{"id":1585,"date":"2015-11-29T12:39:16","date_gmt":"2015-11-29T12:39:16","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1585"},"modified":"2024-06-24T15:55:28","modified_gmt":"2024-06-24T15:55:28","slug":"equacao-da-continuidade-equacao-de-bernoulli","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/mecanica\/hidrodinamica\/equacao-da-continuidade-equacao-de-bernoulli\/","title":{"rendered":"Equa\u00e7\u00e3o da Continuidade \u2013 Equa\u00e7\u00e3o de Bernoulli"},"content":{"rendered":"

Equa\u00e7\u00e3o da Continuidade \u2013 Equa\u00e7\u00e3o de Bernoulli<\/b><\/span><\/span><\/span><\/p>\n

Hidrodin\u00e2mica<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>Hidrodin\u00e2mica<\/b><\/span><\/span><\/span> \"\" estuda o <\/b><\/span><\/span><\/span>comportamento de fluidos <\/b><\/span><\/span><\/span>(l\u00edquidos e gases) em <\/b><\/span><\/span><\/span>movimento<\/b><\/span><\/span><\/span>. Esse <\/b><\/span><\/span><\/span>movimento pode ocorrer de modo que a velocidade do fluido varie<\/b><\/span><\/span><\/span>, como nas <\/b><\/span><\/span><\/span>corredeiras ou<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

cachoeiras, ou permane\u00e7a constante,<\/b><\/span><\/span><\/span> ou seja, em <\/b><\/span><\/span><\/span>cada ponto cada part\u00edcula do fluido tem a mesma velocidade (regime estacion\u00e1rio ou permanente).<\/b><\/span><\/span><\/span><\/p>\n

\"\" \u00a0<\/span>Em termos de <\/b><\/span><\/span><\/span>n\u00edvel m\u00e9dio<\/b><\/span><\/span><\/span> considera-se o <\/b><\/span><\/span><\/span>fluido ideal (incompress\u00edvel, ou seja, em todos os pontos tem sempre a mesma densidade) e n\u00e3o viscoso (atrito interno nulo).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

Equa\u00e7\u00e3o da continuidade<\/b><\/span><\/span><\/span><\/p>\n

Considere <\/b><\/span><\/span><\/span>tr\u00eas peda\u00e7os de tubos com di\u00e2metros diversos e \u00e1reas de se\u00e7\u00e3o transversal S<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>, S<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0e<\/b><\/span><\/span><\/span> <\/b>S<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>\u00a0conectados, e com \u00e1gua escoando atrav\u00e9s deles no sentido de A para B, com velocidades de intensidades V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>, V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0e V<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>, respectivamente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Essa equa\u00e7\u00e3o <\/b><\/span><\/span><\/span>Z = S.v,<\/b><\/span><\/span><\/span> denominada <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o da continuidade<\/b><\/span><\/span><\/span> afirma que a <\/b><\/span><\/span><\/span>velocidade <\/b><\/span><\/span><\/span>com que o l\u00edquido escoa no interior do tubo \u00e9 <\/b><\/span><\/span><\/span>inversamente proporcional \u00e0 \u00e1rea de se\u00e7\u00e3o transversal (S)<\/b><\/span><\/span><\/span> do mesmo, ou seja, <\/b><\/span><\/span><\/span>diminuindo a \u00e1rea, a velocidade (v) com que o l\u00edquido flui aumenta na mesma<\/b><\/span><\/span><\/span> <\/b>propor\u00e7\u00e3o<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Equa\u00e7\u00e3o de Bernoulli<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Considere <\/b><\/span><\/span><\/span>dois peda\u00e7os de tubos com di\u00e2metros diversos e \u00e1reas de se\u00e7\u00e3o transversal S<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e\u00a0 S<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 <\/b><\/span><\/span><\/span>conectados<\/b><\/span><\/span><\/span>, e com <\/b><\/span><\/span><\/span>\u00e1gua escoando atrav\u00e9s deles no sentido de A para B, com velocidades de intensidades V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>, respectivamente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Equa\u00e7\u00e3o deduzida por Bernoulli:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se os<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>tubos estiverem na horizontal<\/b><\/span><\/span><\/span>, as alturas h<\/b><\/span><\/span><\/span>1\u00a0<\/b><\/span><\/span><\/sub><\/span>e h<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0ser\u00e3o iguais<\/b><\/span><\/span><\/span> e a equa\u00e7\u00e3o <\/b><\/span><\/span><\/span>fica\u00a0\u00a0<\/b><\/span><\/span><\/span>P<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0+ d(v<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2 = P<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0+ d.(v<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2.<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0Observe na <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o P + d.v<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2 = constante<\/b><\/span><\/span><\/span> que\u00a0<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>press\u00e3o P \u00e9 inversamente proporcional \u00e0<\/b><\/span><\/span><\/span> <\/b>velocidade v,<\/b><\/span><\/span><\/span> ou seja, <\/b><\/span><\/span><\/span>quanto menor a \u00e1rea, maior a velocidade e menor a press\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

\"\" \u00a0<\/span>Equa\u00e7\u00e3o de Torricelli<\/b><\/span><\/span><\/span> \"\"<\/b><\/span><\/span><\/span>\u00a0A figura ilustra um <\/b><\/span><\/span><\/span>reservat\u00f3rio contendo um fluido de densidade d.<\/b><\/span><\/span><\/span><\/b><\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\"\"<\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

\"\"\u00a0 <\/span>Viscosidade \"\"<\/b><\/span><\/span><\/span> <\/b>\u00e9 <\/b><\/span><\/span><\/span>definida<\/b><\/span><\/span><\/span> como a <\/b><\/span><\/span><\/span>resist\u00eancia que um fluido oferece ao seu pr\u00f3prio<\/b><\/span><\/span><\/span> <\/b>movimento.<\/b><\/span><\/span><\/span> Quanto <\/b><\/span><\/span><\/span>maior<\/b><\/span><\/span><\/span> for a<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span>viscosidade<\/b><\/span><\/span><\/span> do fluido, <\/b><\/span><\/span><\/span>menor ser\u00e1 a sua capacidade de escoar (fluir)<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>maior ser\u00e1 a for\u00e7a de atrito<\/b><\/span><\/span><\/span> entre o <\/b><\/span><\/span><\/span>fluido e as paredes do recipiente<\/b><\/span><\/span><\/span> onde ele est\u00e1 escoando, pois o fluido <\/b><\/span><\/span><\/span>diretamente em<\/b><\/span><\/span><\/span> <\/b>contato como cada placa fica preso \u00e0 superf\u00edcie de contato<\/b><\/span><\/span><\/span>, devido a exist\u00eancia de uma <\/b><\/span><\/span><\/span>for\u00e7a coesiva<\/b><\/span><\/span><\/span> entre as <\/b><\/span><\/span><\/span>mol\u00e9culas do l\u00edquido e da placa.<\/b><\/span><\/span><\/span><\/b><\/p>\n

Assim, na <\/b><\/span><\/span><\/span>figura acima o l\u00edquido B \u00e9 mais viscoso que o l\u00edquido A.<\/b><\/span><\/span><\/span> \u00a0<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Aplica\u00e7\u00f5es da equa\u00e7\u00e3o de Bernoulli<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00e3o comentada<\/a><\/span><\/h3>\n

 <\/p>\n

Clique aqui para ver sobre o tema!<\/a><\/p>\n

Confira as v\u00eddeo aulas!<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Equa\u00e7\u00e3o da Continuidade \u2013 Equa\u00e7\u00e3o de Bernoulli Hidrodin\u00e2mica \u00a0Hidrodin\u00e2mica estuda o comportamento de fluidos (l\u00edquidos e gases) em movimento. Esse movimento pode ocorrer de modo que a velocidade do fluido varie, como nas corredeiras ou cachoeiras, ou permane\u00e7a constante, ou seja, em cada ponto cada part\u00edcula do fluido tem a mesma velocidade (regime estacion\u00e1rio ou permanente). \u00a0Em termos de n\u00edvel<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1582,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-1585","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=1585"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1585\/revisions"}],"predecessor-version":[{"id":9740,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1585\/revisions\/9740"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1582"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=1585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}