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): **
I've responded by email concerning your test, including specific feedback. Let me know if you didn't receive my message.
** Is flow rate increasing, decreasing, etc.? **
I would expect the rate of flow to decrease with time as the weight of the water decreases resulting in lower pressure and thus less flow.
** Is the velocity of the water surface increasing, decreasing, etc.? **
If the rate of flow decreases as a function of time and the level of the water in the tube, then the tube empties slower as the amount of water left in the tube decreases and so I would expect the velocity of the buoy to decrease with time.
** 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? **
The source of the pressure creating the flow is the weight of the water in the cylinder which is equal to the volume of the water in the cylinder (pi r^2) * depth * specific gravity (1.0)*g.
Since A1*V1=A2*V2, the ratio of the the water flowing from the hole would be the ratio of the area of the small hole to the area of the cylinder or the ratio between the square of their respective radii. I think torricelli's theorom applies here. The velocity of the water leaving the hole is equal to the square root of 2*g*(y2-y1)
** Explain how we know that a change in velocity implies the action of a force: **
by newton's 2nd law, accel = F/m
** 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 force is the acceleration of gravity on the water column. The depth is changer at a slower and slower rate as the hieght of the water column, and thus its weight, drops.
** What do you think a graph of depth vs. time would look like? **
I think it would be described by the function 1/r^2 since the pressure and thus rate of flow at the small hole varies with the decreasing volume of the water in the tube which is pi r^2 *h
** 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? **
It deceases as the difference in height between the water in the tube and the hole decreases (Torricelli's theorom)
** Does this distance change at an increasing, decreasing or steady rate? **
It changes at a decreasing rate (I think)
** What do you think a graph of this horizontal distance vs. time would look like? **
Not sure.
** The contents of TIMER program as you submitted them: **
0,2.2,4.5,7.0,9.7,12.6,15.4,18.7,22.5,26.5,31.6,38.2
** The vertical positions of the large marks as you reported them, relative to the center of the outflow hole **
1.5cm,3.0,4.5,6.0,7.5,9.0,10.5,12.0,13.5,15.0,16.5
** Your table for depth (in cm) vs clock time (in seconds) **
0,16.5
2.2,15.0
4.5,13.5
7.0,12.0
9.7,10.5
12.6,9.0
15.4,7.5
18.7,6.0
22.5,4.5
26.5,3.0
31.6,1.5
38.2,0
** 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 an ever slower rate as I predicted
** Your description of your depth vs. t graph: **
The rate of change in the height of the water vs time declines. Not sure if the function is the inverse of the radius of cylinder or not.
** Your explanation and list of average average velocities: **
the movement was 1.5 cm for each interval. Dividing this by the time for the interval gives velocity in cm/s as follows:
.68,.65,.6,.55,.51,.5,.45,.39,.38,.29,.23
** The midpoints of your time intervals and how you obtained them: **
midpoint clock time would be:
1.1,3.3,5.2,8.4,11.2,14,17,20.6,24.5,29.3,34.9
Got these by taking half the difference between the two clock running times and adding it to the beginning clock times.
This will work. If you're using a spreadsheet the the 'fill handle' this is as efficient as any other method. If you're punching buttons on a calculator then it's probably quicker to add the numbers and divide by 2, which gives the same result. Either way, it looks like you've got them.
** Your table of average velocity of water surface vs. clock time: **
1.1,.68
3.3,.65
5.2,.6
8.4,.55
11.2,.51
14,.5
17,.45
20.6,.39
24.5,.38
29.3,.29
34.9,.23
** Your description of your graph of average velocity vs clock time: **
The average velocity drops with time but it seems to be a roughly linear decline.
** Your explanation of how acceleration values were obtained: **
Since acceleration is the first derivative of velocity, saying the rate of change in velocity is steady is the same as saying the acceleration is constant
** Your acceleration vs clock time table: **
The acceleration at the various intervals changes slightly but there is no clear trend with the average accel being around .012 cm/s^2
** According to the evidence here, is acceleration increasing, decreasing, staying the same or is in not possible to tell? **
The data would indicate that the accelaeration is constant.
I think this makes sense since gravity is constant and the mass of the water declines as the cylinder empties. The velocity of the water drop declines but the time intervals increase and so dv/dt stays constant?
The actual reason the acceleration turns out to be constant is easiest to understand by integrating the differential equation that describes this process. By the time we're through with fluids you'll know enough to understand the differential equation; when you take the second semester of calculus remind me of this problem, which is a neat application of what you'll be learning.