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Re: [Phys-l] Bernoulli's Principle

On 12/21/2007 09:05 AM, Rick Swanson wrote:

1. Flying things interact with a lot more than the near air — the
interaction of the near fluid with all the rest of it is extremely
important. Pictures of vorticies, contrails and other neat things help.
I also mention the "ground effect" observed when you see water fowl
skimming across the lake. The air knows that the rest of the air is

That's all good. Other useful things to mention include:
-- Why do gliders have long skinny wings?
-- Why do geese migrate in that V formation?

And BTW beware that ground effect is widely misunderstood,
even among pilots.

2. If something interacts with the air and goes up, some air must go
down. It's a conservation of momentum thing.

I wouldn't have said that. That confuses force with motion.
In level flight, the airplane /pushes/ down on the air, but
that does not mean the air /goes/ down. Newton's cradle provides
a good way to visualize momentum transport without mass transport.

Helicopters help this discussion.

Or not. A helicopter in hover is a very nasty thing. I'm
not sure anybody really understands it. I would never bring
it up in an introductory discussion. A helicopter in level
cruising flight is not much different from an airplane, in
terms of wake vortices, induced drag, and all that.

My most difficult calculation in a fluid dynamics class,
which I never quite understood, was a 2-D calculation of the momentum of
the air after interaction with an airfoil. Good luck with a 3-D

Actually the 3D calculation is in many ways easier. The
2D wing is /always/ in ground effect, which can be confusing,
and which makes it utterly impossible to discuss induced
drag. In 2D there are lots of integrals that converge poorly
if at all, whereas in 3D the corresponding integral is well
behaved. (I'm talking about integrals such as the total
amount of momentum in a given column of air.)


Another point to keep in mind, and to impress upon students,
is that fluid dynamics is just plain difficult and tricky.

Students sometimes get the impression that physics is a "dead"
subject, in the sense that all the answers can be looked up
in a book somewhere. Fluid dynamics easily disproves this.
There are lots of fluid dynamics questions where the student
can understand the question but nobody knows the answer.

I once asked Feynman if he were forced to start over, and
couldn't do particle physics, what would he do. He immediately
replied "fluid dynamics". Why? Because it's important, and
because there are lots of unsolved problems.

People spend their lives surrounded by fluids, and they think
that makes them knowledgeable about fluid dynamics, but it
really doesn't. I had a really good education, literally
beyond what most people can imagine, leading to a PhD in
physics and a research career. But when I got interested in
fluid dynamics, it took me a year of hard work to get up to

CFD helps a lot. Computational Fluid Dynamics. I reckon most
people would rather look at a picture of the airflow than look
at the partial differential equation that describes the airflow.
For serious research it's a two-way street; the CFD tells you
what to look for in the equations, and vice versa. I for one
would never have figured out how wings work if I hadn't been
able to write a bunch of CFD programs.


On 12/21/2007 03:00 PM, Robert Cohen wrote in part:

Suppose you hold a wood board out the car window while driving down the
road. If the board is oriented with its plane oriented vertically, what
"causes" the pressure on the leading side to be greater than the
pressure on the trailing side?

This is called pressure drag. The hand-wavy explanation is
that Bernoulli's principle more-or-less applies on the front
side, so you get the full static + dynamic pressure P+Q, while
on the back side the air is "spoiled" and all you see is the
static pressure P, so the drag force is nearly equal to the
dynamic pressure times the area, i.e. the coefficient of drag
is on the order of unity.

If you want the mathematical details on this, I don't know,
and it is possible that nobody knows.

Is your explanation of this much
different when the plane of the board is at an angle?

Completely different. Lift is incomparably easier to explain
than form drag. The basic explanation of lift survives in the
face of all sorts of simplifications and approximations, while
pressure drag does not.

You might think aircraft designers would just ignore the issue,
because nobody in his right mind would take a flat plate and
orient it face-on to the airstream -- but in fact there are
things like speed brakes that are oriented so. Similar issues
arise when considering the "all aspect" behavior of the aircraft,
such as might be relevant during a spin, or during taxi in a
crosswind. Until a few years ago designers didn't even try to
model such things analytically; they took a principled approach
to basic lift and stability, and then built a scale model to
obtain the all-aspect behavior data. Nowadays you can just do
ab-initio CFD for things the size of an airliner, if you have a
big enough computer.