  An 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.
