  We argue that flows of the quantum electronic liquid in the Fractional
Quantum Hall state are comprehensively described by the hydrodynamics of
vortices in the quantum incompressible rotating liquid. We obtain the quantum
hydrodynamics of vortex flow by quantizing Kirchhoff equations for vortex
dynamics. We demonstrate that quantized Kirchhoff equations capture all major
features of FQH states including subtle effects of Lorentz shear force,
magneto-roton spectrum, Hall current in a non-uniform electromagnetic field,
thus providing a powerful framework to study FQHE and superfluids. The results
are also useful for classical vortex flows.
