PHY 122
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 of water from the cylinder is decreasing. Using the Equation of Continuity and Bernulli's equation we find that flow is proportional to the height of the water in the cylinder.
You're using the right concepts; very good. You do have one error in your reasoning:
Bernoulli's Equation does apply, but it tells you that the squared velocity of the exiting stream is proportional to the height. This and the continuity equation imply that the rate of flow is proportional to the square root of the height.
** Is the velocity of the water surface increasing, decreasing, etc.? **
The velocity of the water surface and hence of the buoy is decreasing. We find that once again flow is proportional to the height of the water in the cylinder. The area of the top of the cylinder compared with the area of the spout is responsible for determining any difference in velocity at the two regions.
** 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? **
We can calculate both the velocity of the water surface and the velocity of the exiting water using The Equation of Continuity and Bernulli's equation. The diameter of the cylinder and the diameter of the hole are constant; therefore, rearranging our final equation we solve for the velocity at both points.
The ratio of the two diameters determines the ratio of velocities.
** Explain how we know that a change in velocity implies the action of a force: **
Using the assumptions related to Bernulli's equation we say that the fluid is incompressible. Pressure is constant because it is atmospheric pressure; therefore, some force of action contributes to the change in velocity. The nature of the force is the force of gravity.
** 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 depth seems to be changing at a slower rate.
** What do you think a graph of depth vs. time would look like? **
I think the graph of depth vs. time would resemble a linear graph with a negative slope.
** 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 traveled by the stream is decreasing over time.
** Does this distance change at an increasing, decreasing or steady rate? **
The horizontal distance is decreasing at a steady rate according to my observations.
** What do you think a graph of this horizontal distance vs. time would look like? **
A graph of horizontal distance vs. time would be a horizontal straight line based on these three intervals of time.
** The contents of TIMER program as you submitted them: **
1 1675.68 1675.68
2 1676.641 .9609375
3 1677.617 .9765625
4 1678.734 1.117188
5 1679.93 1.195313
6 1681.117 1.1875
7 1682.641 1.523438
8 1684.195 1.554688
9 1686.18 1.984375
10 1688.641 2.460938
11 1694.422 5.78125
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
20 mm
40
60
80
100
120
140
160
180
200
220
** Your table for depth (in cm) vs clock time (in seconds) **
** 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. My data supports the answer I presented above.
** Your description of your depth vs. t graph: **
**Downward slope; quadratic or parabola.
** Your explanation and list of average average velocities: **
I obtained the average velocities by calculating the change in depth over the change in clock time.
** The midpoints of your time intervals and how you obtained them: **
0
0.4805
1.449
2.4955
3.652
4.8435
6.199
7.738
9.5075
11.7305
15.8515
** Your table of average velocity of water surface vs. clock time: **
Clock time Avg. Velocity
0
0.4805,-2.081165453
1.449,-2.049180328
2.4955,-1.790510295
3.652,-1.672240803
4.8435,-1.684919966
6.199,-1.312335958
7.738,-1.287001287
9.5075,-1.007556675
11.7305,-0.812677773
15.8515,-0.345960906
** Your description of your graph of average velocity vs clock time: **
Positive slope; curved line.
** Your explanation of how acceleration values were obtained: **
The acceleration values were calculated by finding the midpoint values between each velocity interval. The average acceleration is the change in velocity over midpoint.
** Your acceleration vs clock time table: **
0.96475,0.033025426
1.97225,0.247176333
3.07375,0.102265018
4.24775,-0.010641346
5.52125,0.27486832
6.9685,0.016461775
8.62275,0.157922923
10.619,0.087664823
13.791,0.113253304
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
My results are inconclusive. I did not recognize a pattern in acceleration values. I believe that the acceleration of the water surface is actually constant.
** **
3.5 hours
Your work is of very good quality, demonstrating excellent preparation for this course. It appears that you have very good aptitude and had a fine first-semester course.
There was one flaw in your reasoning, so see my notes. That particular subtlety in the proportionality is a little beyond what I expect of most Phy 122 students, but you appear to have the preparation to understand it.