  Symmetries and Casimirs are studied for the Hamiltonian equations of radial
compressible fluid flow in n>1 dimensions. An explicit determination of all Lie
point symmetries is carried out, from which a complete classification of all
maximal Lie symmetry algebras is obtained. The classification includes all Lie
point symmetries that exist only for special equations of state. For a general
equation of state, the hierarchy of advected conserved integrals found in
recent work is proved to consist of Hamiltonian Casimirs. A second hierarchy
that holds only for an entropic equation of state is explicitly shown to
comprise non-Casimirs which yield a corresponding hierarchy of generalized
symmetries through the Hamiltonian structure of the equations of radial fluid
flow. The first-order symmetries are shown to generate a non-abelian Lie
algebra. Two new kinematic conserved integrals found in recent work are
likewise shown to yield additional first-order generalized symmetries holding
for a barotropic equation of state and an entropic equation of state. These
symmetries produce an explicit transformation group acting on solutions of the
fluid equations. Since these equations are well known to be equivalent to the
equations of gas dynamics, all of the results obtained for n-dimensional radial
fluid flow carry over to radial gas dynamics.
