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.? **
It will decrease.
** Is the velocity of the water surface increasing, decreasing, etc.? **
It will decrease.
** 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? **
The velocity of the water surface is going to be proportional to the velocity of the exiting water. The diameter of the hole will determine how much water can leave the cylinder. The diameter of the cylinder will also contribute to the velocity of the water surface. Timing the the water as it drains out would be the best way to determine the velocity of the water surface.
** Explain how we know that a change in velocity implies the action of a force: **
If there was no force, velocity would have remained constant as we learned in Newton's First Law.
** Does the depth seem to be changing at a regular rate, at a faster and faster rate, or at a slower and slower rate **
It appears to be changing at a slower and slower rate.
** What do you think a graph of depth vs. time would look like? **
It will be decreasing at a decreasing rate.
** 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? **
It decreases.
** Does this distance change at an increasing, decreasing or steady rate? **
It is changing at a decreasing rate.
** What do you think a graph of this horizontal distance vs. time would look like? **
It will be decreasing at a decreasing rate.
** The contents of TIMER program as you submitted them: **
1 47.03125 47.03125
2 48.15625 1.125
3 49.17188 1.015625
4 50.32813 1.15625
5 51.125 .796875
6 52.3125 1.1875
7 53.53125 1.21875
8 54.76563 1.234375
9 55.98438 1.21875
10 57.375 1.390625
11 58.79688 1.421875
12 60.01563 1.21875
13 61.42188 1.40625
14 63.09375 1.671875
15 64.71875 1.625
16 66.45313 1.734375
17 68.1875 1.734375
18 70.4375 2.25
19 72.85938 2.421875
20 75.79688 2.9375
21 79.15625 3.359375
22 85.375 6.21875
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
.5
1.3
2.1
2.9
3.65
4.45
5.25
6
6.8
7.5
8.3
9.05
9.8
10.6
11.3
12.05
12.75
13.5
14.25
14.95
15.7
16.4
** Your table for depth (in cm) vs clock time (in seconds) **
0,16.4
1.125,15.7
2.141,14.95
3.297,14.25
4.094,13.5
5.281,12.75
6.5,12.05
7.734,11.3
8.953,10.6
10.34,9.8
11.77,9.05
12.98,8.3
14.39,7.5
16.06,6.8
17.69,6
19.42,5.25
21.16,4.45
23.41,3.65
25.83,2.9
28.77,2.1
32.13,1.3
38.34,.5
** Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? **
The data supports the answers that I gave previously. The depth is changing at a slower and slower rate.
** Your description of your depth vs. t graph: **
The graph is decreasing at a decreasing rate.
** Your explanation and list of average average velocities: **
-0.62
-0.74
-0.61
-0.94
-0.63
-0.57
-0.61
-0.57
-0.58
-0.52
-0.62
-0.57
-0.42
-0.49
-0.43
-0.46
-0.36
-0.31
-0.27
-0.24
-0.13
The average velocity was obtained by dividing the displacement by the time interval. The units are in cm/s.
** The midpoints of your time intervals and how you obtained them: **
0.56
1.63
2.72
3.7
4.69
5.89
7.12
8.34
9.65
11.06
12.38
13.69
15.23
16.88
18.56
20.29
22.29
24.62
27.3
30.45
35.24
These clocktimes are found by averaging the clocktimes of an interval which gives a clocktime halfway through the interval.
** Your table of average velocity of water surface vs. clock time: **
0.56,-0.62
1.63,-0.74
2.72,-0.61
3.7,-0.94
4.69,-0.63
5.89,-0.57
7.12,-0.61
8.34,-0.57
9.65,-0.58
11.06,-0.52
12.38,-0.62
13.69,-0.57
15.23,-0.42
16.88,-0.49
18.56,-0.43
20.29,-0.46
22.29,-0.36
24.62,-0.31
27.3,-0.27
30.45,-0.24
35.24,-0.13
** Your description of your graph of average velocity vs clock time: **
The graph is increasing at an increasing rate. This is because the velocities are negative. Had they been calculated differently, it would be decreasing at a decreasing rate.
When I look at the data I can't spot any trend that indicates a changing rate.
I went ahead and opened this table in Excel. The graph appeared to be a straight line, though with some 'noise' which scattered the points a bit. However the straight line
v = 0.0167t - 0.7409
fit the graph very well, with no significant pattern to the residuals.
This means that you have excellent data, and that your table above gives good support to a hypothesis of uniform acceleration.
This also agrees with the theoretical prediction based on zero viscosity and no friction. In fact there is low viscosity and some friction involved here, but the effect on linearity would be too small to be observed with the present setup and timing mechanism.
** Your explanation of how acceleration values were obtained: **
The average acceleration for each time interval was obtained by dividing the change in velocity by the time interval. The velocities were obtained from the average velocities and the assumption of uniform acceleration.
** Your acceleration vs clock time table: **
0.56,-1.11
1.63,1
2.72,-0.65
3.7,0.1
4.69,0.46
5.89,-0.35
7.12,0.29
8.34,-0.24
9.65,0.21
11.06,-0.13
12.38,-0.01
13.69,0.08
15.23,0.11
16.88,-0.2
18.56,0.26
20.29,-0.28
22.29,0.31
24.62,-0.25
27.3,0.23
30.45,-0.18
35.24,0.13
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
I think that the data is inconclusive due to the wild variations in the acceleration, but I think that the acceleration is constant.
The unavoidable 'noise' in your time observations is doubly amplified in these calculations (re deterioration of difference quotients). A graph of your data is consitent with a near-zero constant acceleration, but the R coefficient is very low, meaning that the data are inconclusive.
The v vs. t graph does, however, give strong support to the hypothesis of uniform acceleration.
** **
About an hour.
Excellent work. See my notes to amplify your results a little, and confirm most of your comments.