by Marek Kordos
Seemingly Archimedes's screw is
indeed Archimedes's invention. Its mathematical name - or rather
that of its ideal model - is helicoid. This is a surface
generated by a straight line uniformly rotating around a fixed
axis orthogonal to it, and simultaneously sliding in a uniform
and rectilinear way along the axis. If you replace the straight
line by a segment meeting the axis at its midpoint, make the surface
of sheet metal, choose a strong rod for the axis and place the
whole thing within a tube, the device will pump water.
That's what it looks like,
more or less.
You must place the axis at a slant
and turn the crank fixed to it as if it were a hand-operated mincer.
The water inside the tube will constantly stream down the sheet
metal to compensate for the upwards-directed force due to rotation.
It will not entirely succeed, so after some (how large) number
of rotations, it will start overflowing at the top of the tube.
This is how poor Egyptian peasants still pump the water from one
irrigation channel to another.