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): **
4th time the charm? Resubmitting data at the end (last two tables) and now have put in some previous data for reference as you recommended.
** Is flow rate increasing, decreasing, etc.? **
** Is the velocity of the water surface increasing, decreasing, etc.? **
** 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? **
** Explain how we know that a change in velocity implies the action of a force: **
** Does the depth seem to be changing at a regular rate, at a faster and faster rate, or at a slower and slower rate **
** What do you think a graph of depth vs. time would look like? **
** 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? **
** Does this distance change at an increasing, decreasing or steady rate? **
** What do you think a graph of this horizontal distance vs. time would look like? **
** The contents of TIMER program as you submitted them: **
1 1597.703 1597.703
2 1598.516 .8125
3 1599.672 1.15625
4 1601.297 1.625
5 1602.547 1.25
6 1604.266 1.71875
7 1605.75 1.484375
8 1607.141 1.390625
9 1608.766 1.625
10 1610.578 1.8125
11 1612.031 1.453125
12 1613.734 1.703125
13 1615.5 1.765625
14 1617.375 1.875
15 1619.156 1.78125
16 1621.281 2.125
17 1623.047 1.765625
18 1625.156 2.109375
19 1627.063 1.90625
20 1629.5 2.4375
21 1631.891 2.390625
22 1633.656 1.765625
23 1636.719 3.0625
24 1639.359 2.640625
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
0.3
1.4
2.2
3.1
3.9
4.7
5.5
6.3
7.0
7.7
8.5
9.3
10.1
10.8
11.5
12.3
12.8
13.8
14.5
15.2
15.9
16.6
17.4
** Your table for depth (in cm) vs clock time (in seconds) **
0, 17.4
0.81, 16.6
1.96, 15.9
3.59, 15.2
4.84, 14.5
6.56, 13.8
8.04, 13.0
9.43, 12.3
11.06, 12.8
12.87, 11.5
14.32, 10.8
16.02, 10.1
17.79, 9.3
19.67, 8.5
21.45, 7.7
23.58, 7.0
25.35, 6.3
27.46, 5.5
29.37, 4.7
31.81, 3.9
34.21, 3.1
35.98, 2.2
39.04, 1.4
41.68, 0.3
** Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? **
** Your description of your depth vs. t graph: **
This graph decreases at a decreasing rate. It starts on the vertical axis at 17.4 and 0 seconds and as the line moves to the right the time elapsed is longer for each marked graduation drop.
** Your explanation and list of average average velocities: **
.8125 sec -> 0.98 cm/sec
1.15625 sec -> 0.61 cm/sec
1.625 sec -> 0.43 cm/sec
1.25 sec -> 0.56 cm/sec
1.71875 sec -> 0.41 cm/sec
1.484375 sec -> 0.54 cm/sec
1.390625 sec -> 0.50 cm/sec
1.625 sec -> 0.43 cm/sec
1.8125 sec -> 0.44 cm/sec
1.453125 sec -> 0.48 cm/sec
1.703125 sec -> 0.41 cm/sec
1.765625 sec -> 0.45 cm/sec
1.875 sec -> 0.43 cm/sec
1.78125 sec -> 0.44 cm/sec
2.125 sec -> 0.32 cm/sec
1.765625 sec -> 0.39 cm/sec
2.109375 sec -> 0.33 cm/sec
1.90625 sec -> 0.42 cm/sec
2.4375 sec -> 0.33 cm/sec
2.390625 sec -> 0.33 cm/sec
1.765625 sec -> 0.45 cm/sec
3.0625 sec -> 0.26 cm/sec
2.640625 sec -> 0.30 cm/sec
** The midpoints of your time intervals and how you obtained them: **
0.40
1.39
2.21
4.22
5.70
7.30
8.74
10.25
11.97
13.60
15.17
16.91
18.73
20.56
22.52
24.47
26.41
28.42
30.59
31.81
35.41
37.51
40.36
I found these by dividing the time interval in half and adding to the preceding clock time.
** Your table of average velocity of water surface vs. clock time: **
0.40, 0.98
1.39, 0.61
2.21, 0.43
4.22, 0.56
5.70, 0.41
7.30, 0.54
8.74, 0.50
10.25, 0.43
11.97, 0.44
13.60, 0.48
15.17, 0.41
16.91, 0.45
18.73, 0.43
20.56, 0.44
22.52, 0.32
24.47, 0.39
26.41, 0.33
28.42, 0.42
30.59, 0.33
31.81, 0.33
35.41, 0.45
37.51, 0.26
40.36, 0.30
** Your description of your graph of average velocity vs clock time: **
The overall tendency seems to be decreasing average velocities.
** Your explanation of how acceleration values were obtained: **
&&&&
-0.37 cm/sec^2
-0.22
0.06
-0.10
0.08
-0.03
-0.05
0.01
0.02
-0.04
0.02
-0.01
0.01
-0.06
0.04
-0.03
0.04
-0.04
0.00
0.03
-0.09
0.01
This was accomplished by delta v / delta t and getting average acceleration. I.E. First interval was 0.99 seconds (1.39 - 0.40) divided by difference in average velocity of -0.37 (0.61-0.98) which equals -0.37 cm/sec^2.
&&&&
** Your acceleration vs clock time table: **
&&&&
0.40 sec, -0.37 cm/sec^2
1.39, -0.22
2.21, 0.06
4.22, -0.10
5.70, 0.08
7.30, -0.03
8.74, -0.05
10.25, 0.01
11.97, 0.02
13.60,-0.04
15.17, 0.02
16.91,-0.01
18.73, 0.01
20.56,-0.06
22.52, 0.04
24.47,-0.03
26.41, 0.04
28.42,-0.04
30.59, 0.00
31.81, 0.03
35.41,-0.09
37.51, 0.01
&&&&&
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
My result would lead between decreasing to inconclusive. There are, based on my human fallibility, some times that do not seem to correlate with a linear progression of readings. I believe that the acceleration is decreasing.
Good. The 'deterioration of difference quotients' problem is at work here, so your individual accelerations won't be particularly accurate; however their trend will be interesting.