Volume of water moved

There are times when simple questions should be answered with simple answers, and times when an approximate answer is better than no answer at all. The author of the OP has clearly stated that he doesn't need the complications you are introducing. By the way, a propeller is not an actuator disc. That would have been a more fundamental objection to the proposed method, than the one you are insisting on. However, the actuator disc model can give a simple answer which the author of the OP was looking for.

For me, questioning the reasons and usefulness of the original request, without knowing anything about authors motivation or intentions, is a much bigger nonsense.

 

Indeed

 

I have found this issue of how much water was "moved" about as rivetting as how much poop was moved by the world's production of All-Bran.

 

If this needs to be explained to a 12 tear old, get a traditional hand crank meat grinder. It is easy to show how much mass of meat was moved x the number of times the crank was rotated.

 

Sometimes questions may arrive out of a sheer curiosity. Curiosity is imo as valid motivation for learning and discovering things as any other, more practically oriented ones.

 

Absolutely!

 

Maybe you can look at this like it is a rocket and not a boat... ie... for every action there is an equal and opposite reaction. Thrust is governed by the volume and speed of the water that is moved by the prop in the opposite direction as you want the boat to travel.

To find the amount of water the prop pushes you would need to know the force you need to apply to the boat (resistance at its current speed) and also the speed of the water as it leaves the prop.... you could then solve for the volume of water "ejected".