Variable Area Meter

From the Wikipedia article, "Rotameter":

History

The first variable area meter with rotating float was invented by Karl Kueppers in Aachen in 1908. This is described in the German patent 215225. Felix Meyer found the first industrial company "Deutsche Rotawerke GmbH" in Aachen recognizing the fundamental importance of this invention. They improved this invention with new shapes of the float and of the glass tube. Kueppers invented the special shape for the inside of the glass tube that realized a symmetrical flow scale. The brand name Rotameter was registered by the British company GEC Rotameter Co, in Crawley, and still exists, having been passed down through the acquisition chain: KDG Instruments, Solartron Mobrey, and Emerson Process Management (Brooks Instrument). Rota with their "Rotamesser" are now owned by Yokogawa Electric Corp.

It is not a "Variable area meter" but uses the known area at the point of float to calculate the force and flow to keep it at that level.

It's not a float because it doesn't float unless the fluid is flowing upwards past it.

Yes it is floating at the point where the gravity is in balance with the upward force.

The tube is tapered !!