This is given by Eq. (4), the Euler Lagrange equation is given by Eq. (5). Its ECE2 covariant (relativistic) version is given by Eq. (10). This appears to be the first time that a lagrangian has been clearly defined for fluid dynamics. This theory achieves a completely self consistent description of orbital precession, forging together precession due to ECE2 covariance and precession due to ECE2 fluid gravitation. The non central nature of the general gravitational potential leds to many interesting types of orbit. After an extensive literature search I found that some very abstract and obscure attempts have been made in mathematical physics to find the lagrangian for fluid dynamics. The result (4) seems to have been missed by the mathematical physicists.