Electromagnetism is complicated. Fluid dynamics is also complicated. For a real headache, though, try working on a problem where both kinds of effect are relevant (sadly, this covers most of astrophysics). Even if you make some simplifying assumptions and get the theory of magnetohydrodynamics, you are still left with all sorts of complicated effects. Leaving aside from the much more complicated equations you might expect, magnetic fields and velocity fields define two potentially different directions at each point, meaning that you can very rarely get away with assuming spherical symmetry to get down to a one-dimensional problem. Nevertheless there are some neat phenomena that occur.
One gadget I'd like to build is a demonstration of is a fluid pump in which the only moving material is the fluid. It turns out there are simple effective designs (PDF) (some of which are in use in nuclear power plants). The biggest problem turns out to be choosing an appropriate fluid.
The basic requirement is that the fluid be conductive. A low resistivity would make the design easier, but as long as the resistivity isn't too high something can probably be arranged. So as I see it the feasible solutions are:
- Aqueous solution of some sort (e.g. salt water, vinegar). Unfortunately you tend to get electrochemistry happening: the current is carried by the motion of the ions, but as you add and remove electrons at the electrodes you get things like 2Cl- -> 2Cl∙ -> Cl2, which aren't good for your electrodes or your health. You might be able to work around this with a sufficiently low voltage - as I understand it these reactions need a minimum of a volt or so to happen at any significant rate - but supplying power at such a low voltage is awkward. Apparently high frequencies work too - at tens of kilohertz or megahertz the ions don't migrate enough in any one direction to make much difference. But this means you have to use electromagnets, and moreover, electromagnets that work at those high frequencies.
- Mercury. Liquid metal, nice and conductive. Quite poisonous, at least in vapor form or when reacted with other things. Also very dense (so hard to get moving) and somewhat expensive per milliliter. It's really the poisonousness that's the problem.
- Wood's metal or "cerrobend". Melts in hot water. Contains a lot of cadmium, which is rather poisonous. Not too expensive. The gadget would need some means of heating to keep the metal liquid; for a demonstration that's meant to run for very long, this means a thermostat and safety systems.
- NaK. Eutectic alloy of sodium and potassium, liquid at room temperature. More reactive with water than either sodium or potassium. Non-toxic, at least in the subtle environmental sense, though even after the sodium and potassium have reacted with water you're left with concentrated hydroxides which will destroy skin. Might be possible to handle safely under clear mineral oil (but is a fire hazard if ever broken). May wet glass easily, making a sealed arrangement problematic. May be expensive.
- Galinstan. Eutectic alloy of gallium indium and tin. Liquid at room temperature. Not very toxic (probably safe provided you don't eat it or bathe in it, though oxide dust in the atmosphere is possibly a problem). Wets glass, so it would quickly render a container opaque. Is oxidation an issue? Expensive.
I think the way to go is with galinstan and a fairly small fountain. This conveniently lets you use little permanent "supermagnets". I'd aim for a U-shaped channel, with an electrode in the middle and on either side of the U. I'd have to figure out what voltage and current would be needed, but I could probably arrange to use a few volts at a few amps, which should be easy to get (out of a PC power supply, maybe even). The electrode material is another question - it looks like copper or aluminum would be attacked by the galinstan, but stainless steel should be okay.