RE: Bernoulli vs Newton
Tim:
You are right.
Nobody exposing here is wrong, I believe.
Just relocate your helicopter 1000 feet up, and the result will be the same: the plate blocks the mass of air being pushed downwards, killing the velocity of the mass of air; hence, killing the force upwards.
Your assembly of helicopter-plate has the same flying capacity than a closed cardboard box.
The atmosphere doesn't feel any stream of air pushing on it (because the entire storm is happening inside the closed box), and it does not see the need to react to non-action.
All the forces generated by the rotor of your helicopter are internal to the assembly, and do not affect the surroundings.
Sir Newton stated three laws, one of which dictates that only an external force can modify the physical state of an object, regarding speed.
Bernoulli calculated the jig-saw of the energy of an ideal and non-compressible fluid: the amount of energy remains the same within the fluid, becoming kinetic (fluid with velocity), potential (fluid with pressure), or a combination of both.
Pressure above the rotor and under the plate is the atmospheric pressure.
There, the velocity of the fluid is zero.
Remember that nothing is transferring energy to the atmosphere.
Between the rotor and the plate, the velocity and the pressure of the fluid is high, because it is receiving the energy from the burning fuel.
But unfortunately, because your box is closed, that energy is not transferred to the atmosphere.
All you have is a furious blender inside a cardboard box, which is falling like a stone.
In addition, your assembly will not have any stability while falling down.
You will have the same effect as if a strong spring is compressed inside the box.
The rotor of your helicopter and the propeller of my model airplane produce a force in direct proportion to the mass of air that they can move times the velocity that they can make that mass of air move, in reference to the velocity of the surrounding air.
The EXTERNAL reaction to that EXTERNAL force makes the models move in the opposite direction, or just hover in the air.
Same applies to any bullet or rocket: action and reaction of external forces.
Regardless of the lifting process or method, part of the chemical energy (mentioned by Bernoulli) contained in the fuel, is transferred (as explained by Sir Isaac Newton) to the atmosphere.
Regards!!!