Buoyant force in a nonuniform gravitational field

Abstract

When an arbitrarily-shaped body is fully immersed in a liquid in equilibrium, it gets from the liquid a non-null hydrostatic force known as buoyant force. It is an easy task to apply the divergence theorem to show that this force agrees to that predicted by the well-known Archimedes' principle, namely an upward force whose magnitude equals the weight of the displaced liquid. Whenever this topic is treated in physics and engineering textbooks, a uniform gravitational field is assumed, which is a good approximation near the surface of the Earth. Would this approximation be essential for that law to be valid? In this note, starting from a surface integral of the pressure forces exerted by the fluid, we obtain a volume integral for the buoyant force valid for nonuniform gravitational fields. By comparing this force to the weight of the displaced fluid we show that the above question admits a negative answer as long as these forces are measured in the same place. The subtle possibility, missed in literature, of these forces to be distinct when measured in different places is pointed out.

Assessment of Knowledge Integration in Student Learning of Buoyant Force

“…In this regard, many studies have shown that understanding the nature of buoyant force may be such an effective way (Loverude et al, 2003;Paik et al, 2017;Young & Meredith, 2017). In other words, the most important thing in learning about the buoyant force is to understand its essential meaning, that is, the buoyant force is an effect force, which is caused by the effect of liquid gravity on the surfaces of an immersed object (Kim & Paik, 2021;Lima & Monteiro, 2013). With this understanding basis, the interpretation of buoyant force related phenomena and the solution of buoyant force related problems ISSN 1648-3898 /Print/ ISSN 2538-7138 /Online/ are correct (Paik et al, 2017;Radovanovic, 2012;Young & Meredith, 2017).…”

“…The above findings of literature review were consistent with the results of expert consultation and demonstration. Most of the experts who participated in this study mentioned that the biggest difficulty for students in learning buoyant force is that they cannot completely understand the definition of the buoyant force, which is usually expressed as "the net force exerted by liquid pressures on the surface of an object" or simply as "F b = ΔF" (Kim & Paik, 2021;Lima & Monteiro, 2013). In fact, this definition not only reflects a mathematical relationship, but also contains the nature of buoyant force, when problems related to buoyant force need to be solved, the most important thing is to understand that the buoyant force is an effect force, which is caused by the gravity acting on the liquid.…”

“…In the case where the object is emerging or sinking, it is no longer in equilibrium, so the force analysis of the object from the perspective of balance force is no longer effective. At the time, we need to turn our attention to the Archimedes principle, which asserts that the buoyant force of an object immersed in a liquid is equal to the gravity of the displaced liquid (Kim & Paik, 2021;Lima & Monteiro, 2013;Minogue & Borland, 2016;Young & Meredith, 2017). Imaging without the object, the same immersed space will be occupied by the same volume of liquid, the weight of those liquid is supported by other parts of the liquid.…”

The Law of Buoyancy Force

“…An object does has float on fluid; why? This floating is caused by the buoyancy force [1,2,3]. The buoyancy force is upward push to it.…”

A short note on the buoyant force in nonuniform gravitational fields

“…where p = p (r) and ρ = ρ (r) are pressure and mass density nonuniform scalar fields and g = g (r) is a nonuniform gravitational vector field; the buoyant force is compared to the weight per volume element of the displaced fluid d W f ; vectors B and W f are in opposite direction to each other. Equation (1) has a corresponding integral form in equation (7) of Lima and Monteiro [1]. From equation (1) the pressure field * Correspondence email address: pfnali@alice.it plays the role of an effective scalar potential associated with the buoyant force.…”