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PHY-242
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.
** Flow Experiment_labelMessages **
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The picture below shows a graduated cylindercontaining water, with dark coloring (actually a soft drink). Water is flowing out of the cylinder through a short thin tube in the side of the cylinder. The dark stream is not obvious but it can be seen against the brick background.
You will use a similar graduated cylinder, which is included in your lab kit, in this experiment. If you do not yet have the kit, then you may substitute a soft-drink bottle. Click here for instructions for using the soft-drink bottle.
In this experiment we will observe how the depth of water changes with clock time.
In the three pictures below the stream is shown at approximately equal time intervals. The stream is most easily found by looking for a series of droplets, with the sidewalk as background.
Based on your knowledge of physics, answer the following, and do your best to justify your answers with physical reasoning and insight:
As water flows from the cylinder, would you expect the rate of flowto increase, decreaseor remain the sameas water flows from the cylinder?
Your answer (start in the next line):
Rate of flow to decrease
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As water flows out of the cylinder, an imaginary buoy floating on the water surface in the cylinder would descend.
Would you expect the velocityof the water surface and hence of the buoy to increase, decreaseor remain the same?
Your answer (start in the next line):
If we compare the buoy to the ground, then the velocity would decrease. If we compare the buoy to the water surface, then it will remain the same, since the distancebuoy and float on top of water. (We are asked to find velocity of
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How would the velocityof the water surface, the velocityof the exiting water, the diameterof the cylinderand the diameterof the holebe interrelated? More specifically how could you determine the velocity of the water surface from the values of the other quantities?
Your answer (start in the next line):
I would need to run this experiment with different diameter cylinders, with different holes in the cylinders, measuring different heights. I would also need a formula sheet with area of a circle and volume of a cylinder. After doing a lot of trial-error with formulas, I would work out on designing a formula which would determine the velocity of the water surface.
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The water exiting the hole has been accelerated, since its exit velocity is clearly different than the velocity it had in the cylinder.
Explain how we know that a change in velocityimplies the action of a force?
Your answer (start in the next line):
Derivative of velocity is acceleration, so a change in velocity implies the action of a force
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What do you think is the nature of the force that accelerates the water from inside the cylinder to the outside of the outflow hole?
Your answer (start in the next line):
Gravity of the earth
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From the pictures, answer the following and justify your answers, or explain in detail how you might answer the questions if the pictures were clearer:
Does the depthseem to be changingat a regular rate, at a faster and fasterrate, or at a slower and slowerrate?
Your answer (start in the next line):
Slower and slower rate
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What do you think a graphof depthvs. timewould look like?
Your answer (start in the next line):
A half parabola which decreases with decreasing rate
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Does the horizontal distance(the distance to the right, ignoring the up and down distance) traveled by the stream increaseor decreaseas time goes on?
Your answer (start in the next line):
decrease
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Does this distance changeat an increasing, decreasingor steady rate?
Your answer (start in the next line):
Decreasing rate
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What do you think a graphof this horizontal distancevs. timewould look like? Describe in the language of the Describing Graphs exercise.
Your answer (start in the next line):
A half parabola which decreases with decreasing rate
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You can easily performthis experiment in a few minutesusing the graduated cylinder that came with your kit. If you don't yet have the lab materials, see the end of this document for instructions an alternative setupusing a soft-drink bottle instead of the graduated cylinder. If you will be using that alternative, read all the instructions, then at the end you will see instructions for modifying the procedure to use a soft drink bottle.
Setup of the experiment is easy. You will need to set it up near your computer, so you can use a timing program that runs on the computer. The cylinder will be set on the edge of a desk or tabletop, and you will need a container (e.g., a bucket or trash can) to catch the water that flows out of the cylinder. You might also want to use a couple of towels to prevent damage to furniture, because the cylinder will leak a little bit around the holes into which the tubes are inserted.
Your kit included pieces of 1/4-inch and 1/8-inch tubing. The 1/8-inch tubing fits inside the 1/4-inch tubing, which in turn fits inside the two holes drilled into the sides of the graduated cylinder.
Fit a short piece of 1/8-inch tubing inside a short piece of 1/4-inch tubing, and insert this combination into the lower of the two holes in the cylinder. If the only pieces of 1/4-inch tubing you have available are sealed, you can cut off a short section of the unsealed part and use it; however don't cut off more than about half of the unsealed part--be sure the sealed piece that remains has enough unsealed length left to insert and securely 'cap off' a piece of 1/4-inch tubing.
Your kit also includes two pieces of 1/8-inch tubing inside pieces of 1/4-inch tubing, with one end of the 1/8-inch tubing sealed. Place one of these pieces inside the upper hole in the side of the cylinder, to seal it.
While holding a finger against the lower tube to prevent water from flowing out, fill the cylinder to the top mark (this will be the 250 milliliter mark).
Remove your thumb from the tube at the same instant you click the mouse to trigger the TIMER program.
The cylinder is marked at small intervals of 2 milliliters, and also at larger intervals of 20 milliliters. Each time the water surface in the cylinder passes one of the 'large-interval' marks, click the TIMER.
When the water surface reaches the level of the outflow hole, water will start dripping rather than flowing continuously through the tube. The first time the water drips, click the TIMER. This will be your final clock time.
We will use 'clock time'to refer to the timesince the first click, when you released your thumb from the tube and allowed the water to begin flowing.
The clock timeat which you removed your thumb will therefore be t = 0.
Run the experiment, and copy and paste the contents of the TIMER program below:
Your answer (start in the next line):
1 8.296875 8.296875
2 10.30469 2.007813
3 12.58594 2.28125
4 14.87109 2.285156
5 17.125 2.253906
6 19.60547 2.480469
7 22.53516 2.929688
8 25.64063 3.105469
9 29 3.359375
10 32.82422 3.824219
11 38.44922 5.625
12 47.10938 8.660156
13 49.67578 2.566406
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Measure the large marks on the side of the cylinder, relative to the height of the outflow tube. Put the vertical distance from the center of the outflow tube to each large mark in the box below, from smallest to largest distance. Put one distance on each line.
Your answer (start in the next line):
15
35
55
75
95
115
135
155
175
195
215
235
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Now make a table of the position of the water surface vs. clock time. The water surface positions will be the positions of the large marks on the cylinder relative to the outflow position (i.e., the distances you measured in the preceding question) and the clock times will as specified above (the clock time at the first position will be 0). Enter 1 line for each event, and put clock time first, position second, with a comma between.
For example, if the first mark is 25.4 cm above the outflow position and the second is 22.1 cm above that position, and water reached the second mark 2.45 seconds after release, then the first two lines of your data table will be
0, 25.4
2.45, 22.1
If it took another 3.05 seconds to reach the third mark at 19.0 cm then the third line of your data table would be
5.50, 19.0
Note that it would NOT be 3.05, 19.0. 3.05 seconds is a time interval, not a clock time. Again, be sure that you understand that clock times represent the times that would show on a running clock.
The second column of your TIMER output gives clock times (though that clock probably doesn't read zero on your first click), the third column gives time intervals. The clock times requested here are those for a clock which starts at 0 at the instant the water begins to flow; this requires an easy and obvious modification of your TIMER's clock times.
For example if your TIMER reported clock times of 223, 225.45, 228.50 these would be converted to 0, 2.45 and 5.50 (just subtract the initial 223 from each), and these would be the times on a clock which reads 0 at the instant of the first event.
Do not make the common error of reporting the time intervals (third column of the TIMER output) as clock times. Time intervals are the intervals between clicks; these are not clock times.
Your answer (start in the next line):
0, 235
2.007815, 215
4.289065, 195
6.574215, 175
8.828125, 155
11.308595, 135
14.238285, 115
17.343755, 95
20.703125, 75
24.527345, 55
30.152345, 35
38.812505, 15
Clock time in seconds, relative height in cm
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You data could be put into the following format:
clock time (in seconds, measured from first reading) Depth of water (in centimeters, measured from the hole)
0 14
10 10
20 7
etc. etc.
Your numbers will of course differfrom those on the table.
The following questionswere posed above. Do your data supportor contradictthe answersyou gave above?
Is the depthchanging at a regular rate, at a faster and fasterrate, or at a slower and slowerrate?
Your answer (start in the next line):
Slower and slower rate
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Sketch a graph of depthvs. clock time(remember that the convention is y vs. x; the quantity in front of the 'vs.' goes on the vertical axis, the quantity after the 'vs.' on the horizontal axis). You may if you wish print out and use the grid below.
Describe your graph in the language of the Describing Graphs exercise.
Your answer (start in the next line):
The graph is half parabola which decreases at a decreasing rate
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caution: Be sure you didn't make the common mistake of putting time intervals into the first column; you should put in clock times. If you made that error you still have time to correct it. If you aren't sure you are welcome to submit your work to this point in order to verify that you really have clock times and not time intervals
Now analyze the motionof the water surface:
For each time interval, find the average velocityof the water surface.
Explain how you obtained your average velocities, and list them:
Your answer (start in the next line):
2.007815, 9.961077091
4.289065, 9.326041923
6.574215, 9.126564921
8.828125, 9.061946903
11.308595, 8.842831492
14.238285, 8.427981319
17.343755, 8.072069745
20.703125, 7.728301887
24.527345, 7.338747834
30.152345, 6.632983272
38.812505, 5.668276242
Time interval in seconds, average velocity of the water surface in cm per seconds.
I found average velocity of the water surface by taking the height of water decrease and dividing by time passed
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Assume that this average velocityoccurs at the midpointof the corresponding time interval.
What are the clock times at the midpoints of your time intervals, and how did you obtain them? (Give one midpoint for each time interval; note that it is midpoint clock time that is being requested, not just half of the time interval. The midpoint clock time is what the clock would read halfway through the interval. Again be sure you haven't confused clock times with time intervals. Do not make the common mistake of reporting half of the time interval, i.e., half the number in the third column of the TIMER's output):
Your answer (start in the next line):
1.0039075
3.14844
5.43164
7.70117
10.06836
12.77344
15.79102
19.02344
22.615235
27.339845
34.482425
40.095705
I added the current time clock and the next time clock. Then I divided the result by 2.
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Make a table of average velocityvs. clock time. The clock time on your table should be the midpoint clock time calculated above.
Give your table below, giving one average velocity and one clock time in each line. You will have a line for each time interval, with clock time first, followed by a comma, then the average velocity.
Your answer (start in the next line):
1.0039075, 9.643559507
3.14844, 9.226303422
5.43164, 9.094255912
7.70117, 8.952389197
10.06836, 8.635406406
12.77344, 8.250025532
15.79102, 7.900185816
19.02344, 7.533524861
22.615235, 6.985865553
27.339845, 6.150629757
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Sketch a graph of average velocity vs. clock time. Describe your graph, using the language of the Describing Graphs exercise.
Your answer (start in the next line):
Linear line with negative slope with y-intercept at about 9.5
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For eachtime interval of your average velocity vs. clock time table determine the average accelerationof the water surface. Explain how you obtained your acceleration values.
Your answer (start in the next line):
-.1320
-.1419
-.3169
-.3854
-.3498
-.3667
-.5477
-.8352
I took the average velocities, inserted them into the dataProgram and clicked “first difference”
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Make a table of average acceleration vs. clock time, using the clock time at the midpoint of each time interval with the corresponding acceleration.
Give your table in the box below, giving on each line a midpoint clock time followed by a comma followed by acceleration.
Your answer (start in the next line):
2.007815, -0.132
4.289065, -0.1419
6.574215, -0.3169
8.828125, -0.3854
11.308595, -0.3498
14.238285, -0.3667
17.343755, -0.5477
20.703125, -0.8352
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Answer two questions below:
Do your data indicate that the accelerationof the water surface is constant, increasingor decreasing, or are your results inconclusive on this question?
Do you think the accelerationof the water surface is actually constant, increasingor decreasing?
Your answer (start in the next line):
By looking at my data, the acceleration is decreasing
I think the acceleration of the water is actually decreasing
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Go back to your graph of average velocity vs. midpoint clock time. Fit the best straight line you can to your data.
What is the slope of your straight line, and what does this slope represent? Give the slope in the first line, your interpretation of the slope in the second.
How well do you think your straight line represents the actual behavior of the system? Answer this question and explain your answer.
Is your average velocity vs. midpoint clock time graph more consistent with constant, increasing or decreasing acceleration? Answer this question and explain your answer.
Your answer (start in the next line):
-0.14 = slope
Average approximation of how quickly the water decreases
Looking at the graphed points, I think that a straight line would be appropriate to represent the actual behavior of the system
Average velocity seems to have a constant acceleration
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Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
Approximately how long did it take you to complete this experiment?
Your answer (start in the next line):
I didn’t time, but I would guess maybe 2 hours
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You may add any further comments, questions, etc. below:
Your answer (start in the next line):
N/A
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*#&!
&#Your work on this lab exercise is good. Let me know if you have questions. &#