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Name: Amanda
Status: student
Grade: 9-12
Location: IL
Country: USA
Date: Winter 2012-2013


Question:
I am very interested in the physics of waterfalls, but am having difficulty finding source material that can be understood by a high school student. Would you please refer me to any sources of information? I understand that there is projectile motion, but I am struggling a bit with how the stream narrows as it falls, and how it necks down into droplets.

Replies:
Hi Amanda,

Thanks for the question. Yes, the physics of waterfalls includes projectile motion. Please see Wikipedia or look up "projectile motion" on the Internet--there are many good resources for that topic. The waterfall stream narrows as it falls (just like the water from your faucet). This narrowing is due to the law of continuity, A1v1 = A2v2 = flow rate. I would also recommend looking up the law of continuity on the Internet or in a high school physics textbook. If you are unable to find any good material, please let me know and I will write some explanations for you.

I hope this helps. Please let me know if you have any more questions. Thanks Jeff Grell

http://www.newton.dep.anl.gov/askasci/eng99/eng99439.htm

http://sbainvent.com/fluid-mechanics/continuity-equation.php#.URQZWqXm44k

http://en.wikipedia.org/wiki/Law_of_Continuity

http://en.wikipedia.org/wiki/Continuity_equation

http://www.youtube.com/watch?v=8binWHRAfUk&noredirect=1

http://www.aplusphysics.com/courses/honors/fluids/continuity.html




Amanda,

Wow, this is a surprisingly complex subject, so it is no shock that finding scientific info was not easy. Based on your question, I think you are not interested in geology, erosion, and the formation of waterfalls, so I will focus on just the water falling. The short answer is _fluid dynamics_. Unfortunately, most info in this field assumes you know calculus (which the equations of fluid motion are built on). But most high schoolers do not have that math in their toolbox. At a high school level, you are going to be restricted to qualitative explanations and examples rather than the core phenomenon, so let me see if I can help.

Here is a progression you might follow: Start by reading about basic fluid mechanics -- viscosity and surface tension especially. How molecules of water act on their neighbors, and how they 'like' each other more than they like air. You can look up lots of videos on fluid motion, viscosity, and surface tension and "see" what these mean (most texts just explain them in terms of math, but I find 'seeing' is really helpful too). Next, read about water droplets -- this includes surface tension, gravity, and viscosity. You can learn how and why droplets form. There are cool videos out there that zoom in on a stream of water breaking up into droplets that may help a lot. Next, read about fluid flow in a pipe with constrictions, and water flowing out of a hose -- that will teach you about how pressure affects water (as water drops, it experiences pressure from the water around it and the air around it). Especially look at how the width of the water stream changes as it leaves the pipe. Some videos also get into the stream breaking up into droplets too. Then, you can get into aerodynamics, look at airflow over different shapes like spheres, squares, and wings, which will give you a sense of the forces that water experiences, and why it breaks up. Remember, air is a fluid too, and follows a lot of the same rules that water follows. Next, look up evaporation, and evaporative cooling -- this will talk about what goes on thermally in a waterfall (and why it is so cold in that waterfall mist) I would also read about diffraction and refraction -- Taylor dispersion as well. Diffraction is when light shines through small particles/openings, while refraction is when light moves into and out of materials (like from air to water to air). You will learn why and how rainbows form around waterfalls (and why the sky is blue too), and why you cannot see through mist very well but you can see through a pool of clean water. Finally, look for videos of water streams hitting surfaces of water or solid objects. Watch the waves that form when they impact, and how the energy in those waves is transferred away from the impact location. This explains waterfalls' sound too.

In sum, these subjects give you a few foundational elements of what is going on in a waterfall. Feel free to write back with more questions.

Hope this helps! Burr Zimmerman


The reason that you have difficulty finding source material on the hydrodynamics of waterfalls at the high school level is that it probably does not exist.

The flow of water through another fluid, in this case air, is very complex. In addition to the flow of water, there is the counter-current of turbulent air, over a non-uniform base of rocks and soil. In addition, the water is not “pure” it contains soil, rocks, and dissolved substances, including components of the atmosphere – all of which alter the flow characteristics. As the water flows through the air these various components alter the surface tension of the water in a very complex manner that changes how the water’s surface tension that is a function of time and temperature. So the lack of any simple model is because the whole process is not simple.

Vince Calder


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