Saturday, October 09, 2010

"The Simple" Tend to be Not So Simple

What could be more basic or common in life than stepping up to a drinking fountain and taking a sip of water. A stream of water becomes a fluid projectile, and it lands on the metal surface of the fountain, splashing a bit, but nothing too extreme. At least, nothing too extreme at a first, quick glance.

I do an activity from time to time with students, as well as science teacher colleagues at some past workshops, where we reproduce the water fountain experience in an even simpler way. Simply take a large beaker full of water and pour it gently on a hard surface. When one does this and then begins to observe what happens a little more closely, they quickly realize there is more to this event. First, a smooth circular region appears around where the stream of water lands on the surface, and then at a certain radius, the water level dramatically lifts up. This is the well-known hydraulic jump. Most people have never paid attention to water from a faucet landing in their sinks at home, so this tends to be a surprise. But then, I will ask the students or colleagues to do something else. Make a list of any variables you can think of where the size and pattern you see could be changed. That is, what could the hydraulic jump depend on, and what are the variables you could select to investigate in controlled experiments to better understand this feature of fluid flow? Here is one list that developed from this simple demonstration of a hydraulic jump:

• The amount of water in the stream, or ‘jet,’ being poured out of the cup – this is the flow rate of the water;
• The height the water is poured from the cup – this determines the energy and speed at which the water hits the surface;
• The diameter of the stream coming down to the surface;
• The temperature of the water;
• The temperature of the surface;
• The material the surface is made from;
• Whether the surface is horizontal or sloped relative to the ground;
• The type of liquid being poured – one student said syrup being poured would look very different compared to water, so this would refer to viscosity;
• The strength of gravity – some students predicted the jump would look different if this experiment were performed on the Moon;
• Whether the surface is still or rotating;
• Whether the stream of water was laminar flow versus turbulent flow before hitting the surface;
• Whether the stream hit perpendicular to the surface or at another angle relative to the surface;
• The topology of the surface – differences would likely appear if there was a curve to the surface, instead of being flat;
• If there were any barriers or obstacles on the surface close to where the stream hit the surface;
• If there was more than one stream of water coming down – what would the consequences be if there were multiple, interacting hydraulic jumps?
• The size of the surface;
• If there were any horizontal vibrations of the surface;
• If there were any vertical vibrations of the surface.

Again, this long list catches even colleagues by complete surprise. After all, this is a very "simple" physical event - water pouring onto a surface. A simple pattern appears. But when one begins to really think about the phenomenon, clearly it is more complicated than one could initially imagine.

This is a wonderful way to get students to a new level of observation and thought. It is a wonderful way to get someone out of a textbook way of thinking and step into the complexities of reality. And I am a firm believer that getting students to be able to identify and accept more complexity than what is allowed for in standard textbooks at younger ages (such as in high school, if not middle school) is something we should look to be doing in education. I personally was not exposed to this way of thinking until my second year in college, and I regretted it because I realized I had been missing out on almost being forced to think more creatively about problems and analysis.

While it is vital to simplify problems by making assumptions and approximations, if for any other reason to be able to gain initial insights into the physical system and actually solve the resulting mathematics that appear in the theoretical models,
what we overlook by NOT considering the complexity include second- and third-order effects that can collect together to cause subtle differences in the system when compared to theoretical models. These higher-order effects are also regions to explore for new discoveries and insights into deeper, better models of how the world work. And beyond that, it allows students to have to think about how they could design experiments to test the effects of variables never considered in the textbook, and this usually requires the students to be innovative and creative in trying to solve such design challenges. If the students then actually try the experiments they develop on paper, they then have to troubleshoot their experiment, which inevitably does not work the first time they set it up.

Complexity is all around us, even in what we would categorize as the most "simple" systems. In an age where creativity and advanced problem solving is in decline even though such skills are some of the most important to have in this day and age, educators should not be shy about pointing out how to break-down the 'simple' to find the complex, and then allow the student to attack the complex and unknown with abandon, developing new ideas and getting their hands dirty trying out their ideas. There is A LOT to be learned by all involved in such a dynamic process!

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