{"id":34580,"date":"2021-03-22T13:00:40","date_gmt":"2021-03-22T13:00:40","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34580"},"modified":"2025-09-19T09:43:42","modified_gmt":"2025-09-19T09:43:42","slug":"pressio-fluidi-in-quiete","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/pressio-fluidi-in-quiete\/","title":{"rendered":"Pressio Fluidi in Quiete"},"content":{"rendered":"<p><center><\/p>\n<h1>Pressio Fluidorum<\/h1>\n<p style=\"text-align:center;\"><em><strong>Summarium:<\/strong><br \/>\nHaec classis in notione pressionis fluidorum in quiete consistet atque quomodo illa cum profunditate variatur. Discemus pressionem in puncto intra fluidum directe pendere ab eius densitate, gravitate et profunditate<br \/>\n<\/em><br \/>\n<strong>Proposita Discendi:<\/strong><br \/>\nAd finem classis discipulus poterit<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>Intellegere<\/strong> relationem inter pressionem in fluido et variabiles ut densitatem, gravitatem et profunditatem.<\/li>\n<li><strong>Applicare<\/strong> formulam P = \u03c1gh ad pressionem in fluidis in quiete computandam.<\/li>\n<li><strong>Explicare<\/strong> differentiam inter pressionem manometricam, atmosphaericam et absolutam.<\/li>\n<\/ol>\n<p><strong>INDEX CONTENTORUM<\/strong><br \/>\n<a href=\"#1\">Pressio fluidorum in quiete<\/a><br \/>\n<a href=\"#1\">Pressio Relativa<\/a><br \/>\n<a href=\"#1\">Exempla practica<\/a>\n<\/p>\n<p><\/center><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/Qt4mdRDEc44\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Pressio fluidorum in quiete<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Qt4mdRDEc44&amp;t=105s\" target=\"_blank\" rel=\"noopener\"><strong>Quid scimus de pressione fluidi in quiete?<\/strong><\/a> Scimus quod si illud in quodam vase ponimus, cum relatio <span class=\"katex-eq\" data-katex-display=\"false\">P=F\/A,<\/span> valeat, et propter pondus eius, in omni puncto interioris erit pressio secundum profunditatem.<\/p>\n<p style=\"text-align: justify;\"><strong>Pressio fluidi in quiete<\/strong> in quodam puncto interioris directe proportionalis est profunditati eius. Id scimus per expressionem:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P = \\rho g h<\/span>\n<p style=\"text-align: justify;\">Ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\rho<\/span> est densitas fluidi, <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> acceleratio gravitatis et <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> profunditas.<\/p>\n<p>   <center><\/center><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-M64DeuX1K_8\/YGDR2Dr6MLI\/AAAAAAAAEvU\/dsWvpC_qUaUqXYxIY_kdFz_RegsAQ8jNQCLcBGAsYHQ\/s0\/presionProfundidad.PNG\" alt=\"Pressio Profunditas\" class=\"alignnone size-full lazyload\" width=\"360\" height=\"380\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-M64DeuX1K_8\/YGDR2Dr6MLI\/AAAAAAAAEvU\/dsWvpC_qUaUqXYxIY_kdFz_RegsAQ8jNQCLcBGAsYHQ\/s0\/presionProfundidad.PNG\" alt=\"Pressio Profunditas\" class=\"alignnone size-full lazyload\" width=\"360\" height=\"380\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">Hoc demonstrare possumus immergendo cylindrum imaginarium cuius area basis <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> est, horizontaliter positum (simplicitatis causa) in quodam puncto profunditatis <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> intra fluidum.<\/p>\n<p>   <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-4xXHikobfLg\/YGDR2CIDEWI\/AAAAAAAAEvQ\/vMap5iq_jHoL_vHicMEvWiOJbP_CX3pNACLcBGAsYHQ\/s0\/FuerzaProfundidad.PNG\" alt=\"Pressio Profunditas\" class=\"alignnone size-full lazyload\" width=\"364\" height=\"448\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-4xXHikobfLg\/YGDR2CIDEWI\/AAAAAAAAEvQ\/vMap5iq_jHoL_vHicMEvWiOJbP_CX3pNACLcBGAsYHQ\/s0\/FuerzaProfundidad.PNG\" alt=\"Pressio Profunditas\" class=\"alignnone size-full lazyload\" width=\"364\" height=\"448\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">Videbimus discum opprimi pondere fluidi quod superius est atque vi normali inferius, quae aequa et contraria est pondere (quoniam systema in quiete assumimus).<\/p>\n<h4>Deductio formulae pressionis fluidi in quiete: <span class=\"katex-eq\" data-katex-display=\"false\">{P=\\rho g h}<\/span><\/h4>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Qt4mdRDEc44&amp;t=195s\" target=\"_blank\" rel=\"noopener\">Fluidum supra corpus immersum constituit<\/a> alium cylindrum quoque areae basalis <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>, sed altitudinis <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span>, atque consequenter volumen habet.<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">V=A h<\/span>\n<p style=\"text-align: justify;\">Unde inferimus quod<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle A=\\frac{V}{h}<\/span>\n<p style=\"text-align: justify;\">Si fluidum densitatem <span class=\"katex-eq\" data-katex-display=\"false\">\\rho<\/span> habet, tunc massa fluidi quae discum comprimit est <span class=\"katex-eq\" data-katex-display=\"false\">m=\\rho V<\/span>, atque igitur vim ponderis exercet<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F_p=m g = \\rho V g<\/span>\n<p style=\"text-align: justify;\">Et similiter, vis normalis in faciem inferiorem cylindri exercetur eadem magnitudine sed in faciem oppositam.<\/p>\n<p style=\"text-align: justify;\">Cum pondus et vis normalis sint verticales, hae nullam pressionem exercent in latera cylindri.<\/p>\n<p style=\"text-align: justify;\">Si cylindrum satis planum et leve consideramus, tunc pondus eius nihil conferet quod a vi normali compensari debeat, praeterea quivis effectus in latera erit neglegendus respectu reliquorum. Ita vis totalis in corpus erit:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F_{total}=F_p + F_n = 2\\rho V g<\/span>\n<p style=\"text-align: justify;\">Hoc \u00ab+\u00bb in hac vi debetur quod vires versus interiorem superficiei diriguntur.<\/p>\n<p style=\"text-align: justify;\">Hoc modo, pressio in corpus immersum erit:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P = \\frac{F_{total}}{A_{inferior}+A_{superior}}=\\frac{2 \\rho V h}{2A} = \\frac{\\rho V g}{\\frac{V}{h}} = \\rho g h<\/span>\n<p style=\"text-align: justify;\">Ex hoc videmus pressionem quam fluidum (in quiete) exercet eandem esse in omnibus punctis eiusdem profunditatis. Hoc valet tam pro liquidis quam pro gasibus (dum in quiete sint), ita ut si columnam aeris supra nos consideremus, loqui possimus etiam de \u00abpressione atmosphaerica\u00bb.<\/p>\n<p style=\"text-align: justify;\">Pressio atmosphaerica ad planum maris est<\/p>\n<p><p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_{atm} = 1[atm] = 101.325,0 [Pa] = 760 [Torr]=0.981[barr].<\/span>\n<p>Meminisse debemus <span class=\"katex-eq\" data-katex-display=\"false\">1[Pa] = 1[N\/m^2].<\/span>\n<p style=\"text-align: justify;\">Combinando pressionem atmosphaericam cum ea quam fluidum ob proprium pondus exercet habemus <strong>pressionem hydrostaticam<\/strong><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P = P_{atm} + \\rho g h<\/span>\n<p><a name=\"2\"><\/a>  <\/p>\n<h2>Pressio Relativa<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Qt4mdRDEc44&amp;t=590s\" target=\"_blank\" rel=\"noopener\"><strong>Cum pressionem metimur, plerumque id facimus immersi in medio.<\/strong><\/a> Aliquando pressio medii est momenti et alias minus est. Exempli gratia, cum pressionem rotarum vehiculi tui metiris, non cures addere pressionem atmosphaericam quia quod revera refert ad rectum functionem est differentia pressionis inter interiorem rotae et ambientem externum:<\/p>\n<p style=\"text-align: justify;\"><em>Si nimis alta est, plus quam necesse inflatur; si nimis humilis est, deflat.<\/em><\/p>\n<p style=\"text-align: justify;\">Hac de causa varias habemus formas loquendi de pressione.<\/p>\n<h3>Pressio Atmosphaerica<\/h3>\n<p style=\"text-align: justify;\">Iam antea de hac locuti sumus, et est pressio quae propria est medii in quo immersi sumus. Exempli gratia, in Himalaya pressio atmosphaerica potest fieri usque ad 1\/3 pressionis quam ad planum maris habemus. Generaliter repraesentatur per <span class=\"katex-eq\" data-katex-display=\"false\">P_{atm}<\/span> vel <span class=\"katex-eq\" data-katex-display=\"false\">P_{0}.<\/span>\n<h3>Pressio Absoluta<\/h3>\n<p style=\"text-align: justify;\">Cum consideramus pressionem quae ex summa omnium virium in corpus agentium provenit, loquimur de <strong>Pressione Absoluta.<\/strong> Pressio hydrostatica quam antea recensuimus est species pressionis absolutae quia considerat summam pressionum propter pondus liquidi + pressionem a atmosphaera exercitam. Alia ratio exprimendi pressionem absolutam est sicut \u00abpressio relativa ad vacuum\u00bb. Repraesentatur per <span class=\"katex-eq\" data-katex-display=\"false\">P_{abs}.<\/span>\n<h3>Pressio Manometrica et Pressio Vacui<\/h3>\n<p style=\"text-align: justify;\">Cum pressionem rotarum vehiculi metimur, et rota et instrumentum mensurandi a circumiecta atmosphaera comprimuntur. Hac de causa, quod instrumentum re vera metitur est differentia pressionis inter interiorem et exteriorem. Haec pressio \u00abpressio manometrica\u00bb appellatur, repraesentatur per <span class=\"katex-eq\" data-katex-display=\"false\">P_{man}<\/span> et relationem satisfacit:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_{man} = P_{abs} - P_{atm}<\/span>\n<p style=\"text-align: justify;\">Pressio quam metimur considerantes solum pondus fluidi est exemplum pressionis manometricae. Si pressio absoluta altior est quam atmosphaerica, metimus pressionem manometricam; sin autem, metimus pressionem vacui <span class=\"katex-eq\" data-katex-display=\"false\">P_{vac}<\/span>, quae similiter definita est:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_{vac} = P_{atm} - P_{abs}<\/span>\n<p style=\"text-align: justify;\">Hoc fit, exempli gratia, cum aerem e siringa extrahis, introitum\/exitum aeris obturas et deinde pistonem retrahis; pressio atmosphaerica pistonem retro comprimere conabitur et pressio in interiori siringae erit, proinde, pressio vacui.<\/p>\n<p><a name=\"3\"><\/a>   <\/p>\n<h2>Exempla practica<\/h2>\n<p style=\"text-align: justify;\">Quidam vir modo piscinam aedificavit 39[pedes] longam, 26[pedes] latam et 5.2[pedes] profundam et haec dubia habet:<\/p>\n<ol style=\"text-align: justify;\">\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=Qt4mdRDEc44&amp;t=814s\" target=\"_blank\" rel=\"noopener\"><strong>Pumpam pro piscina emit,<\/strong><\/a> sed solum cum domum venit cogitavit de inspiciendis specificationibus fabricatoris. Hae dicunt in usu non debere superari pressionem manometricam 0,193[atm]. Potestne pompam in fundo piscinae suae instituere?<\/li>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=Qt4mdRDEc44&amp;t=1101s\" target=\"_blank\" rel=\"noopener\"><strong>Non contentus quod oblitus est<\/strong><\/a> specificationum pompae, hic vir problema auditivum habet. Fit ut tympana eius non possint sustinere vim maiorem quam 10[N]. Si tympana eius diametrum 1[cm] habent, forma fere circulari, poteritne hic vir tranquille in fundo piscinae suae submergi?<\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #0000d0;\"><strong>SOLUTIO:<\/strong><\/p>\n<ol style=\"text-align: justify;\">\n<li style=\"list-style-type: none;\">\n<ol style=\"text-align: justify;\">\n<li>Hoc in casu, pressionem manometricam fundi piscinae determinare possumus ut eam quae sola aqua piscinae exercetur. Ergo ex formula pressionis fluidi in quiete habebimus:\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_{man} = \\rho g h<\/span>\n<p>Sumendo densitatem aquae <span class=\"katex-eq\" data-katex-display=\"false\">\\rho=997[kg\/m^3],<\/span>, profunditatem in metra conversam <span class=\"katex-eq\" data-katex-display=\"false\">h=5.2[pes] = 5.2\\cdot 0.3048[m]<\/span> et accelerationem gravitatis <span class=\"katex-eq\" data-katex-display=\"false\">g=9.81[m\/s^2],<\/span> habetur quod pressio manometrica in fundo piscinae erit<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_{man} =997[kg\/m^3]\\cdot 9.81[m\/s^2] \\cdot5.2\\cdot 0.3048[m] \\approx 15.501,81[Pa]<\/span>\n<p>Sed <span class=\"katex-eq\" data-katex-display=\"false\">1[atm] = 101.325[Pa]<\/span>, ita ut<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P_{man} \\approx \\frac{15.501,81}{101.325}[atm]\\approx 0.1523[atm]<\/span>\n<p>Itaque sic. Cum pressio manometrica fundi piscinae infra <span class=\"katex-eq\" data-katex-display=\"false\">0,193[atm]<\/span> sit quam fabricator indicavit ut limitem pro bono functione pompae, haec recte operabitur et vir pecuniam suam non perdidit.<\/li>\n<li>Ex parte priore iam calculavimus pressionem manometricam in fundo piscinae, sed nunc pressionem totalem necesse est. Nullum problema in hoc, sufficit meminisse quod:<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_{total} = P_{man} + P_{atm}<\/span>\n<p><span>et utramque iam habemus. Ex hoc consequitur quod<\/span><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_{total} \\approx 15.501,81[Pa] + 101.325[Pa] = 116.286,81[Pa]<\/span>\n<p><span>Nunc necesse est cognoscere aream tympani huius boni viri. Cum tympanum fere circulare sit, habetur:<\/span><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle A = \\pi r^2 = \\pi \\left(\\frac{d}{2}\\right)^2 = \\frac{\\pi d^2}{4}<\/span>\n<p><span>Hic expresi aream circuli ut functionem diametri <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span>, quae est <span class=\"katex-eq\" data-katex-display=\"false\">1[cm]<\/span>. Itaque:<\/span><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle A \\approx \\frac{3.14 \\cdot 1[cm^2]}{4} = \\frac{3.14 \\left[\\frac{m}{100}\\right]^2}{4} = \\frac{3.14}{4\\cdot 10.000}[m^2]=0.785\\cdot 10^{-4}[m^2]<\/span>\n<p><span>Denique, cum <span class=\"katex-eq\" data-katex-display=\"false\">P=F\/A<\/span>, vis totalis a pressione in fundo piscinae super tympanum huius viri applicata erit<\/span><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F=PA\\approx 116.826,81[Pa] \\cdot 0.785\\cdot 10^{-4}[m^2] \\approx 9.17[N]<\/span>\n<p><span>Cum non superet <span class=\"katex-eq\" data-katex-display=\"false\">10[N]<\/span>, vix potest ille vir sine difficultatibus in fundo piscinae submergi. Quantopere felix est hic vir.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pressio Fluidorum Summarium: Haec classis in notione pressionis fluidorum in quiete consistet atque quomodo illa cum profunditate variatur. Discemus pressionem in puncto intra fluidum directe pendere ab eius densitate, gravitate et profunditate Proposita Discendi: Ad finem classis discipulus poterit Intellegere relationem inter pressionem in fluido et variabiles ut densitatem, gravitatem et profunditatem. Applicare formulam P [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29154,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":3,"footnotes":""},"categories":[1274,1250],"tags":[],"citadela-post-location":[],"class_list":["post-34580","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanica-fluidorum","category-physica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pressio Fluidi in Quiete - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Pressio fluidi in quiete cum profunditate augetur et pendet a densitate eius atque gravitate. 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