Ah Rick,
You used the important words... Conservation of energy, conservation of mass,
continuity equation. This is why Bernoulli's principle works, this is what
Bernoulli's principle is about! If we have an incompressible fluid in a pipe
and the pipe gets smaller continuity says to get all the fluid through the
smaller pipe it has to go faster. Now if it is going faster it has more
kinetic energy. Conservation of energy says this energy came from somewhere.
Where? Why the random motion of the molecules that make up the fluid. They
now have more motion in the direction of flow and less motion in other
directions. This means they can't bang on the pipe as much or as hard so they
exhert less pressure on the pipe. Now if the pipe gets bigger they don't
go forward as much, have more random motion and beat on the pipe more. This is
what Bernoulli's law is all about.
The question to ask about curve balls, airplanes, and shower curtains is not if
Bernoulli's law makes things go the right way, but if the conditions to which
Bernoulli's law apply exist for these events. I submit that they do not. For
the curve ball the spinning ball does work on the air so energy within the
fluid is not conserved. For airplanes the engines do work, in a glider gravity
does work, again energy in the fluid is not conserved. For the shower curtain
falling water does work on the air and there is no need or continuity on
opposite sides of the curtain.
I suppose it is fair to ask if we account for the effects of the energy inputs,
might there not still be a Bernoulli contribution. In the case of the baseball
I think not. The only reason there is a velocity difference on the opposite
sides of the ball is because of friction between the air and the ball. Take
away the effects of the friction and you take away the curve! With the
airplane it seems to me that a Bernoulli component should exist and as previous
posts by others on the list have shown, it is possible to calculate the
relative magnitude of Bernoulli effects and the lift provided by change of
momentum of air molecules hitting the underside of the wing. Frankly, I don't
see anything close to Bernoulli conditions in the shower.