Variable area meters are special form of head meters where in the area of flow restrictor is varied. So as to hold the differential pressure constant. The rotameters consists of a vertical tapered tube through which the metered fluid flows in upward direction.
A “float” either spherical or cone shaped, actually more dense than the fluid being measured, creates an annular passage between its maximum circumference and the weight of the tapered tube. As the flow varies the “float” rises or falls to vary the area of the passage so that the differential across it just balances the gravitational force on the “float” i.e. the differential pressure is maintained constant. The position of the “float” is the measured of the rate of flow.