A short note on the buoyant force in nonuniform gravitational fields

TL;DR

This paper explores an alternative fluid mechanics approach to deriving the buoyant force in nonuniform gravitational fields, emphasizing energy formulations over previous methods.

Contribution

It introduces a new derivation method based on energy formulations of equations of state, differing from the divergence theorem approach.

Findings

Provides an alternative derivation of buoyant force in nonuniform gravity

Highlights the role of energy formulations in fluid mechanics

Offers insights into compressible fluid behavior in gravitational fields

Abstract

Lima and Monteiro [1] derived the buoyant force in a nonuniform gravitational field by applying a gradient version of the divergence theorem to the surface integral of the pressure forces [2]. Here it is outlined an alternate approach in the framework of fluid mechanics, based on the energy formulations of the equations of state for compressible fluids.