Buoyant force in a nonuniform gravitational field

Detalhes bibliográficos
Autor(a) principal: Lima,F.M.S.
Data de Publicação: 2013
Outros Autores: Monteiro,F.F.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300030
Resumo: 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.
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spelling Buoyant force in a nonuniform gravitational fieldhydrostaticsArchimedes' principledivergence theoremWhen 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.Sociedade Brasileira de Física2013-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300030Revista Brasileira de Ensino de Física v.35 n.3 2013reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S1806-11172013000300030info:eu-repo/semantics/openAccessLima,F.M.S.Monteiro,F.F.eng2013-10-31T00:00:00Zoai:scielo:S1806-11172013000300030Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2013-10-31T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Buoyant force in a nonuniform gravitational field
title Buoyant force in a nonuniform gravitational field
spellingShingle Buoyant force in a nonuniform gravitational field
Lima,F.M.S.
hydrostatics
Archimedes' principle
divergence theorem
title_short Buoyant force in a nonuniform gravitational field
title_full Buoyant force in a nonuniform gravitational field
title_fullStr Buoyant force in a nonuniform gravitational field
title_full_unstemmed Buoyant force in a nonuniform gravitational field
title_sort Buoyant force in a nonuniform gravitational field
author Lima,F.M.S.
author_facet Lima,F.M.S.
Monteiro,F.F.
author_role author
author2 Monteiro,F.F.
author2_role author
dc.contributor.author.fl_str_mv Lima,F.M.S.
Monteiro,F.F.
dc.subject.por.fl_str_mv hydrostatics
Archimedes' principle
divergence theorem
topic hydrostatics
Archimedes' principle
divergence theorem
description 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.
publishDate 2013
dc.date.none.fl_str_mv 2013-09-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300030
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dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1806-11172013000300030
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.35 n.3 2013
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
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instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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