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.