[set fair (OP)]

If you made a disc which was like a squashed WWII British army helmet on the top and flat on the bottom and set it spinning, I think it should rise because the air would move faster over the top because of its greater surface area. So suppose you made a bunch of discs on a common axis with a motor and enclosed all this in a tube. You could arange gears so that alternate discs spin in opposite directions if you wanted. Would it fly?

[alancalverd]

If the atmosphere is sufficiently dense, yes.  There are various forms of centrifugal separator for oil/water, milk/cream and suchlike, that effectively induce radial flow over a spinning disc, and thus effectively reduce the pressure above the disc, but when dealing with a low viscosity, low density material like terrestrial air, it's a lot easier to use a thin aerofoil like a propellor or helicopter rotor,

Leonardo da Vinci sketched a contra-rotor helicopter, and I think the Russian military use them - no asymmetric torque makes them easier to fly. Contrarotating propellors confer high efficiency over a limited range of speeds and were used on the Gannet and Shackleton marine patrol aircraft.