#$&*
Phy 202
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 **
1/29 8pm
I calculated my line of best fit at the end of the assignment using a graphing calculator, instead of drawing what I thought my line should be and then coming up with an equation.
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The picture below shows a graduated cylinder containing 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 flow to increase, decrease or
remain the same as water flows from the cylinder?
Your answer (start in the next line):
I would expect the rate of flow to drecrease as water flows from the cylinder
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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 velocity of the water surface and hence of the buoy to increase,
decrease or remain the same?
Your answer (start in the next line):
I would expect it to decrease
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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? 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):
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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 velocity implies the action of a force?
Your answer (start in the next line):
The exiting hole has not changed in size therefore something else must be acting upon the
water itself. Some force has been applied to the water in the cylinder to increase its
exiting velocity.
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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):
Pressure
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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 depth seem to be changing at a regular rate, at a faster and faster rate, or at a
slower and slower rate?
Your answer (start in the next line):
It appears, based on the pictures that it is decreasing at a regular rate. The second
picture seems to be about 1/3 less than the first, the third picture seems to be 2/3 less
than the first. It also stated that the pictures were taken at regular intervals.
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What do you think a graph of depth vs. time would look like?
Your answer (start in the next line):
I think it would be linear, if it is decreasing at a regular rate.
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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?
Your answer (start in the next line):
appears to decrease as time goes on
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Does this distance change at an increasing, decreasing or steady rate?
Your answer (start in the next line):
steady
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What do you think a graph of this horizontal distance vs. time would look like? Describe in
the language of the Describing Graphs exercise.
Your answer (start in the next line):
I think the distance will begin high, but as times goes on will decrease steadily. It will
form a straight line with a negative slope.
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You can easily perform this experiment in a few minutes using 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 setup using 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 time since the first click, when you released your
thumb from the tube and allowed the water to begin flowing.
The clock time at 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):
used a stopwatch to time it. These are my time intervals, I converted them 2 questions down
2.33
2.46
2.58
2.69
3.32
3.45
3.64
3.91
4.92
6.47
8.82
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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):
.5
3.4
6.3
9
11.7
14.4
17.1
19.7
22.2
24.7
27
29.5
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@&
This is fine, but I can't help but think the TIMER program would have been less work.
*@
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, 29.5
2.33, 27.0
4.79, 24.7
7.37, 22.2
10.06, 19.7
13.38, 17.1
16.83, 14.4
20.47, 11.7
24.38, 9.0
29.30, 6.3
35.77, 3.4
44.59, .5
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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 differ from those on the table.
The following questions were posed above. Do your data support or contradict the answers
you gave above?
Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and
slower rate?
Your answer (start in the next line):
it contradicts what I stated earlier.
at a slower and slower rate
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Sketch a graph of depth vs. 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.
image110.gif (4103 bytes)
Describe your graph in the language of the Describing Graphs exercise.
Your answer (start in the next line):
My points almost form a straight line. They do curve. The points are pretty linear until
after the 6th mark, then the points begin to make a curve.
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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 motion of the water surface:
For each time interval, find the average velocity of the water surface.
Explain how you obtained your average velocities, and list them:
Your answer (start in the next line):
-1.073
-.9349
-.9689
-.9294
-.7831
-.7826
-.7418
-.6905
-.5488
-.4482
-.3288
I obtained these values by taking my depth vs clock times and finding the difference
quotients
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Assume that this average velocity occurs at the midpoint of 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):
1.17
3.56
6.08
8.72
11.72
15.11
18.65
22.43
26.84
32.54
40.18
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Make a table of average velocity vs. 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):
1.17,-1.073
3.56,-.9349
6.08,-.9689
8.72,-.9294
11.72,-.7831
15.11,-.7826
18.65,-.7418
22.43,-.6905
26.84,-.5488
32.54,-.4482
40.18,-.3288
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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):
my points form a straight line, they have a strong correlation with a best fit equation of
y=0.01828x-1.05888
@&
Very good. This is exactly what would be expected.
*@
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For each time interval of your average velocity vs. clock time table determine the average
acceleration of the water surface. Explain how you obtained your acceleration values.
Your answer (start in the next line):
-0.05778
0.01349
-0.01496
-0.04877
-0.0001474
-0.01153
-0.01357
-0.03213
-0.01764
-0.01563
acceleration = change in velocity/ time elapsed so I entered my average velocity vs. clock
time comma delimited and did the difference quotient again.
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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):
2.365,-0.05778
4.82, 0.01349
7.4,-0.01496
10.22,-0.04877
13.42,-0.0001474
16.88,-0.01153
20.54,-0.01357
24.64,-0.03213
29.69,-0.01764
36.36,-0.01563
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Answer two questions below:
Do your data indicate that the acceleration of the water surface is constant, increasing or
decreasing, or are your results inconclusive on this question?
Do you think the acceleration of the water surface is actually constant, increasing or
decreasing?
Your answer (start in the next line):
I would say based on the 2 values above that it acceleration was constant
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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):
0.01828
? The water is leaving the cylinder at a average rate of 0.01828 cm/sec
constant
The points had a strong, positive correlation. Forming a pretty good straight line.
Straight lines indicate 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):
1.5 hours give or take
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&#Very good data and responses. Let me know if you have questions. &#