  Lagrangian formulation for perfect fluid equations which hold invariant under
the $\ell$-conformal Galilei group with half-integer $\ell$ is proposed. It is
based on a Clebsch-type parametrization and reproduces Lagrangian description
of the Euler fluid equations for $\ell=\frac12$. The transition from the
Lagrangian formulation to the Hamiltonian one is analyzed in detail.
