Re: [Phys-L] Terminal velocity in water

[John Denker <jsd@av8n.com>]

Hi --

Y'all know I like to emphasize the importance of scaling laws.

It turns out that one of the all-time great experts on scaling
laws was a guy named ... wait for it ... Osborne Reynolds. He
popularized the idea of Reynolds number in 1883. Roughly speaking,
it indicates the ratio of inertial forces to viscous forces.

The Wright brothers succeeded because they -- mostly -- did the
homework. Among other things, they built a wind tunnel so that
they could make meticulous measurements on scale models.

However, alas, they were not sophisticated enough to know about
Reynolds numbers. As a result, their experiments were not nearly
as helpful as they should have been. They would have been vastly
better off using a *water tunnel*. A smallish object in a water
tunnel has about the same Reynolds number as a much larger, faster
airplane.

Here's how to convince yourself that inertial forces are large
compared to frictional forces. Take a look at the diagram and
brief discussion here:
  
https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/shaped.html
NASA: "Shape Effects on Drag".

Additional shapes are here:
https://physics.stackexchange.com/questions/201633/what-shape-has-the-highest-drag-coefficient

Then repeat the experiment using different shapes. I predict that
a streamlined shape will fall much faster than a sphere, given the
same frontal area and the same driving force (accounting for both
gravity and buoyancy).

Note that a cup facing into the flow has a much higher drag than a
cup facing the other way. This is the idea behind a spinning cup
anemometer. This cannot be explained by viscosity.

People have lots of experience with situations where the Reynolds
number is low. Their intuition about high Reynolds numbers is usually
terrible. Fluid dynamics is a very difficult subject. I once asked
Richard Feynman what he would do if he couldn't work on elementary
particles. He said fluid dynamics, because it is just as challenging,
perhaps more challenging, and there are lots of fundamental unsolved
problems. Also lots of practical applications.

Amusing albeit overly-detailed video of a water tunnel in the teaching
lab at (I think) University of Central Florida:
  https://youtu.be/zFMKehbbw_M
Start here if you're in a hurry:
  https://youtu.be/zFMKehbbw_M?t=672