Jim Logajan wrote:

Uncle Al wrote:
2) Bernoulli's law is strictly a 2-D analysis.

Are you sure? I ask because I know the application of Bernoulli's theorem
to airfoils is typically restricted to 2-D and wondering if that is what
you meant. Otherwise there doesn't appear to be any dimensional assumption
in the theory itself or its derivation. Here's one typical presentation of
Bernoulli's theorem:

"In the steady motion of an inviscid fluid the quantity

p/rho + K

is constant along a streamline, where p is the pressure, rho is the density
and K is the energy per unit mass of fluid."

And the definition of streamline also appears void of dimensional
restriction:

"A line drawn in the fluid so that its tangent at each point is in the
direction of the fluid velocity at that point is called a streamline."

Both quotes from "Theoretical Aerodynamics" by L. M. Milne-Thomson.

So unless I'm mistaken (and I could be) it appears that Bernoulli's
theorem:
1) Applies to compressible or incompressible fluids.
2) Does not necessarily apply to viscous fluid flows.
3) Does not necessarily apply to turbulent flow (it's not "steady motion".)
4) Does not itself define the flow streamlines.
5) Is not restricted to 1 or 2 dimensional analysis.

3-D wings are more than Bernoulli's law. If they weren't they
wouldn't vastly benefit from shaped distal winglets to control vortex
shedding. Adding small drag surfaces at the wingtips normal to the
wings' surfaces does not have beneficial - much less hugely beneficial
- effects in 2-D analysis. In the real world airlines madly scrambled
to add winglets to improve fuel economy.

Look at the ratio of surface areas, wing and its winglet. The real
world benefits are wholly disproportional to area ratio. It is a
matter of leverage. A tiny tweaking of vortices rolling off distal
wing ends creates major energy control.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2