the stream shoots out does decrease as time goes by. This is due to the decreasing of the force acting on the velocity of the exiting water.
Does this distance change at an increasing, decreasing or steady rate?
The distance would most likely change at a decreasing rate as did the velocity of the water exiting the hole.
What do you think a graph of this horizontal distance vs. time would look like?
I think that the graph of the horizontal distance vs. time would look similar in most respects to the graph for the depth vs. time since they both rely on the same forces to act upon them.
The contents of TIMER program as you submitted them:
1 290.1406 290.1406
2 293.2344 3.09375
3 295.8438 2.609375
4 299.1406 3.296875
5 302.1563 3.015625
6 305.1719 3.015625
7 308.75 3.578125
8 312.25 3.5
9 316.6563 4.40625
10 321.8438 5.1875
11 328.2656 6.421875
12 336.7813 8.515625
13 345.5469 8.765625
The vertical positions of the large marks as you reported them, relative to the center of the outflow hole
0.375 inch
1.25 inches
2 inches
2.75 inches
3.5 inches
4.25 inches
5 inches
5.75 inches
6.5 inches
7.25 inches
8 inches
8.75 inches
Your table for depth (in cm) vs clock time (in seconds)
0, 8.75 in
3.09375, 8 in
2.609375, 7.25 in
3.296875, 6.5 in
3.015625, 5.75 in
3.015625, 5 in
3.578125, 4.25 in
3.5, 3.5 in
4.40625, 2.75 in
5.1875, 2 in
6.421875, 1.25 in
8.515625, 0.375 in
8.765625, 0 in
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. This is despite a few of my measurements being less than perfect. The overall information show that though the same distance is being traveled, the time elapsed between each is growing.
Your description of your depth vs. t graph:
The graph starts out at point (0,8.75) as the line progresses the graph begins to decrease at first rapidly then it levels off so I would say that the graph is decreasing at a decreasing rate.
Your explanation and list of average velocities:
I took the distance changed between each 20 mL interval which was 0.75 in. and divided it by the time elapsed. For the last one I took 0.375 in (the distance from the last interval to the center of the tube) and divided by the time elapsed.
0.243 in/s
0.287 in/s
0.227 in/s
0.248 in/s
0.248 in/s
0.209 in/s
0.214 in/s
0.170 in/s
0.146 in/s
0.117 in/s
0.088 in/s
0.043 in/s
The midpoints of your time intervals and how you obtained them:
I obtained the midpoint by dividing the total time elapsed for the interval and then added this number to the total time elapsed for the system.
1.545 seconds
3.33
7.35
10.51
12.02
13.81
15.56
17.76
20.325
23.535
27.795
32.18
These are the midpoints of the total time where the average velocity would have been what was stated earlier.
Your table of average velocity of water surface vs. clock time:
0.243 in/s, 1.545 s
0.287 in/s, 3.33 s
0.227 in/s, 7.35 s
0.248 in/s, 10.51 s
0.248 in/s, 12.02 s
0.209 in/s, 13.81 s
0.214 in/s, 15.56 s
0.170 in/s, 17.76 s
0.146 in/s, 20.325 s
0.117 in/s, 23.535 s
0.088 in/s, 27.795 s
0.043 in/s, 32.18 s
Your description of your graph of average velocity vs clock time:
The graph begins at the point (1.545, 0.243). As the time increases the graph is decreasing. Except for a few points that should probably be thrown out, the graph seems to be decreasing at a constant rate. When I did the regression analysis to see if the graph could be linear I got back an R^2 value of 0.900 which indicates a linear graph.
Your explanation of how acceleration values were obtained:
I took the change in velocity of each interval and divided by the change in time of each interval.
0.0245 in/s^2
-0.0149
0.00665
0
-0.0218
0.00286
-0.02
-0.00936
-0.00903
-0.00681
-0.0103
As you can see my acceleration was not constant and in some cases was negative. The negative is there becaus the water surface is actually slowing down.
Your acceleration vs clock time table:
2.4375, 0.0245
5.34, -0.0149
8.93, 0.00665
11.265, 0
12.915, -0.0218
14.685, 0.00286
16.6625, -0.02
19.045, -0.00936
21.93, -0.00903
25.665, -0.00681
29.9875, -0.010
According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell?
I data shows an initial decrease and then the acceleeration of the water surface beings to show a constant. However, given my data in off according to my graph I would think that the acceleration of the water surface is supposed to be constant.
You have good results and a very good analysis.
For an ideal fluid (zero viscosity, no friction-related pressure loss in the cylinder or at the outflow point, zero surface tension) the acceleration would be constant.
Water has low enough viscosity that it approximates an ideal fluid quite well, except at the very end where surface tension can begin to affect the flow rate.