Year: 2000 Pages: 7

The Euler fluid equations, which can be expressed as the vector equation (-?*pr*)-*g*=(*v*??)*v*+?*v *?*t*, are shown to be missing three important terms and to contain a simplistic version of a fourth. Whenever the fluid is significantly affected by an external thrust and by either a gravitational field or a set of gravitational fields, the Euler fluid equations must be replaced by ( ) ( ) ( 2 ) ( ) ( ) e e e e e -?*p r *+??2 *f*-3 *p*3*rr*??*R*- *M G r R*-*Fr*= *v*??*v*+(?*v *?*t*, where two of the three missing terms are combined into the first term times the unit vector e *R *(which points radially away from the effective center of gravity), ? *f *? is numerically the degrees of freedom of the fluid, and ? e *r *? is the distance from the effective center of gravity to the differential volume. The third missing term, F, is the non-gravitational force. The simplistic gravitational acceleration term, g, is replaced by a more general expression that takes into account the ubiquitous nature of gravity. The Euler fluid equations are used in the derivation of the Navier-Stokes equations, so the foregoing developments cause these equations to change.