Everglades

Mitchell's Landing Florida

Mitchell's landing is a narrow spot at the end of the road where you can put an airboat or a canoe in. You can also register for a permit to camp in some cleared patches along the road. They have trash cans and two portable toilets, and a dozen circles of broken limestone if you want to pick one out for a fire pit. Its drained swamp and hammocks, with a canal running along the main road, full of fish. You ought to see the heron over in Mitchell's Landing.

I learned just a little bit about teaching once, some concept called building bridges and digging tunnels. Its all about building new knowledge on top of old and showing how things interconnect. I don't know much about lecturing, except that when I was in school there were some really bad examples, and one really good one - my electronics teacher gave a lecture that was absorbing and breathtaking, and you couldn't believe how he could write equations for 47 minutes without looking at notes.

I can't lecture like that but what I am good at is showing new ideas to one person, and telling if they are lost or not. The people I was working with asked me what I do when the person gets a glazed look in their eye and I said - "review" Then take a break. So here is a review of fluids, in about 200 words.

You already know what fluids are, things that flow. It can be a solid or a gas. Hundreds of years ago some good ideas about fluids were written down, someone named Dalton and someone named Boyle. There is a concept of perfect fluids - fluids where every atom behaves like every other one. And there is a concept of partial pressures, where in a mixed gas if the whole volume has a pressure, then each component gas, such as nitrogen or oxygen, also has that pressure. The last thing we know for sure about fluids is that temperature is a function of pressure and volume. PV=kRT where R is Boltzmann's constant.

Then quite a bit of time passed and Navier - the great mathematician, and Stokes - who explained fluorescence, independently came up with some calculus equations that described the state of a gas and how it changed. Navier Stokes is a big deal, and as far as math describing a system its hard to find anything more elegant, but I'm no expert in it. The short answer is Navier Stokes works and can make you a lot of money if you need something like it.

The long answer is different. The long answer says - well what is pressure, really - when we measure temperature what is it really we are measuring - what is involved in being a 'mixed gas' - how do partial pressures get to be the same - in what way is my gas different from ideal. The long answer is we don't really know, pressure and volume and temperature are the most easily observed things. We can observe the gas to have a value for those variables, we can observe how the gas behaves according to Navier-Stokes if we heat it up, and we can observe that for common air it is really hard to tell the difference between our gas and a 'perfect gas'

The variables of pressure volume and temperature are observable and they are also controllable. We can press the gas into a smaller space, or heat it up, or add more gas to change the variables. P V and T are at the same time observable and controllable. So it is safe to use the equations without worrying about the molecular shape of the nitrogen molecule, or the fact that water vapor has an ionic value - it's an electrical dipole, or worrying about the fact that oxygen is likely to combust with other molecules in an oxidation-reduction reaction. We don't need to worry about the fact that 'temperature' is mostly just a measurement of atomic vibrations, and we don't need to worry about the spinning energy of rotation of molecules because we can't observe that easily and we can't control it. We don't need to know. That's eight weeks worth of fluids lectures, without the homework.

Fluid dynamics is a little different. This is when you put fluids in motion and few hundred years ago some ideas were written down by Magnus and one of the Bernoulli's. These ideas are generalizations of more complicated things just like the Boyle Dalton and Navier-Stokes ideas. The generalizations are useful, and they usually work, but moving fluids are more complicated. In my opinion, Magnus and Bernoulli have led to generations of confusion in systems that involve dynamic fluid flow.

What Magnus said is that when a fluid passes over a rotating object it creates lift. What Bernoulli said is that when a fluid speeds up the pressure decreases, useful for creating lift on the top side of a wing. Both are right, and both are generalizations of what is really going on with the molecules in the fluid. In addition I think that both ideas are specific instances of the other man's ideas.

For Magnus the rotating object creates a relative difference in air speeds. One side of the disk speeds up the air, the other side slows it down. Thus you can apply Bernoulli to the relative changes in air speed in the Magnus rotating object. A Bernoulli wing is just a Magnus disk cut in half, and with an angular speed of zero. It might be nice to have a deformable rotating object so that we could spin it and still have it be flat on the bottom, and see what happens. That would be a good test of what Magnus says.

I think that what is really happening with 'lift' is something funny in the air that is not observable. Bernoulli says lift is related to velocity, and Prandtl wrote the equations that determine lift over a two dimensional line along the wing. But velocity is a vector, it has a direction and a magnitude, so it could be that Bernoulli should apply to air that changes direction but does not change speed. That would be a good test of what Bernoulli says.

There are two other basic ideas in fluid dynamics. One is the vortex, or the circulation of fluid that is created by a rotating cylinder. The other is the wake, or the chaotic flow that occurs downstream from an obstruction in the fluid flow. All the other ideas, such as boundary layer, laminar flow, wake vortex, von Karman Streets, modelling wings as if they were a pair or vortexes, Kutta-Joukouski transformations, streamlines, potentials and potential flows, all these ideas come from the basic ideas. The basic ideas are that there is a bow shock, there is a wake flow, vortexes occur naturally in the presence of magnetic fields, and air changes pressure when it changes speed or direction.

That's the review, and I'm glad I got it out of the way!