The dual transformation is applied to non-Abelian gauge theories in four dimensions. It is shown that after the dual transformation the SU(2) Higgs-Kibble models give the same partition functions as the relativistic hydrodynamics of Freedman coupled to Higgs scalars and that these two theories have various dual relations. The hydrodynamics thus obtained is naturally defined as an expansion in the inverse of the original coupling constant. There exists a simple classical solution representing a circulation flow of fluid (vorticity) in the hydrodynamics with two triplets of Higgs scalars. This vorticity solution satisfies a flux quantization rule and corresponds to the vortex solution of Nielsen and Olesen in the non-Abelian Higgs-Kibble model.