phy202
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.? **
The rate of flow will slow down because the height of the fluid has what I call head pressure and as the head of height of the level gets lower the pressure will get lower. I use as a rule of thumb the level in heights of about 1/2 psi per foot for an estimate of pressure I will need to overcome to pump the fluid back up the column.
** Is the velocity of the water surface increasing, decreasing, etc.? **
For some reason I would expect it to be the same because the object's buoyancy doesn't change only the level of the water. I'm thinking of a ship in the ocean and the changing tides and the ship is still floating. I'm not too sure my analogy is the same.
** 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? **
I know that this is a type of venturi effect when changing the area from a larger area to a smaller area and that the velocity of the larger area will be slower than the velocity of the smaller area. This is how we maintain our velocity in HVAC applications by going smaller in the duct work to get the velocity out of the last opening. But to answer the question I think they are interrelated proportionally by vel 1 * area 1 = vel 2 * area 2
This is very relevant to the first part of the course.
** Explain how we know that a change in velocity implies the action of a force: **
Well if F = m * a and the velocity is increasing and acceleration is proportional to the velocity then the acceleration will be increasing but in this example as the stream slows down the acceleration will be slowing down
** 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 nature of the force is the Earth's gravity. I believe the depth is changing at a slower and slower rate because of the Earth's gravity acceleration of 9.8 m/s^2 and the mass is getting less and less in the cylinder. With this I suppose the force would be getting less and the water would be exiting slower and slower.
** What do you think a graph of depth vs. time would look like? **
The graph would be decreasing at a decreasing rate I think. I don't know if this is what I'm thinking but the graph of depth on the y axis and the time on the x axis has a curve downward and to the right to the x axis with a sharper drop at the beginning of the time (more distance down per unit of time) then the distance would slow down its decent where it would take more time to change the comparable amount.
** 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 would decrease as time goes on.
** Does this distance change at an increasing, decreasing or steady rate? **
I believe the distance would change at a decreasing rate because at first the stream is flowing full blast out of the opening then as the level falls in the cylinder; the stream would begin to not travel as far or is slowing up. I think that because the area is determined by squaring the radius that as the flow flows out of the cylinder it wouldn't be steady and it is not increasing.
** What do you think a graph of this horizontal distance vs. time would look like? **
I really don't remember the describing graphs exercise but I think that the graph is the horizontal distance is decreasing at a decreasing rate.
** The contents of TIMER program as you submitted them: **
1 136.6094 136.6094
2 138.8125 2.203125
3 141.2969 2.484375
4 143.8281 2.53125
5 147 3.171875
6 150.2656 3.265625
7 153.6719 3.40625
8 157.7031 4.03125
9 162.3438 4.640625
10 168.4688 6.125
11 175.7813 7.3125
12 189.8438 14.0625
13 194.3438 4.5
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
3 mm
18.1 mm
33.2 mm
48.3 mm
63.4 mm
78.5 mm
93.5 mm
108.6 mm
123.7 mm
138.8 mm
153.9 mm
168.9 mm
** Your table for depth (in cm) vs clock time (in seconds) **
0s, 168.9mm
2.2s, 153.9mm
4.687s, 138.8mm
7.218s, 123.7mm
10.39s, 108.6mm
13.656s, 93.5mm
17.062s, 78.5mm
21.093s, 63.4mm
25.732s, 48.3mm
31.858s, 33.2mm
39.171s, 18.1mm
53.234s, 18.1mm
57.734s, 0mm
** 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 water depth is decreasing at a decreasing rate
** Your explanation and list of average average velocities: **
The average velocity is equal to the change in distance divided by the change in time. This is where the time intervals come in handy not the clock times.
6.809 mm/s
6.079 mm/s
5.927 mm/s
4.729 mm/s
4.593 mm/s
4.404 mm/s
3.721 mm/s
3.23 mm/s
2.449 mm/s
2.051 mm/s
1.067 mm/s
.667 mm/s
** The midpoints of your time intervals and how you obtained them: **
The midpoint clock times were determined by adding the clock times of the two points and dividing by 2 to get the midpoint time between the two clock times
1.1s
3.444s
5.953s
8.804s
12.023s
15.359s
19.078s
23.413s
28.795s
35.515s
46.203s
55.484s
** Your table of average velocity of water surface vs. clock time: **
1.1s, 6.809mm/s
3.444s, 6.079 mm/s
5.953s, 5.927 mm/s
8.804s, 4.729 mm/s
12.023s, 4.593 mm/s
15.359s, 4.404 mm/s
19.078s, 3.721 mm/s
23.413s, 3.23 mm/s
28.795s, 2.449 mm/s
35.515s, 2.051 mm/s
46.203s, 1.067 mm/s
55.484s , .667 mm/s
** Your description of your graph of average velocity vs clock time: **
The average velocity is decreasing at a decreasing rate
** Your explanation of how acceleration values were obtained: **
The average acceleration is the change in velocity divided by the change in time.
** Your acceleration vs clock time table: **
3.44s, .29 mm/s
5.953s, .06 mm/s
8.804s, .378 mm/s
12.02s, .054 mm/s
15.359s, .169 mm/s
19.078s, .106 mm/s
23.413s, .128 mm/s
28.795s, .054 mm/s
35.515s, .069 mm/s
46.203s, .089 mm/s
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
My results are somewhat erratic because the acceleration is acting like it is spewing or pulsing.
I actually think the acceleration would be decreasing at a decreasing rate
You are seeing a deterioration of the difference quotients.
Your data was depth vs. clock time. It is impossible to determine, and click the mouse at the exact instant the depth reaches a given value.
Your calculations of velocities are identical to a set of difference quotient calculations, based on your original data. The uncertainties in your original data therefore cause some scattering in your velocity results.
Your calculations of accelerations are identical to a set of difference quotient calculations, based on your velocities (i.e., you are calculating a difference quotient of a difference quotient). The uncertainties in your original data are magnified in your first difference quotient (velocity) and further magnified in your second difference quotient (acceleration), causing a great deal of scattering. This is what makes it difficult to discern the actual pattern.
For an ideal fluid we expect that the acceleration will be constant. Water isn't an ideal fluid, but in this situation it does exhibit very nearly constant acceleration. However because of the magnification of uncertainties in succeeding difference quotients, this is difficult to verify for the present system using data obtained by human senses.
It is possible to obtain more precise data using electronic probes or other means. A cylinder with larger diameter would slow the process sufficiently that data obtained by a human observer would be sufficiently accurate.
** **
3.5 hrs
Very good work. See my notes.