2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148570An intrinsic metric tensor, a flat connexion and the corresponding distance-like function are constructed in the configuration space formed by velocity field {\bf and} the thermodynamic variables of an inviscid fluid. The kinetic-energy norm is obtained as a limiting case; all physical quantities are Galilean invariant. Explicit expressions are given for the case of an ideal gas. The flat connexion is {\bf not} metric-compatible. These results are achieved by applying the formalism of statistical manifolds \cite{amari,otros} to the statistical mechanics of a moving fluid.20 pages, LaTeX. This version is almost identical to the one submitted for publication in October 1995Chaotic DynamicsFluid Dynamicstext