{"id":34593,"date":"2021-03-25T13:00:48","date_gmt":"2021-03-25T13:00:48","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34593"},"modified":"2025-09-19T10:01:20","modified_gmt":"2025-09-19T10:01:20","slug":"principium-pascalis","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/principium-pascalis\/","title":{"rendered":"Principium Pascalis"},"content":{"rendered":"<p><center><\/p>\n<h1>Principium Pascalis<\/h1>\n<p><em><strong>Summarium:<\/strong><br \/>\nIn hac lectione explicabitur Principium Pascalis, quod affirmat pressionem in liquido incompressibili applicatam aequaliter distribui. Huius consequentiae tractabuntur, sicut aequum planum in vasis et relatio inter volumina dislocata. Praeterea ostendentur applicationes in machinis hydraulicis atque solvuntur exempla practica ut aequatio terrarum, differentiae nivelli in liquidis diversae densitatis, ac operatio elevatoriae hydraulicae.<br \/>\n<\/em><br \/>\n<strong>Proposita Discendi:<\/strong><\/p>\n<ol style=\"text-align:left;\">\n<li><strong>Intelligere<\/strong> Principium Pascalis eiusque applicationem in liquidis incompressibilibus.<\/li>\n<li><strong>Analyzare<\/strong> consequentias principii, ut distributionem uniformem pressionis et habitum nivelli liquidi.<\/li>\n<li><strong>Applicare<\/strong> Principium Pascalis in rebus practicis, ut in functione machinarum hydraulicorum.<\/li>\n<li><strong>Solvere<\/strong> problemata practica de aequatione terrarum et differentiis nivelli in liquidis diversae densitatis.<\/li>\n<li><strong>Explicare<\/strong> usum Barometri Torricelliani ad metiendam pressionem atmosphaericam atque functionem elevatoriis hydraulicis.<\/li>\n<\/ol>\n<p><strong>INDEX CONTENTORUM<\/strong><br \/>\n<a href=\"#1\">Transmissio virium in liquidis<\/a><br \/>\n<a href=\"#2\">Consequentiae Principii Pascalis<\/a><br \/>\n<a href=\"#3\">Principium Pascalis in Machinis Hydraulicis Applicatum<\/a><br \/>\n<a href=\"#4\">Exempla Applicationis<\/a>\n<\/p>\n<p><\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/9IAFRXx0Cns\" 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>Transmissio virium in liquidis<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=9IAFRXx0Cns&amp;t=84s\" target=\"_blank\" rel=\"noopener\"><strong>Principium Pascalis applicatur cum agitur de liquidis incompressibilibus<\/strong><\/a>. Particulae in hoc genere substantiarum inter se vires exercent quae non servant positionem, sed distantiam relativam mediocrem inter eas. Nisi hoc fieret, particulae mutarent distantiam relativam mediocrem in quibusdam regionibus, voluminis totius alterationem afferentes, quod indicaret nos agere cum liquido compressibili. Plurimi liquidi sunt, re vera, valde incompressibiles, ideoque, cum vis in regione quadam applicatur, haec per totum fluidum integre transmittitur.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Consequentiae Principii Pascalis<\/h2>\n<h3>Nivellus idem est ubique<\/h3>\n<p style=\"text-align: justify;\">Exemplum manifestum huius rei ostenditur in figura sequenti. Si haec repletur Liquido, nivellus eodem modo ascendet per omnes locos praesto, forma conductuum non obstante.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-SD1TKOVRBrw\/YF0upu1TqEI\/AAAAAAAAEtc\/3r34Qw4kXgwJpbXqylLBaKJX45tFH1S9gCLcBGAsYHQ\/s763\/principio%2Bde%2Bpascal%2B-%2Bnivel%2Bde%2Bliquido.png\" alt=\"Principium Pascalis\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-SD1TKOVRBrw\/YF0upu1TqEI\/AAAAAAAAEtc\/3r34Qw4kXgwJpbXqylLBaKJX45tFH1S9gCLcBGAsYHQ\/s763\/principio%2Bde%2Bpascal%2B-%2Bnivel%2Bde%2Bliquido.png\" alt=\"Principium Pascalis\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">Hoc accidit quia, ut iam vidimus, pressio est functio altitudinis.<\/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;\">Si differentia altitudinis inter diversas partes liquidi exstaret, tunc necessario esset differentia pressionis inter easdem partes.<\/p>\n<h3>Volumen Dislocatum = Volumen Concessum<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=9IAFRXx0Cns&amp;t=323s\" target=\"_blank\" rel=\"noopener\"><strong>Si pressio in aliquo puncto liquidi applicatur,<\/strong><\/a> hic movebitur servans semper eundem nivellem in omnibus aliis partibus. Volumen concessum <span class=\"katex-eq\" data-katex-display=\"false\">v_1<\/span> aequabit volumen dislocatum <span class=\"katex-eq\" data-katex-display=\"false\">v_2+v_3.<\/span>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-nDStNasYWZQ\/YF0upq_20xI\/AAAAAAAAEtg\/bPPlgi4vpug4i70kHoMpkPsvtRtfbQrVACLcBGAsYHQ\/s767\/principio%2Bde%2Bpascalnivel%2Bde%2Bliquido2.png\" alt=\"Principium Pascalis, volumen concessum aequale volumini dislocato\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-nDStNasYWZQ\/YF0upq_20xI\/AAAAAAAAEtg\/bPPlgi4vpug4i70kHoMpkPsvtRtfbQrVACLcBGAsYHQ\/s767\/principio%2Bde%2Bpascalnivel%2Bde%2Bliquido2.png\" alt=\"Principium Pascalis, volumen concessum aequale volumini dislocato\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300\" \/><\/noscript><br \/>\n<a name=\"3\"><\/a><\/p>\n<h2>Principium Pascalis in Machinis Hydraulicis Applicatum<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=9IAFRXx0Cns&amp;t=426s\" target=\"_blank\" rel=\"noopener\"><strong>Principium Pascalis adhibetur ad constructionem pressarum hydraulicorum.<\/strong><\/a> Evenit enim ut, cum pressio aequaliter distribuitur in omnibus partibus liquidi, tunc valet haec expressio:<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-hpJeg_iRsgw\/YF0uplM2GnI\/AAAAAAAAEtY\/tBztNE2eUJQe2uHlrzgZlh_y0QPLGyCnwCLcBGAsYHQ\/s805\/prensahidr%25C3%25A1ulica.PNG\" alt=\"Principium Pascalis, Elevatorium Hydraulicum\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"200\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-hpJeg_iRsgw\/YF0uplM2GnI\/AAAAAAAAEtY\/tBztNE2eUJQe2uHlrzgZlh_y0QPLGyCnwCLcBGAsYHQ\/s805\/prensahidr%25C3%25A1ulica.PNG\" alt=\"Principium Pascalis, Elevatorium Hydraulicum\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"200\" \/><\/noscript><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P_2 = P_1<\/span>\n<p style=\"text-align: justify;\">Cum autem pressio exprimi possit ut vis per unitatem areae, <span class=\"katex-eq\" data-katex-display=\"false\">P=F\/A<\/span>, tunc habebitur:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{F_2}{A_2} = \\frac{F_1}{A_1}<\/span>\n<p style=\"text-align: justify;\">Hoc significat quod, si vim <span class=\"katex-eq\" data-katex-display=\"false\">F_1<\/span> in pistone 1 applicamus, ex pistone 2 exibit vis <span class=\"katex-eq\" data-katex-display=\"false\">F_2<\/span> huius formae<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F_2 = \\frac{A_2}{A_1} \\cdot F_1<\/span>\n<p style=\"text-align: justify;\">Factor <span class=\"katex-eq\" data-katex-display=\"false\">A_2\/A_1<\/span> est quod vocabimus \u00abCoefficientem amplificationis vel diminutionis virium\u00bb. Amplificabit si maior est quam 1, minuet si inter 0 et 1.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Exempla Applicationis<\/h2>\n<ol>\n<li style=\"text-align: justify;\">Duo homines volunt aequare solum in clivo. Ad hoc sumunt fistulam et eam aqua implent ut postea extremos eius ponant in distantia horizontali 275[cm]. Altitudo nivelli aquae in uno puncto est 110[cm] et in altero 175[cm].<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-qmCq1t6szPU\/YF0uopFj2HI\/AAAAAAAAEtM\/Bo__H3vPJ9YZCms__pgwk-26VxjBbiYmgCLcBGAsYHQ\/s625\/nivel%2Bde%2Bagua.PNG\" alt=\"Principium Pascalis, Nivellus Aquae\" class=\"aligncenter size-full lazyload\" width=\"625\" height=\"313\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-qmCq1t6szPU\/YF0uopFj2HI\/AAAAAAAAEtM\/Bo__H3vPJ9YZCms__pgwk-26VxjBbiYmgCLcBGAsYHQ\/s625\/nivel%2Bde%2Bagua.PNG\" alt=\"Principium Pascalis, Nivellus Aquae\" class=\"aligncenter size-full lazyload\" width=\"625\" height=\"313\" \/><\/noscript>a) Quid est disnivellum soli?\n<p>b) Quantus est angulus inclinationis soli?<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=9IAFRXx0Cns&amp;t=691s\" target=\"_blank\" rel=\"noopener\"><strong>SOLUTIO<\/strong><\/a><\/li>\n<li style=\"text-align: justify;\">Fistula in forma U aquam in suo interiori continet, cum densitate <span class=\"katex-eq\" data-katex-display=\"false\">1000 [kg\/m^3].<\/span> Si in uno extremo fistulae oleum effunditur usque ad altitudinem <span class=\"katex-eq\" data-katex-display=\"false\">20[cm]<\/span>, cum densitate <span class=\"katex-eq\" data-katex-display=\"false\">800[kg\/m^3]<\/span>, quae differentia nivelli fiet inter extremos fistulae?<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-EYBgWw2b6jY\/YF0uoq4c5AI\/AAAAAAAAEtU\/LCAin5GVeSoRDCIgn3widW9kaTwfJwFRACLcBGAsYHQ\/s596\/nivel-agua-aceite.PNG\" alt=\"Principium Pascalis - Mixturae\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-EYBgWw2b6jY\/YF0uoq4c5AI\/AAAAAAAAEtU\/LCAin5GVeSoRDCIgn3widW9kaTwfJwFRACLcBGAsYHQ\/s596\/nivel-agua-aceite.PNG\" alt=\"Principium Pascalis - Mixturae\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300\" \/><\/noscript><a href=\"https:\/\/www.youtube.com\/watch?v=9IAFRXx0Cns&amp;t=867s\" target=\"_blank\" rel=\"noopener\"><strong>SOLUTIO<\/strong><\/a><\/li>\n<li style=\"text-align: justify;\"><strong>Barometrum Torricellianum:<\/strong> Torricellus hoc instrumentum designavit ad mensurandam pressionem atmosphaericam:<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-hB2h_82Yg6A\/YF0uol0V-OI\/AAAAAAAAEtQ\/1w25pez7rj4LE3-tanK4NMo5NBy_0xJQgCLcBGAsYHQ\/s572\/Principio%2Bde%2Bpascal%2B-%2Btorricelli.PNG\" principio=\"\" de=\"\" pascal=\"\" bar=\"\" metro=\"\" torricelli=\"\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300 alt=\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-hB2h_82Yg6A\/YF0uol0V-OI\/AAAAAAAAEtQ\/1w25pez7rj4LE3-tanK4NMo5NBy_0xJQgCLcBGAsYHQ\/s572\/Principio%2Bde%2Bpascal%2B-%2Btorricelli.PNG\" principio=\"\" de=\"\" pascal=\"\" bar=\"\" metro=\"\" torricelli=\"\" class=\"aligncenter size-full lazyload\" width=\"400\" height=\"300 alt=\" \/><\/noscript>a) Si densitas hydrargyri est <span class=\"katex-eq\" data-katex-display=\"false\">13.534,0[kg\/m3]<\/span>, quanta erit altitudo columnae hydrargyri propter pressionem atmosphaericam? Considera <span class=\"katex-eq\" data-katex-display=\"false\">P_{atm}=1,0[atm]=101.325,0[Pa]<\/span>?\n<p>b) Si loco hydrargyri aqua esset, quanti esset columna aquae ad eandem pressionem metiendam?<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=9IAFRXx0Cns&amp;t=1049s\" target=\"_blank\" rel=\"noopener\"><strong>SOLUTIO<\/strong><\/a><\/li>\n<li style=\"text-align: justify;\">Elevatorium hydraulicum duos pistones habet, unum 2[pedes] et alterum 30[pedes] radii. a) Quantum pondus poni oportet in pistone minore si in pistone maiore elevare volumus massam unius toneladae? b) Si volumus ut piston maior elevet massam concreti in altitudine <span class=\"katex-eq\" data-katex-display=\"false\">50[cm]<\/span>, quantam distantiam piston minor percurrere debet?\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=9IAFRXx0Cns&amp;t=1403s\" target=\"_blank\" rel=\"noopener\"><strong>SOLUTIO<\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Principium Pascalis Summarium: In hac lectione explicabitur Principium Pascalis, quod affirmat pressionem in liquido incompressibili applicatam aequaliter distribui. Huius consequentiae tractabuntur, sicut aequum planum in vasis et relatio inter volumina dislocata. Praeterea ostendentur applicationes in machinis hydraulicis atque solvuntur exempla practica ut aequatio terrarum, differentiae nivelli in liquidis diversae densitatis, ac operatio elevatoriae hydraulicae. Proposita [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29196,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1274,1250],"tags":[],"class_list":["post-34593","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Principium Pascalis - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Principium Pascalis statuit quod, cum pressio in liquido incompressibili applicatur, haec aequaliter in omnes directiones transmittitur. 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