Potential of a homogeneous gravitational field
A homogeneous gravitational field is characterized by a constant vector field , the well known gravitational acceleration. Let us consider some volume or vessel filled with an incompressible fluid of density . The gravitational field exerts a force on the fluid. Its force density is given by the following well known formula It is a simple task to find a potential to (). Let us remind, a potential (if it exists) of some given force field is defined as a certain function satisfying the following equation We can see that to the given by () there exists a potential, let us denote it by , stating where is a constant of integration8.4 and is a position vector8.5.