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Potential of a homogeneous gravitational field

A homogeneous gravitational field is characterized by a constant vector field $\color{white} \vec{g}$ , the well known gravitational acceleration. Let us consider some volume or vessel filled with an incompressible fluid of density $\color{white} \varrho$ . The gravitational field exerts a force on the fluid. Its force density $\color{white} \vec{f}$ is given by the following well known formula

It is a simple task to potential to (). Let us remind, a potential (if it exists) of some given force field $\color{white} \vec{F}$ is defined as a certain function $\color{white} \phi$ satisfying the following equation

We can see that to the $\color{white} \vec{f}$ given by (

) there exists a potential, let us denote it by $\color{white} \varphi$ , stating

where $\color{white} C \in \mathbb{R}$ is a constant of integration^3.3 and $\color{white} \vec{r}$ is a position vector^3.4.

Next: Hydrostatic pressure Up: Notes on gravitational potential Previous: Notes on gravitational potential Contents Index