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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 **
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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 expect the rate of flow to decrease as water level decreases due to flow.
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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 the velocity of the buoy 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):
The more water in the graduated cylinder, the higher the velocity would be of the water surface and of the exiting water. The larger the diameter of the exit hole, the lower the velocity of exiting water and of water surface. You could measure the velocity of the exiting water to determine the velocity of the water surface as it drops; they are related by the area of the tube they are exiting through via the continuity equation (A1v1 = A2v2).
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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):
According to Newtons First Law, a body at rest will stay at rest unless acted upon by an outside force. The same goes for a body in motion: a force must be applied in order to change that 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):
The smaller diameter of the outflow tube versus the larger diameter of the cylinder. The smaller diameter increases the velocity of the outflowing water.
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Your answer implies that the smaller diameter has the effect of increasing the exit velocity. This has cause and effect backwards.
The smaller diameter dictates less flow than a larger diameter, for a given pressure.
The velocity of the water is dictated by the pressure difference and has nothing to do with the diameter of the container.
The larger diameter of the container means that water descends with less velocity than it exits.
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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):
The depth seems to be changing at a slower and slower rate, which could be determined from clearer pictures by reading the depths in each picture (the pictures would need to show time, too). Assuming these photos were taken at the same time intervals between each, the water level drops more between the first and second photos than between the second and third photos.
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What do you think a graph of depth vs. time would look like?
Your answer (start in the next line):
It would look like a negative exponent graph. It would start at a high y-value at 0 seconds, then drop steeply at first before tapering off and slowing down over time.
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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):
The horizontal distance of the stream would 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):
This would also change at a decreasing rate.
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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):
A graph of horizontal distance vs time would look like the graph for water depth vs time. It would start at a high y-value at 0 seconds, then it would face a steep drop, decreasing at a decreasing rate, tapering off and slowing down over time.
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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):
**The graduated cylinder provided in the kit was marked off in small intervals of 5mL and larger intervals of 25mL, so I set up my experiment using the 25mL marks (instead of 20mL marks).**
1 376.4688 376.4688
2 378.3047 1.835938
3 379.5234 1.21875
4 381.2188 1.695313
5 383.0859 1.867188
6 385.6797 2.59375
7 388.3984 2.71875
8 392.1484 3.75
9 399.2734 7.125
10 401.4844 2.210938
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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):
2.3cm
5.2
8.1
11.0
13.9
16.8
19.7
22.6
25.5
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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, 25.5
1.8359, 22.6
3.0546, 19.7
4.75, 16.8
6.6171, 13.9
9.2109, 11.0
11.9296, 8.1
15.6796, 5.2
22.8046, 2.3
25.0156, 0
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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):
My data support the predictions I made above. Just by looking at the time clock it is easy to see that it gradually takes longer to reach the next mark in the graduated cylinder. Thus the depth is changing 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.
Describe your graph in the language of the Describing Graphs exercise.
Your answer (start in the next line):
My graph looks like a negative exponential curve, as it starts high on the y-axis with a low x-value (0 seconds). As time goes on, the slope decreases in steepness, indicating that the speed at which the water level drops is decreasing. The curve is decreasing 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 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):
Time Interval (s) Velocity (cm/s)
1.835938 -1.58
1.21875 -2.38
1.695313 -1.71
1.867188 -1.55
2.59375 -1.12
2.71875 -1.07
3.75 -0.77
7.125 -0.41
2.210938 -1.04
I divided the change in depth by the change in time (time interval) to find the velocity for that interval in centimeters per second.
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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):
Midpoint Time (s), Avg Velocity (cm/s)
0.917969, -1.58
2.445275, -2.38
3.9022565, -1.71
5.683594, -1.55
7.913975, -1.12
10.570275, -1.07
13.8046, -0.77
19.2421, -0.41
23.910069, -1.04
I found the midpoints of each clock time by dividing their difference by 2, then adding that half to the first of the two time intervals.
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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):
Midpoint Time (s), Avg Velocity (cm/s)
0.917969, -1.58
2.445275, -2.38
3.9022565, -1.71
5.683594, -1.55
7.913975, -1.12
10.570275, -1.07
13.8046, -0.77
19.2421, -0.41
23.910069, -1.04
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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):
With the exception of two data points (the second and the last, due to human error, more than likely) the velocity is on a decreasing trend, though it does not appear to be decreasing at a decreasing rate, increasing at an increasing rate, nor steady. It is difficult to determine from the irregularities in the data points (human error) what this graph should look like and the reality of the system it represents. It has the slightest hint of decreasing at a decreasing rate, but this may be my bias when deciphering it.
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We expect the velocity to be a linear function of clock time, provided we have an ideal fluid.
Water isn't ideal, but when this experiment is done with more sophisticated instruments we nevertheless do get a very nearly linear relationship.
From your responses it appears that a straight line could be pretty well fit to the data, which would be consistent with expectations.
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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):
0.86 cm/s/s
-0.66
0.40
0.086
0.17
0.39
0.08
0.51
-0.29
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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):
Midpoint Time (s), Acceleration (cm/s/s)
0.917969, 0.86
2.445275, -0.66
3.9022565, 0.40
5.683594, 0.086
7.913975, 0.17
10.570275, 0.39
13.8046, 0.08
19.2421, 0.51
23.910069, -0.29
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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):
My results are inconclusive on this question because the discrepancies in the data are magnified by second difference of this data (taking the average twice).
I think the acceleration of the water surface is actually decreasing (due to the decreasing rate of the decreasing velocity).
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As you say it is difficult to see the trend of the data, due to all the 'noise' resulting from second differences.
Your data are not inconsistent with a horizontal best-fit line, but they don't dictate that the line should be horizontal.
in reality, with an ideal fluid and good instrumentation, that line would be very nearly horizontal.
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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):
The slope of the best fit line is approximately -0.11 from my best estimates.
Since this slope is calculated by finding the change in velocity over the change in time, it represents acceleration.
Due to the discrepancies in the data, I do not have a lot of confidence in the representation of the straight line of the actual behavior of the system. The greater the discrepancies (ie from human error), the less representative of the data is a line of best fit.
It is difficult to determine whether this graph is consistent with constant, increasing, or decreasing acceleration due to the discrepancies in the data, but there is some indication of a decreasing acceleration since the slopes between data points appear to become more shallow as time goes on.
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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
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You may add any further comments, questions, etc. below:
Your answer (start in the next line):
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Very good. All your conclusions and speculations are reasonable in terms of your data.
See my notes for an indication of what happens in the ideal case.
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