  We consider hydrodynamics with non conserved number of particles and show
that it can be modeled with effective fluid Lagrangians which explicitly depend
on the velocity potentials. For such theories, the {}``shift symetry''
$\phi\to\phi+$const. leading to the conserved number of fluid particles in
conventional hydrodynamics is globaly broken and, as a result, the non
conservation of particle number appears as a source term in the continuity
equation. The particle number non-conservation is balanced by the entropy
change, with both the entropy and the source term expresed in terms of the
fluid velocity potential. Equations of hydrodynamics are derived using a
modified version of Schutz's variational principle method. Examples of fluids
described by such Lagrangians (tachyon condensate, k-essence) in spatially flat
isotropic universe are briefly discussed.
