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Propellers operate by developing lift. How do riverboat paddlewheels work? Is it traction, like a wheel "rolling" across the water, but slipping? Is it the force developed by an opposing drag? Is it the thrust developed by water moving in the opposite direction?

I think you are on the right track. In the simplest form, the paddle wheel blade is pushing on the water. Water is considered an incompressible fluid. So, when something is pushed into water and the water essentially has no where to go, the water will push back (the whole theory behind hydraulic devices is the fact that water is incompressible). While the water may have some direction to go around the blade, for the most part, the water pushes back against the paddle wheel blade, which in turn allows the boat to move in the opposite direction.

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