The two of these things that I have both have/had troughs through which the wheel turned.
The wooden pieces of the older pedal-powered one are mostly rotted away and it's hard to see if water was fed in, poured in, or what. The newer ride-on, caster-mounted, double-reduction electric-powered monster also has a trough with a drain valve built in and everything. I believe the newer one turns away from the seat, like a forward-traveling wheel. There's a little flappy brush thing screwed to the trough where the leading edge of the wheel emerges to reduce the amount of water flung at your crotch.
The first I was given by a neighbor and had planned to rebuild (never started). The second I bought with the foolish notion that it was already rebuilt - I'd traveled an hour to look at it and guess I didn't want to go home empty handed... It's in decent mechanical shape, but the wheel surface needs help.
Anyway, both are rather eccentric in shape. They should probably be on their way to someone who will put the time into the stones and/or frame to make 'em into something usable.