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A common misconception by laymen is that the force is derived from "pushing against" the water/air as in pushing against a wall. In reality, the force is derived from the acceleration of the water/air. The force would be the same in a vacuum for the same amount of water/air accelerated even though there would be no air/water to push against.

It's not a misconception at all. Pushing against a brick wall (or against the ground) is the same thing as pushing against a mass of air or pushing against a jet of hydrazine in a hard vacuum. In each of these cases, it's Newton's Third Law that moves you about. In the case of a brick wall or a planet, the reaction mass is gigantic (never infinite, however), whereas in the case of hydrazine molecules, the reaction mass is tiny. The principle is the same, though. The differences are only quantitative.

Ok. Please provide me a source that says a propellor derives it's thrust from pushing against the air.

It's not a misconception at all.

OK. Go ask 100 high school drop outs how a propellor gets it's thrust. Then ask them how a rocket gets it's thrust in outer space where their is NO air to push against! You will get 100 shrugged shoulders.

It's not a misconception at all. Pushing against a brick wall (or against the ground) is the same thing as pushing against a mass of air or pushing against a jet of hydrazine in a hard vacuum. In each of these cases, it's Newton's Third Law that moves you about. In the case of a brick wall or a planet, the reaction mass is gigantic (never infinite, however), whereas in the case of hydrazine molecules, the reaction mass is tiny. The principle is the same, though. The differences are only quantitative.

IMHO, this is an accurate description of the operation of a ship's propellor, but overly simplifed in describing the action of an airplane propellor. Both are fluid dynamic systems, but hydrodynamics differs from aerodynamics primarily because air is compressible, and water is not. Depending on you POV, the statement that an aircraft propellor derives it thrust from pushing on the air could still be perfectly valid when you consider that the "forward lift" on the front of the blade was created by the leading edge pushing on the air and compressing it in order to induce that lift - it just isn't pushing it backward.