Video of the “Pendulums and deriving the work energy equation” demonstration

Here is a video of the “Pendulums and deriving the work energy equation” demonstration The full video is here.

WESpring

The video clearly shows that the amplitude of oscillation decreases due to losses in the first minute. The spring is almost not moving after 3 minutes (not shown).

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

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Pendulums and deriving the work energy equation

Obviously deriving the work energy equation is not a demonstration (other than a demonstration of one’s memory and math ability). This demonstration was used by Ben Sill to illustrate the terms in the work energy equation that can then form the basis for the derivation.

Equipment

You will need either a string pendulum with a weight on the end or a spring with some mass on the end. I use the spring mass system that I also use for dimensional analysis.

Photo Apr 21, 11 16 48 AM

Demonstration

Start the pendulum or spring moving with some initial deflection. Talk to the students about what they observe. Perhaps ask them to predict what will eventually happen (maybe a clicker question). Maybe get them to reflect on why the amplitude of the oscillation decreases over time. Once there is a substantial, noticeable reduction in the amplitude stop the demonstration.

Analysis 

Write down a generic work energy equation

Total energy at time (2) = Total energy at time (1) + work done on the system – losses (i.e. work done by the system)

I keep the losses separate even though they are work done by the system and hence work done with a minus sign. This just keeps things a little more physically accessible as students seem to be able to think in terms of losses rather than in terms of the pendulum or spring doing work on the surroundings. The work done is the energy spent initially raising the pendulum or pulling down the spring. The total energy at time (1) is zero if you take this time to be before you touch it. The losses are due to drag on the object and internal damping. There is no need to get into details of how to model these terms, it is the bulk equation that you want to demonstrate.

From this point it is possible to derive the work energy equation with the caveat that the energy terms are energy fluxes and the work and loss terms are rates of work and loss.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Pump performance curves

I sometimes use this as an in class demonstration and sometimes as a lab test toward the end of the semester. It is good for illustrating experimental method and measurement uncertainty while demonstrating pump performance characteristics. I first saw a version of this demonstration at an APS DFD meeting about 8 years ago though I am having trouble recalling who presented it.

Equipment

  1. Bucket
  2. Stopwatch
  3. Tape measure
  4. Measuring cup
  5. Aquarium pump
  6. Extension cord
  7. Tube connected to the outlet of the aquarium pump

Photo Apr 14, 10 44 42 AM

Demonstration

  1. Fill the bucket with enough water to fully cover the pump, attach the tube to the pump outlet and place the pump in the bucket.
  2. Hold the tube vertically above the pump and turn it on (typically there is no on – off switch so plugging it in turns it on). The water should rise up the tube and then stop. Measure the head difference between the top of the water in the tube and the top of the water in the bucket. This is the shut off head.
  3. Lower the tube outlet until water starts to flow. Holding the outlet steady measure the distance from the bucket water surface to the outlet and the time taken to fill the measuring cup. Calculate the flow rate.
  4. Repeat step 3 until you have 6 to 8 different head – flow rate data pairs ranging from the shut off head to negligible elevation difference.
  5. Write up the head flow rate pairs on the board and plot the data by hand with elevation on the vertical axis and flow rate on the horizontal axis.

Analysis The data plotted should show an increase in flow rate with decreasing elevation like a typical pump performance curve. However, the data needs to be corrected to account for head loss in the tubing.

Draw a sketch of the pump – bucket – tube system with a control volume around the whole system.

pumps

Write down the work energy equation from the water surface and the tube outlet.

Z1 + u12/2g + p1/g + EP= Z2 + u22/2g + p2/ g +  hl

All the terms on the left hand side are zero except the pump head EP while the pressure at the outlet is p2=0. Using the Darcy–Weisbach equation for the head loss then Eis given by

EP= h+ (u22/2g)(1+ fL/D)

where f is the friction factor, L is the tube length, and D is the tube diameter. The exit velocity can be calculated based on the flow rate u2=Q/A=4Q/πD2. The main problem here is that the friction factor f varies with the Reynolds number and, therefore, the flow rate. Therefore, you need to calculate the friction factor and exit velocity for each data point. This can be given to the class as an in class exercise. Once the actual EP values have been calculated they can be plotted on the same graph. Some aquariums pumps actually come with a pump performance curve that can be compared to the measured data. In that case you can print the manufacturer curve on an overhead transparency. My experience with this is that cheap pumps rarely behave exactly as given in the manufacturer curve.

The demonstration presents a great opportunity to discuss experimental error. The first major source of error is the head measurement because it is hard to hold the tube steady, the water level in the bucket drops while you are filling the measuring cup, and you need to keep the tape measure vertical (though small angles away from the vertical will not make much difference). The second major error is in the measurement of the time taken to fill the measuring cup. Even if you use a 4 cup measure, it still fills in a few seconds for the larger flow rates. Therefore, a small error in timing of say half a second can lead to 10-20% error in the flow rate calculation. Both of these errors can be reduced by making multiple measurements at each height. It is also possible to estimate the individual errors and use them to place error bars on the pump performance curve data.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Video of Pipe networks and head loss

Here is a video of the “Pipe networks and head loss” demonstration. The full video is here. Sorry that it is sideways.

Video Feb 10, 9 51 27 AM 00_00_00-00_00_10

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Pipe networks and head loss

I find that students often find pipe networks difficult because they have difficulty visualizing that the head change along two different paths that are connected at each end must be the same. One way to demonstrate this is to drain a tank through two different length pipes. You can do this with the same equipment as the siphoning experiment though you will need an extra length of tube. I use a tank with pneumatic tubing connectors in it so that you don’t have to hold the tubes at both ends.

Equipment

  1. A large tank and a table to put it on
  2. Two tubes or pipes of substantially different (known) lengths
  3. Two measuring cups
  4. A stop watch.

Photo Feb 10, 9 45 05 AM

In the example in the photos there is a press-to-connect fitting in the base of the tank which I connect to a T-junction and then have the two pipes connected to that.

Photo Feb 10, 9 45 12 AM

Demonstration

  1. Fill the tank with water and flood the tubes.
  2. Place the measuring cups on the floor so that there is a substantial head difference between the top of the water in the tank and the top of the measuring cups
  3. Lower the outlet of the tubes to the top of each measuring cup and start the water flowing
  4. Record the time taken for each cup to fill. The longer tube should take a longer time

Analysis

The analysis is very similar to the siphoning demonstration so I will only summarize it here.

The total head (H) is the distance from the water surface in the tank to the top of the measuring cups. The head is balanced by the entrance head loss (hen), the head loss in the junction (hj), the head loss in the pipe (hp1 or hp2) and the exit loss from each pipe (hex1 and hex2). That is,

H = hen +hj + hp1 + hex1 = hen +hj + hp2 + hex2.

The first two loss terms cancel. Using the Darcy Weisbach equation we can re-write the remaining terms as

U12/2g (1+f1L1/d1)=U22/2g(1+f2L2/d2)

The ratio of the flow rates is given by

Q2/Q1=((1+f1L1/d1)/(1+f2L2/d2))1/2

Here is where it gets messy and, as a result, you won’t get a nice neat ratio of flow rates. In the example that I show in the video the tubes are 1/4” in diameter and 256” and 64” long respectively. Therefore, if the exit velocity head is negligible, the flow rate in the long tube should be roughly half that in the shorter tube. In the test I ran the ratio was 2.5:1. There are various explanations for this difference. First, the exit velocity head may not have been negligible (though accounting for that would have reduced the predicted flow rate ratio). Second, the friction factors for the tubes would be different due to the different Reynolds number (though again, accounting for that would have reduced the predicted flow rate ratio). The most likely explanation for the difference between the predicted and measured flow rate ratio is that the longer tube was curled up in a series of loops whereas the shorter tube was straight. There are additional measurement errors in the tube lengths, and the time for each cup to fill. For example, the times we measured were 25 seconds and 63. It does not take much of an error to get a substantial change in ratio. For example, there is a parallax error in reading the water level in the cups, and There can also be a delay between the person watching the cup calling out ans the timer registering the time. If the recorded times were each out by say plus or minus 3 seconds then the flow rate ratio would vary from  2.1 to 3.  Clearly the demonstration provides a great opportunity to talk about experimental error and uncertainty.

Thank you to Kate and Austin for helping out with the video.

An index of all the demonstrations posted on this blog can be found on my website here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.