Hello Jonty,
We had a debate about this about 18 months ago in the forum. I thought we documented it in my Bluebird blog but I can't find it now. It has been done (
https://www.youtube.com/watch?v=bR7FJNUCsdI) but I don't think it really worked. We also concluded that it probably wouldn't work - but prove us wrong! Here's what you are up against:
1) Thrust. I did some fag-packet calculations. There's a very simple relationship between power, thrust and speed: Power = speed x thrust. If you take my 1/8th model, assume it will run at 30 mph (13.5 m/s) using about 700W at the prop. The thrust comes out at 53N (5.5 kgf). That's a BIG ducted fan! OK, they are ball-park figures but not a million miles out and suggest that even on a smaller model, you will need a potent fan.
2) Water ingestion. I did rough out a design but declined to publish it on account of I didn't want to be responsible for somebody losing an eye when the fan burst.
3) Intake area. Just as George said, the only (findable) attempt had the cowling riddled with holes to try to get some air in. Looking on HobbyKing, you'd be looking at a 120mm fan for my model. The intakes would need to be at least double the size they are now.
The thing to remember is that ducted fans are nothing at all like turbojets. They work on a completely different principle. DFs are just propellers, shrouded to improve the efficiency. They produce thrust by aerodynamic lift on the blades, not by ejecting a high-speed jet. And they are pretty poor at low speeds. The pitch of the blades is too high and they stall (think 'wheel spin'). They are designed to work on aircraft moving forward fast.
For my money, I think a water screw is the answer. If I were starting again from scratch I think I would do away with the strut and go for a sturdy prop tube (like George). More discreet. But then again, the objective it to get the thing going so fast so can't see all that apparatus hanging off the back anyway.