Molecular diffusion is a very slow process

This is another demonstration that falls in to the category of illustrating the order of magnitude of a process or constant that students have trouble visualizing (just like the plunger tog-o-war illustrated the magnitude of atmospheric pressure). I use this demonstration in my environmental fluid mechanics class to illustrate how slow a process molecular diffusion can be.

Equipment

1. Fish tank half full of water
2. A 10-20 ml syringe
3. Salt water
4. Food coloring

Demonstration

The demonstration takes a full class period so it needs to be started at the very beginning of class. Mix the food coloring into the salt water and fill the syringe. Slowly lower the syringe to the base of the fish tank so that the outlet is touching the base. Very slowly inject the dyed salt water along the base of the tank. The dyed salt water should spread out in a very thin layer at the base of the tank. Have the students look at how thin the layer is. At the end of the class have the students have another look at the tank and they should observe that there has been negligible thickening of the layer during the hour or so since injection. If you can, move the tank without disturbing it, or you can leave it in the class room for a prolonged period of time so you can invite students to return later in the day to see how the layer slowly thickens. If keeping it diffusing is not an option you can mix the tank up by hand at the end of the class to illustrate how rapid turbulent mixing can be  by comparison.

Analysis

I usually use this demonstration on the first day of discussing the advection – diffusion equation. There are plenty of good write-ups on solutions to idealized diffusion problems (see for example https://engineering.dartmouth.edu/~d30345d/courses/engs43/Chapter2.pdf) so I will not write up the analysis here. The demonstration can be modeled as a finite release one dimensional diffusion problem with a reflecting boundary at the base and an infinite environment vertically (that is, the diffusing dyed salt water does not feel the effect of the water surface over the time scale of the demonstration). I try to get through this problem during the class so that we can substitute values in to see if the predicted diffusion over the class period is similar to that observed (i.e. not much). The diffusivity of salt in water is approximately 1.6×10-5 cm2/s (http://pubs.rsc.org/EN/content/articlepdf/1954/tf/tf9545001048).

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 the “Manometers – the curious case of the coiled manometer” demonstration

Here is a video of the “Manometers – the curious case of the coiled manometer” demonstration. The full video is here and shows the rest of the demonstration up to when the funnel (off screen) overflows (on screen).

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.

Manometers – the curious case of the coiled manometer

This is a neat little demonstration that illustrates a slightly odd manometer behavior and can be used as a lead in to a quantitative manometer example in class.

Equipment

1. A circular bucket
2. Transparent plastic tubing long enough that it can be wrapped around the bucket at least 5 times
3. A jug of water with food coloring added
4. A funnel for filling the tube with the dyed water
5. Duct tape

Demonstration

1. Lay the bucket on its side.
2. Wrap the tube around the drum at least five turns leaving about a foot at one end to extend above the bucket
3. Fix the funnel into the tubing at the vertical end which extends above the bucket
4. Tape down the end of the tube in contact with the bucket leaving it open to the atmosphere
5. Have a volunteer pour the water slowly into the funnel. It will fill up the tube and a little will spill over into the second loop.  You may find that a little more will spill over into the third loop, but that should be about as far as the fluid will go.
6. If you keep filling, the water will back up and overflow out of the funnel.

You should try this before doing it in class just to make sure that you have sufficient tubing and liquid, and just to make sure that it will work for you.

Analysis

Wrapping the tube around the bucket forms a manometer that is essentially sinusoidal in shape when stretched out. See the schematic figure below.

As the second loop starts to fill the air path from the first loop to the outlet is blocked off. As such, the pressure on the left surface of the second loop is no-longer atmospheric. As such, the water will rise more on the right hand side of that loop than the left had side. If any water gets into the third loop, then the process is repeated. Eventually, this buildup of pressure causes the water to back up in the first loop and overflow at the funnel.

Based on the diagram above, and ignoring the hydrostatic pressure variation in the trapped air, we can write a series of expressions relating the pressures at the labeled points:

Pa=0

Pb=Pa+γ(Ha-Hb)

Pb=Pc

Pc=Pd+γ(Hd-Hc)

Pd=0

I always write out the equations for each column of water separately in the form Plower point=Pupper point+γ(change in height). Done this way I find that it is harder for students to make mistakes with signs.

Solving this set of equations leads to

Ha-Hb = Hd-Hc

Therefore, when the height difference of the water in the second loop (or the sum of the height differences in the 2nd and 3rd loops) equals the height difference between the top of the first loop and the funnel, the funnel will overflow.

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 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.

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.