[en] A Hamiltonian formulation of hydrodynamics is well known for the case of purely irrotational flows and it now exists in a more general case as well. The minimal extension of the action principle is obtained from two axioms: 1. That the number of independent degrees of freedom be 4, as in standard hydrodynamics. 2. That the equation of continuity must be one of the Euler-Lagrange equations, and that it allows for vorticity. Applications include: 1. Couette flow with a new criterion for the breakdown of laminar motion. 2. A rotating source for Einstein’s equation that respects the Bianchi identity. 3. A new approach to the electromagnetism of fluids. 4. A rigorous virial theorem for fluids. 5. A critique of the current state of the theory of atmospheres.