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 would expect the rate of flow to remain the same since there can only be so much liquid exiting the tube at once. It's not like the water is powerful enough to break open the hole and force more liquid to leave. Instead, it exits at a constant rate. This is for a water supply that remains above the hole, though.
** Is the velocity of the water surface increasing, decreasing, etc.? **
I would expect it to descent with a constant velocity because the flow of water is leaving at a constant rate because the liquid can only exit the cylinder so fast through the hole and tube.
** 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 exiting water is related to the velocity of the water surface because the water level descends as a direct result of the velocity of water exiting the cylinder. Moreover, the diameter of the cylinder and diameter of the hole determine how fast the water surface decreases since it determines the the surface area and volume of water which is a necessary component of determining how fast the water is decreasing. The water would decrease very rapidly if the diameter of the hole was 10 times the size of the diameter of the cylinder. Conversely, the water level would decrease slowly if the diameter of the hole was 1/10 the size of the diameter of the cylinder.
** Explain how we know that a change in velocity implies the action of a force: **
I am not sure why it is accelerating. I would think it would decrease velocity when the water level decreases below the tube hole (obviously), but I would imagine gravity is the only acceleration component to this setup. So, I am not sure what the answer is to this question.
Newton's Second Law tells us that the acceleration of a mass, which is its rate of change of velocity with respect to clock time, is equal to the net force acting on the mass, divided by the mass. If velocity changes, then the rate of change of velocity with respect to clock time is not zero, so that the net force on the mass is not zero.
This question does not in any way assume or imply that there is in fact a change in velocity.
** Does the depth seem to be changing at a regular rate, at a faster and faster rate, or at a slower and slower rate **
Once the liquid begins to flow out of the tube, it appears that the liquid initially began to decrease more rapidly than it did during the majority of the draining process. I would say that mine was changing at a somewhat regular rate.
** What do you think a graph of depth vs. time would look like? **
I think it would look similar to a straight line with a negative slope since my experiment resulted in a pretty constant rate of decreasing water level.
** 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 seems to decrease as time goes on.
** Does this distance change at an increasing, decreasing or steady rate? **
It appears to change at a decreasing rate.
** What do you think a graph of this horizontal distance vs. time would look like? **
The x-axis would be time and the y-axis would be horizontal distance. The curve would be a decreasing curve similar to a -x^2=y curve. The curve would initially be steep and then it would tail off until it hit the x-axis after the time expired.
** The contents of TIMER program as you submitted them: **
2 220.2031 3.0625
3 223.6406 3.4375
4 226.4219 2.78125
5 229.4531 3.03125
6 232.1875 2.734375
7 235.4375 3.25
8 239.1875 3.75
9 242.1719 2.984375
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
10
30
50
70
90
110
130
150
170
** Your table for depth (in cm) vs clock time (in seconds) **
220.2031, 10
223.6406, 30
226.4219, 50
229.4531, 70
232.1875, 90
235.4375, 110
239.1875, 130
242.1719, 150
** Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? **
It is hard to tell, but I think, to an extent, it supports my hypothesis that it would be a relatively regular rate.
** Your description of your depth vs. t graph: **
My clock time is on the x-axis and my depth is on the y-axis. It is not a perfectly straight line, but I could definitely see a best-fit line that is not far from any point. It is jagged and uneven throughout, but with human error that is expected.
** Your explanation and list of average average velocities: **
In order to find the velocity you could take the derivative of the position vector. To find the average velocity, take the difference between the velocities between two points and then divide by the difference in time.
3.25
4.10
3.69
3.94
4.26
3.10
4.13
** The midpoints of your time intervals and how you obtained them: **
221.92185
225.03125
227.9375
230.8203
233.8125
237.3125
240.6797
I added the one time to the next time and divided by 2.
** Your table of average velocity of water surface vs. clock time: **
3.25, 221.92185
4.10, 225.03125
3.69, 227.9375
3.94, 230.8203
4.26, 233.8125
3.10, 237.3125
4.13, 240.6797
A table of v vs. t would have t in the first column, v in the second. Otherwise OK.
** Your description of your graph of average velocity vs clock time: **
The x-axis is time and the y-axis is average velocity. The graph is pretty straight except for what is undoubtedly, to an extent, human error which causes the graph to be in a non-straight line. Overall, the slope is fairly constant.
According to your observations, it does appear that velocity is constant or very nearly so.
In fact the decreasing range of the outflow stream indicates the decreasing velocity of that stream, which means a decreasing rate of volume flow. The only behavior consistent with this observation would be decreasing velocity of the water surface.
** Your explanation of how acceleration values were obtained: **
Acceleration is the derivative of velocity.
That is so, but you don't have a function to take a derivative of.
It isn't clear how you got the results you report below.
1.26
1.64
1.41
1.25
1.03
1.04
1.23
** Your acceleration vs clock time table: **
1.26, 221.92185
1.64, 225.03125
1.41, 227.9375
1.25, 230.8203
1.03, 233.8125
1.04, 237.3125
1.23, 240.6797
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
It assumes that the acceleration was mostly constant, but I believe with amount of human error it is inconclusive. Although, I do believe acceleration is constant. Am I correct?
** **
1 hour and 45 minutes
Your depth vs. clock time observations are consistent with an acceleration of zero.
However your observation of decreasing range of the outflowing stream is not consistent with zero acceleration.
Your analysis is good, except that I can't tell how you got your values for the acceleration.