Buoyant force in a nonuniform gravitational field
Autor(a) principal: | |
---|---|
Data de Publicação: | 2013 |
Outros Autores: | |
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. |
id |
SBF-1_de013785b83d9e6fd4746e96b7c10cf6 |
---|---|
oai_identifier_str |
oai:scielo:S1806-11172013000300030 |
network_acronym_str |
SBF-1 |
network_name_str |
Revista Brasileira de Ensino de Física (Online) |
repository_id_str |
|
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 |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300030 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000300030 |
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 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
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) instacron:SBF |
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 |
_version_ |
1752122421865873408 |