The variational principle for the special and general relativistic hydrodyn
amics is discussed in view of its application to obtain approximate solutio
ns to these problems. We show that effective Lagrangians can be obtained fo
r suitable ansatze for the dynamical variables such as the density profile
of the system. As an example, the relativistic version of spherical droplet
motion (Rayleigh-Plesset equation) is derived from a simple Lagrangian. Fo
r the general relativistic case the most general Lagrangian for spherically
symmetric systems is given.