jduffy77 said:
Are these props powered only by the stream?
If the stream is uniform, you would first have to drop the submarine in and then activate the propellers. This is nothing more than the submarine equivalent of Spork's treadmill. This acts as a break slowing the water behind it, so it is slower as it passes over (water flow, unlike the treadmill conveyor, is not uniform). You then already have a velocity difference. The crane which lowered the submarine can be divorced, and is no longer necessary.
So I can make one correction here. Some object is needed to hold it in place at first, but after that, it should not matter.
So either:
The amount of work required is similar to that required to apply brake discs - it's not very much at all - but that's only if the external actor holding the submarine is fixed (by superior inertia)... or
The external actor is not fixed (due to inferior inertia), in which case, significant work must be done to put the submarine there in the first place.
Otherwise, if you make the submarine lead the front of the water flow (i.e. if the water ahead is stagnant), then you shouldn't need either kind of actor.
So, yes, you would have to have some kind of velocity difference.
Perhaps in the case of an external conservative force such as gravity, we might have an exception to that though. I don't know yet. But if gravity itself is due to velocity differences (GR seems to imply this), then maybe that is not an exception either.