  In this paper we propose a comprehensive framework for the quantum
hydrodynamics of the Fractional Quantum Hall (FQH) states. We suggest that the
electronic fluid in the FQH regime could be phenomenologically described by the
quantized hydrodynamics of vortices in an incompressible rotating liquid. We
demonstrate that such hydrodynamics captures all major features of FQH states
including the subtle effect of Lorentz shear stress. We present a consistent
quantization of hydrodynamics of an incompressible fluid providing a powerful
framework to study FQHE and superfluid. We obtain the quantum hydrodynamics of
the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.
