  We show that the Fractional Quantum Hall Effect can be phenomenologically
described as a special flow of a quantum incompressible Euler liquid. This flow
consists of a large number of vortices of the same chirality. In this approach
each vortex is identified with an electron while the fluid is neutral. We show
that the Laughlin wave function emerges as a stationary flow of the system of
vortices in quantum fluid dynamics. Subtle features of FQHE such as effects of
Lorentz shear stress, the spectral function, the Hall current in a modulated
electric fields, etc., naturally follow from the hydrodynamics approach. In the
paper we develop the hydrodynamics of the vortex liquid, and able consistently
quantize it. As a demonstration of the efficiency of the hydrodynamics we
discuss some new results for FQHE in a non-uniform magnetic field and a curved
space.
