PHY 232
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.? **
I would expect the flow of water escaping the cylinder to remain the same. It should only change if the hole in which it escapes changes.
** Is the velocity of the water surface increasing, decreasing, etc.? **
We are discussing a volume rate of change in comparison with a depth change (dV/dt and dh/dt) The volume of a cynlinder is pi r^2 * h. dV/dt = 2pi*r *h + pi *r^2 dh/dt. dh/dt and dv/dt are proportional to each other. So if my previous assumption is correct about flow rate remaining the same, then the velocity leaving would remain 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? **
You could determine what rate water is escaping using dV/dt (or use the physics equation volume flow rate = Area * velocity. If the diameter is bigger, the area of the hole is bigger which means that more liquid is leaving at a time. You could fine the velocity by dividing volume flow rate by area.
** Explain how we know that a change in velocity implies the action of a force: **
If there is a change in velocity, something caused it to change. Pressure (force / area) must have increased, which in turn increases the action of a force.
** 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 change at a regular rate. Pressure is not a force, but it is directly proportional to what happens to force. There could be several different forces acting on it, one being gravity.
** What do you think a graph of depth vs. time would look like? **
According to my assumptions of a regular rate change, the graph would have to be linear positive slope. As time goes on, there is more of a change in volume rate.
** 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? **
In the tube the horizontal distance does not change. The diameter of the tube is consistent throughout the entire object.
** Does this distance change at an increasing, decreasing or steady rate? **
The distance does not change. Unless I misinterpreted the question.
** What do you think a graph of this horizontal distance vs. time would look like? **
I must have misinterpreted the question. The diameter of the cylinder never changes. In turn, there is no change in distance between one side of the cylinder to the other.
** The contents of TIMER program as you submitted them: **
1 344.0742 344.0742
2 345.0352 .9609375
3 345.8438 .8085938
4 346.9492 1.105469
5 348.3633 1.414063
6 349.8047 1.441406
7 352.1172 2.3125
8 355.9928 3.8756
9 359.9211 3.9283
To see what time everything occurred, simply subtract the number on the left by 344.0742
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
12.1cm
10.70cm
9.35cm
7.99cm
6.75cm
5.00cm
3.50cm
2.01cm
0.5cm
** Your table for depth (in cm) vs clock time (in seconds) **
0, 12.1cm
0.96, 10.70cm
1.77, 9.35cm
2.87, 7.99cm
4.29, 6.75cm
5.73, 5.00cm
8.04, 3.50cm
11.91, 2.01cm
15.83, 0.5cm
** Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? **
The depth changes slower at a slower rate. This contradicts my hypothesis. Observing it, it looked that it was steady until the depth of the water approaches the hole, when it slows down at a slower rate.
** Your description of your depth vs. t graph: **
The graph has a negative slope, almost begins linearly, but then acts like a negative parabola(it goes down like a drop from a roller coaster)
** Your explanation and list of average average velocities: **
1.458
1.667
1.236
0.873
1.125
0.649
0.385
0.3852 cm/sec
These average velocities were obtained by dividing the change in centimeter depth by the change in time.
** The midpoints of your time intervals and how you obtained them: **
If the average velocity is the midpoint then this is at time t = 2.87sec
** Your table of average velocity of water surface vs. clock time: **
1.667, 0.96sec
1.236, 1.77sec
0.873, 2.87sec
1.125, 4.29sec
0.649, 5.73sec
0.385, 8.04sec
0.3852, 11.91
** Your description of your graph of average velocity vs clock time: **
As time went on, velocity decreased. There was one weird point where it sped up again, but that may be some random error. It was a decreasing negative slope. It was not so much to be parabolic, but a little more than linear.
** Your explanation of how acceleration values were obtained: **
0.53cm/sec^2
0.33cm/sec^2
0.18cm/sec^2
0.33cm/sec^2
0.11cm/sec^2
0.0005cm/se^2
Acceleration is found by finding the change in velocity over the change in time.
** Your acceleration vs clock time table: **
This graph is very similar to the velocity vs time graph. Apart from one point, the acceleration decreases.
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
decreasing. I think the acceleration of the water is decreasing.
** **
130 minutes
Very good work. You tested your hypothesis and found, through a correct analysis, that it was not supported.
The key is that as the water depth decreases, the pressure does decrease proportionately, resulting in less force / area and therefore less kinetic energy per unit of volume in the exiting water.