These are exapmles of 'variable area, constant differential pressure flowmeters'.
The rotameter tube tapers, becoming narrower towards the bottom. As a result, the gap between the bobbin and wall changes according to the height of the bobbin and the bobbin will take up a position of equilibrium, balnaced between gravity and pressure due to gas flow.
Towards the bottom of the tube, the relatively long, narrow gap between the bobbin and wall behaves like a tube and pressure drop is related to gas viscosity (Poiseuille). As the flow rate rises and the bobbin ascends, the larger gap between the wall and bobbin changes the configuration to resemble an orifice and pressure drop becomes density dependent (derived from Bernoulli). As a result, rotameters may only be used for the gas against which they have been calibrated.
Rotameter accuracy depends on the bobbin remaining in the center of the lumen. Consequently, the rotameter must be vertical and the bobbins are often spin-stabilized. The bobbin should be visible across its full range of travel (to prevent misinterpretation of zero/full flow).