Variational principles for special and general relativistic hydrodynamics a
re discussed with a view to their application to obtain approximate solutio
ns to these problems. We show that effective Lagrangians can be obtained fo
r a suitable ansatz for the dynamical variables such as the density profile
of the system. As an example, the relativistic version of spherical drople
t motion (Rayleigh-Plesset equation) is derived from a simple Lagrangian. F
or the general relativistic case the most general Lagrangian for sphericall
y symmetric systems is given.