  Determining the velocity field of structures such as galaxies, stars, and
fluid planets is a relevant topic in astrophysics and astronomy. Depending on
the shape of the astrophysical object, the internal velocity field may be
obtained by means of analytical methods. Specifically, ellipsoidal
configurations are the most simple and natural generalization of spherically
symmetric mass distributions, when rotation is present. In this work one
obtains closed analytical expressions of the velocity field and of the kinetic
energy of uniform ellipsoidal configurations composed of compressible fluids.
With this aim, the equation of continuity is solved allowing a description of
the irrotational velocity field within the system. This permits obtaining
analytical expressions of the kinetic energy for each specific mass
distribution.
