  We construct the N=1 supersymmetric extension of the polytropic gas dynamics.
We give both the Lagrangian as well as the Hamiltonian description of this
system. We construct the infinite set of "Eulerian'' conserved charges
associated with this system and show that they are in involution, thereby
proving complete integrability of this system. We construct the SUSY -B
extension of this system as well and comment on the similarities and
differences between this system and an earlier construction of the
supersymmetric Chaplygin gas. We also derive the N=1 supersymmetric extension
of the elastic medium equations, which, however, do not appear to be
integrable.
