🕷️ Crawler Inspector

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Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 152 (from laksa165)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa152.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://en.wikipedia.org/wiki/Hydrostatics\')), getAhrefsUnparsedNoserviceFromURL(\'https://en.wikipedia.org/wiki/Hydrostatics\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/en.wikipedia.org\/wiki\/Hydrostatics","crawl_time":1773156921,"first_indexed_time":1427733534,"http_code":200,"src_unparsed":"org,wikipedia!en,\/wiki\/Hydrostatics s443","src_root_hash":"17790707453426894952","history_drop_reason":null,"meta_title":"Hydrostatics - Wikipedia","meta_descriptions":[],"attrs_boilerpipe_text":"From Wikipedia, the free encyclopedia\nTable of Hydraulics and Hydrostatics, from the 1728\nCyclopædia\nHydrostatics\nis the branch of\nfluid mechanics\nthat studies\nfluids\nat\nhydrostatic equilibrium\n[\n1\n]\nand \"the pressure in a fluid or exerted by a fluid on an immersed body\".\n[\n2\n]\nThe word \"hydrostatics\" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether\ncompressible\nor\nincompressible\n. It encompasses the study of the conditions under which fluids are at rest in\nstable equilibrium\n. It is opposed to\nfluid dynamics\n, the study of fluids in motion.\nHydrostatics is fundamental to\nhydraulics\n, the\nengineering\nof equipment for storing, transporting and using fluids.  It is also relevant to\ngeophysics\nand\nastrophysics\n(for example, in understanding\nplate tectonics\nand the anomalies of the\nEarth's gravitational field\n), to\nmeteorology\n, to\nmedicine\n(in the context of\nblood pressure\n), and many other fields.\nHydrostatics offers physical explanations for many phenomena of everyday life, such as why\natmospheric pressure\nchanges with\naltitude\n, why wood and oil float on water, and why the surface of still water is always\nlevel\naccording to the\ncurvature of the earth\n.\nSome principles of hydrostatics have been known in an empirical and intuitive sense since antiquity,  by the builders of boats,\ncisterns\n,\naqueducts\nand\nfountains\n.\nArchimedes\nis credited with the discovery of\nArchimedes' Principle\n, which relates the\nbuoyancy\nforce on an object that is submerged in a fluid to the weight of fluid displaced by the object. The\nRoman\nengineer\nVitruvius\nwarned readers about\nlead\npipes bursting under hydrostatic pressure.\n[\n3\n]\nThe concept of pressure and the way it is transmitted by fluids was formulated by the\nFrench\nmathematician\nand\nphilosopher\nBlaise Pascal\nin 1647.\n[\ncitation needed\n]\nHydrostatics in ancient Greece and Rome\n[\nedit\n]\nThe \"fair cup\" or\nPythagorean cup\n, which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool.\n[\ncitation needed\n]\nThe cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied.\nHeron's fountain\nis a device invented by\nHeron of Alexandria\nthat consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several\ncannula\n(a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir.\n[\ncitation needed\n]\nPascal's contribution in hydrostatics\n[\nedit\n]\nPascal made contributions to developments in both hydrostatics and hydrodynamics.\nPascal's law\nis a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed.\nLiquids (fluids with free surfaces)\n[\nedit\n]\nLiquids can have\nfree surfaces\nat which they interface with gases, or with a\nvacuum\n. In general, the lack of the ability to sustain a\nshear stress\nentails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from\nsurface tension\n.\nWhen liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales,\nsurface tension\neffects become important leading to the formation of a\nmeniscus\nthrough\ncapillary action\n. This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in\nplant\nxylem\n, the\ntranspirational pull\n.\nWithout surface tension,\ndrops\nwould not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid.\nCommunicating vessels\n – Set of internally connected containers containing a homogeneous fluid\nD-DIA\n – Apparatus used for high pressure and high temperature deformation experiments\nHydrostatic pressure\n – Physical quantity\nHydrostatic test\n – Non-destructive test of pressure vessels\nTriaxial shear test\n – Stress test with different levels of stress in each perpendicular direction\n^\n\"Fluid Mechanics\/Fluid Statics\/Fundamentals of Fluid Statics - Wikibooks, open books for an open world\"\n.\nen.wikibooks.org\n. Retrieved\n2021-04-01\n.\n^\n\"Hydrostatics\"\n.\nMerriam-Webster\n. Retrieved\n11 September\n2018\n.\n^\nMarcus Vitruvius Pollio (ca. 15 BCE),\n\"The Ten Books of Architecture\"\n, Book VIII, Chapter 6.  At the University of Chicago's Penelope site. Accessed on 2013-02-25.\nBatchelor, George K. (1967).\nAn Introduction to Fluid Dynamics\n. Cambridge University Press.\nISBN\n \n0-521-66396-2\n.\nFalkovich, Gregory (2011).\nFluid Mechanics (A short course for physicists)\n. Cambridge University Press.\nISBN\n \n978-1-107-00575-4\n.\nKundu, Pijush K.; Cohen, Ira M. (2008).\nFluid Mechanics\n(4th rev. ed.). Academic Press.\nISBN\n \n978-0-12-373735-9\n.\nCurrie, I. G. (1974).\nFundamental Mechanics of Fluids\n. McGraw-Hill.\nISBN\n \n0-07-015000-1\n.\nMassey, B.; Ward-Smith, J. (2005).\nMechanics of Fluids\n(8th ed.). Taylor & Francis.\nISBN\n \n978-0-415-36206-1\n.\nWhite, Frank M. (2003).\nFluid Mechanics\n. McGraw–Hill.\nISBN\n \n0-07-240217-2\n.\nThe Flow of Dry Water - The Feynman Lectures on Physics","attrs_markdown":"[Jump to content](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#bodyContent)\n\nMain menu\n\nMain menu\n\nmove to sidebar\n\nhide\n\nNavigation\n\n- [Main page](https:\/\/en.wikipedia.org\/wiki\/Main_Page \"Visit the main page [z]\")\n- [Contents](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contents \"Guides to browsing Wikipedia\")\n- [Current events](https:\/\/en.wikipedia.org\/wiki\/Portal:Current_events \"Articles related to current events\")\n- [Random article](https:\/\/en.wikipedia.org\/wiki\/Special:Random \"Visit a randomly selected article [x]\")\n- [About Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:About \"Learn about Wikipedia and how it works\")\n- [Contact us](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contact_us \"How to contact Wikipedia\")\n\nContribute\n\n- [Help](https:\/\/en.wikipedia.org\/wiki\/Help:Contents \"Guidance on how to use and edit Wikipedia\")\n- [Learn to edit](https:\/\/en.wikipedia.org\/wiki\/Help:Introduction \"Learn how to edit Wikipedia\")\n- [Community portal](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Community_portal \"The hub for editors\")\n- [Recent changes](https:\/\/en.wikipedia.org\/wiki\/Special:RecentChanges \"A list of recent changes to Wikipedia [r]\")\n- [Upload file](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:File_upload_wizard \"Add images or other media for use on Wikipedia\")\n- [Special pages](https:\/\/en.wikipedia.org\/wiki\/Special:SpecialPages \"A list of all special pages [q]\")\n\n[![](https:\/\/en.wikipedia.org\/static\/images\/icons\/enwiki-25.svg) ![Wikipedia](https:\/\/en.wikipedia.org\/static\/images\/mobile\/copyright\/wikipedia-wordmark-en-25.svg) ![The Free Encyclopedia](https:\/\/en.wikipedia.org\/static\/images\/mobile\/copyright\/wikipedia-tagline-en-25.svg)](https:\/\/en.wikipedia.org\/wiki\/Main_Page)\n\n[Search](https:\/\/en.wikipedia.org\/wiki\/Special:Search \"Search Wikipedia [f]\")\n\nAppearance\n\n- [Donate](https:\/\/donate.wikimedia.org\/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en)\n- [Create account](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:CreateAccount&returnto=Hydrostatics \"You are encouraged to create an account and log in; however, it is not mandatory\")\n- [Log in](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:UserLogin&returnto=Hydrostatics \"You're encouraged to log in; however, it's not mandatory. [o]\")\n\nPersonal tools\n\n- [Donate](https:\/\/donate.wikimedia.org\/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en)\n- [Create account](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:CreateAccount&returnto=Hydrostatics \"You are encouraged to create an account and log in; however, it is not mandatory\")\n- [Log in](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:UserLogin&returnto=Hydrostatics \"You're encouraged to log in; however, it's not mandatory. [o]\")\n\n## Contents\nmove to sidebar\n\nhide\n\n- [(Top)](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics)\n- [1 History](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#History)\n- [2 Hydrostatics in ancient Greece and Rome](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Hydrostatics_in_ancient_Greece_and_Rome)\n  Toggle Hydrostatics in ancient Greece and Rome subsection\n  - [2\\.1 Pythagorean Cup](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Pythagorean_Cup)\n  - [2\\.2 Heron's fountain](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Heron's_fountain)\n- [3 Pascal's contribution in hydrostatics](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Pascal's_contribution_in_hydrostatics)\n- [4 Liquids (fluids with free surfaces)](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Liquids_\\(fluids_with_free_surfaces\\))\n  Toggle Liquids (fluids with free surfaces) subsection\n  - [4\\.1 Capillary action](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Capillary_action)\n  - [4\\.2 Hanging drops](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Hanging_drops)\n- [5 See also](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#See_also)\n- [6 References](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#References)\n- [7 Further reading](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#Further_reading)\n- [8 External links](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#External_links)\n\nToggle the table of contents\n\n# Hydrostatics\n65 languages\n\n- [Alemannisch](https:\/\/als.wikipedia.org\/wiki\/Hydrostatik \"Hydrostatik – Alemannic\")\n- [العربية](https:\/\/ar.wikipedia.org\/wiki\/%D8%B3%D9%83%D9%88%D9%86%D9%8A%D8%A7%D8%AA_%D8%A7%D9%84%D9%85%D9%88%D8%A7%D8%A6%D8%B9 \"سكونيات الموائع – Arabic\")\n- [Asturianu](https:\/\/ast.wikipedia.org\/wiki\/Hidrost%C3%A1tica \"Hidrostática – Asturian\")\n- [Azərbaycanca](https:\/\/az.wikipedia.org\/wiki\/Hidrostatika \"Hidrostatika – Azerbaijani\")\n- [Беларуская](https:\/\/be.wikipedia.org\/wiki\/%D0%93%D1%96%D0%B4%D1%80%D0%B0%D1%81%D1%82%D0%B0%D1%82%D1%8B%D0%BA%D0%B0 \"Гідрастатыка – Belarusian\")\n- [Български](https:\/\/bg.wikipedia.org\/wiki\/%D0%A5%D0%B8%D0%B4%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 \"Хидростатика – Bulgarian\")\n- [বাংলা](https:\/\/bn.wikipedia.org\/wiki\/%E0%A6%89%E0%A6%A6%E0%A6%B8%E0%A7%8D%E0%A6%A5%E0%A6%BF%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8 \"উদস্থিতিবিজ্ঞান – Bangla\")\n- [Bosanski](https:\/\/bs.wikipedia.org\/wiki\/Statika_fluida \"Statika fluida – Bosnian\")\n- [Català](https:\/\/ca.wikipedia.org\/wiki\/Hidroest%C3%A0tica \"Hidroestàtica – Catalan\")\n- [Čeština](https:\/\/cs.wikipedia.org\/wiki\/Hydrostatika \"Hydrostatika – Czech\")\n- [Чӑвашла](https:\/\/cv.wikipedia.org\/wiki\/%D0%93%D0%B8%D0%B4%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 \"Гидростатика – Chuvash\")\n- [Deutsch](https:\/\/de.wikipedia.org\/wiki\/Hydrostatik \"Hydrostatik – German\")\n- [Ελληνικά](https:\/\/el.wikipedia.org\/wiki\/%CE%A5%CE%B4%CF%81%CE%BF%CF%83%CF%84%CE%B1%CF%84%CE%B9%CE%BA%CE%AE \"Υδροστατική – Greek\")\n- [Esperanto](https:\/\/eo.wikipedia.org\/wiki\/Hidrostatiko \"Hidrostatiko – Esperanto\")\n- [Español](https:\/\/es.wikipedia.org\/wiki\/Hidrost%C3%A1tica \"Hidrostática – Spanish\")\n- [Eesti](https:\/\/et.wikipedia.org\/wiki\/H%C3%BCdrostaatika \"Hüdrostaatika – Estonian\")\n- [Euskara](https:\/\/eu.wikipedia.org\/wiki\/Hidrostatika \"Hidrostatika – Basque\")\n- [فارسی](https:\/\/fa.wikipedia.org\/wiki\/%D8%A7%D8%B3%D8%AA%D8%A7%D8%AA%DB%8C%DA%A9_%D8%B3%DB%8C%D8%A7%D9%84%D8%A7%D8%AA \"استاتیک سیالات – Persian\")\n- [Suomi](https:\/\/fi.wikipedia.org\/wiki\/Hydrostatiikka \"Hydrostatiikka – Finnish\")\n- [Français](https:\/\/fr.wikipedia.org\/wiki\/Hydrostatique \"Hydrostatique – French\")\n- [Gàidhlig](https:\/\/gd.wikipedia.org\/wiki\/Sgoil-uisge \"Sgoil-uisge – Scottish Gaelic\")\n- [Galego](https:\/\/gl.wikipedia.org\/wiki\/Hidrost%C3%A1tica \"Hidrostática – Galician\")\n- [עברית](https:\/\/he.wikipedia.org\/wiki\/%D7%94%D7%99%D7%93%D7%A8%D7%95%D7%A1%D7%98%D7%98%D7%99%D7%A7%D7%94 \"הידרוסטטיקה – Hebrew\")\n- [हिन्दी](https:\/\/hi.wikipedia.org\/wiki\/%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%B5%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A5%88%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80 \"द्रवस्थैतिकी – Hindi\")\n- [Hrvatski](https:\/\/hr.wikipedia.org\/wiki\/Hidrostati%C4%8Dki_tlak \"Hidrostatički tlak – Croatian\")\n- [Magyar](https:\/\/hu.wikipedia.org\/wiki\/Hidrosztatika \"Hidrosztatika – Hungarian\")\n- [Հայերեն](https:\/\/hy.wikipedia.org\/wiki\/%D5%80%D5%AB%D5%A4%D6%80%D5%B8%D5%BD%D5%BF%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1 \"Հիդրոստատիկա – Armenian\")\n- [Bahasa Indonesia](https:\/\/id.wikipedia.org\/wiki\/Hidrostatika \"Hidrostatika – Indonesian\")\n- [Ido](https:\/\/io.wikipedia.org\/wiki\/Hidrostatiko \"Hidrostatiko – Ido\")\n- [Italiano](https:\/\/it.wikipedia.org\/wiki\/Fluidostatica \"Fluidostatica – Italian\")\n- [日本語](https:\/\/ja.wikipedia.org\/wiki\/%E6%B5%81%E4%BD%93%E9%9D%99%E5%8A%9B%E5%AD%A6 \"流体静力学 – Japanese\")\n- [Jawa](https:\/\/jv.wikipedia.org\/wiki\/Hidrostatika \"Hidrostatika – Javanese\")\n- [Қазақша](https:\/\/kk.wikipedia.org\/wiki\/%D0%93%D0%B8%D0%B4%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 \"Гидростатика – Kazakh\")\n- [ភាសាខ្មែរ](https:\/\/km.wikipedia.org\/wiki\/%E1%9E%A2%E1%9F%8A%E1%9E%B8%E1%9E%8A%E1%9F%92%E1%9E%9A%E1%9E%BC%E1%9E%9F%E1%9F%92%E1%9E%8F%E1%9E%B6%E1%9E%91%E1%9E%B7%E1%9E%85 \"អ៊ីដ្រូស្តាទិច – Khmer\")\n- [한국어](https:\/\/ko.wikipedia.org\/wiki\/%EC%9C%A0%EC%B2%B4_%EC%A0%95%EC%97%AD%ED%95%99 \"유체 정역학 – Korean\")\n- [Кыргызча](https:\/\/ky.wikipedia.org\/wiki\/%D0%93%D0%B8%D0%B4%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 \"Гидростатика – Kyrgyz\")\n- [Lietuvių](https:\/\/lt.wikipedia.org\/wiki\/Hidrostatika \"Hidrostatika – Lithuanian\")\n- [Македонски](https:\/\/mk.wikipedia.org\/wiki\/%D0%A5%D0%B8%D0%B4%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 \"Хидростатика – Macedonian\")\n- [Bahasa Melayu](https:\/\/ms.wikipedia.org\/wiki\/Statik_bendalir \"Statik bendalir – Malay\")\n- [Nederlands](https:\/\/nl.wikipedia.org\/wiki\/Hydrostatica \"Hydrostatica – Dutch\")\n- [Norsk nynorsk](https:\/\/nn.wikipedia.org\/wiki\/Hydrostatikk \"Hydrostatikk – Norwegian Nynorsk\")\n- [Norsk bokmål](https:\/\/no.wikipedia.org\/wiki\/Hydrostatikk \"Hydrostatikk – Norwegian Bokmål\")\n- [Polski](https:\/\/pl.wikipedia.org\/wiki\/Hydrostatyka \"Hydrostatyka – Polish\")\n- [Piemontèis](https:\/\/pms.wikipedia.org\/wiki\/Idrost%C3%A0tica \"Idrostàtica – Piedmontese\")\n- [Português](https:\/\/pt.wikipedia.org\/wiki\/Hidrost%C3%A1tica \"Hidrostática – Portuguese\")\n- [Română](https:\/\/ro.wikipedia.org\/wiki\/Hidrostatic%C4%83 \"Hidrostatică – Romanian\")\n- [Русский](https:\/\/ru.wikipedia.org\/wiki\/%D0%93%D0%B8%D0%B4%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 \"Гидростатика – Russian\")\n- [Srpskohrvatski \/ српскохрватски](https:\/\/sh.wikipedia.org\/wiki\/Statika_fluida \"Statika fluida – Serbo-Croatian\")\n- [සිංහල](https:\/\/si.wikipedia.org\/wiki\/%E0%B6%AD%E0%B6%BB%E0%B6%BD_%E0%B7%83%E0%B7%8A%E0%B6%AE%E0%B7%92%E0%B6%AD%E0%B7%92%E0%B6%9A%E0%B6%BA \"තරල ස්ථිතිකය – Sinhala\")\n- [Simple English](https:\/\/simple.wikipedia.org\/wiki\/Fluid_statics \"Fluid statics – Simple English\")\n- [Slovenčina](https:\/\/sk.wikipedia.org\/wiki\/Hydrostatika \"Hydrostatika – Slovak\")\n- [Slovenščina](https:\/\/sl.wikipedia.org\/wiki\/Hidrostatika \"Hidrostatika – Slovenian\")\n- [Српски \/ srpski](https:\/\/sr.wikipedia.org\/wiki\/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D1%84%D0%BB%D1%83%D0%B8%D0%B4%D0%B0 \"Статика флуида – Serbian\")\n- [Svenska](https:\/\/sv.wikipedia.org\/wiki\/Hydrostatik \"Hydrostatik – Swedish\")\n- [தமிழ்](https:\/\/ta.wikipedia.org\/wiki\/%E0%AE%AA%E0%AE%BE%E0%AE%AF%E0%AF%8D%E0%AE%AE_%E0%AE%A8%E0%AE%BF%E0%AE%B2%E0%AF%88%E0%AE%AF%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D \"பாய்ம நிலையியல் – Tamil\")\n- [ไทย](https:\/\/th.wikipedia.org\/wiki\/%E0%B8%AA%E0%B8%96%E0%B8%B4%E0%B8%95%E0%B8%A2%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%84%E0%B8%AB%E0%B8%A5 \"สถิตยศาสตร์ของไหล – Thai\")\n- [Türkçe](https:\/\/tr.wikipedia.org\/wiki\/Hidrostatik \"Hidrostatik – Turkish\")\n- [Українська](https:\/\/uk.wikipedia.org\/wiki\/%D0%93%D1%96%D0%B4%D1%80%D0%BE%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%BA%D0%B0 \"Гідростатика – Ukrainian\")\n- [Oʻzbekcha \/ ўзбекча](https:\/\/uz.wikipedia.org\/wiki\/Gidrostatika \"Gidrostatika – Uzbek\")\n- [Vèneto](https:\/\/vec.wikipedia.org\/wiki\/Idrost%C3%A0tega \"Idrostàtega – Venetian\")\n- [Tiếng Việt](https:\/\/vi.wikipedia.org\/wiki\/Th%E1%BB%A7y_t%C4%A9nh_h%E1%BB%8Dc \"Thủy tĩnh học – Vietnamese\")\n- 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[Wikidata item](https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q177807 \"Structured data on this page hosted by Wikidata [g]\")\n\nAppearance\n\nmove to sidebar\n\nhide\n\nFrom Wikipedia, the free encyclopedia\n\nBranch of fluid mechanics that studies fluids at rest\n\nThis article is about the discipline branch. For the concept, see [Hydrostatic equilibrium](https:\/\/en.wikipedia.org\/wiki\/Hydrostatic_equilibrium \"Hydrostatic equilibrium\").\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e4\/Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg\/250px-Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg)](https:\/\/en.wikipedia.org\/wiki\/File:Table_of_Hydraulics_and_Hydrostatics,_Cyclopaedia,_Volume_1.jpg)\n\nTable of Hydraulics and Hydrostatics, from the 1728 *[Cyclopædia](https:\/\/en.wikipedia.org\/wiki\/Cyclop%C3%A6dia,_or_an_Universal_Dictionary_of_Arts_and_Sciences \"Cyclopædia, or an Universal Dictionary of Arts and Sciences\")*\n\n|   |\n|---|\n| Part of a series on |\n| [Continuum mechanics](https:\/\/en.wikipedia.org\/wiki\/Continuum_mechanics \"Continuum mechanics\") |\n| J \\= − D d φ d x {\\\\displaystyle J=-D{\\\\frac {d\\\\varphi }{dx}}} ![{\\\\displaystyle J=-D{\\\\frac {d\\\\varphi }{dx}}}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/1856f88def2056f28ed27c7d31180a6240820ea6)[Fick's laws of diffusion](https:\/\/en.wikipedia.org\/wiki\/Fick%27s_laws_of_diffusion \"Fick's laws of diffusion\") |\n| [Solid mechanics](https:\/\/en.wikipedia.org\/wiki\/Solid_mechanics \"Solid mechanics\") [Deformation](https:\/\/en.wikipedia.org\/wiki\/Deformation_\\(physics\\) \"Deformation (physics)\") [Elasticity](https:\/\/en.wikipedia.org\/wiki\/Elasticity_\\(physics\\) \"Elasticity (physics)\") [linear](https:\/\/en.wikipedia.org\/wiki\/Linear_elasticity \"Linear elasticity\") [Plasticity](https:\/\/en.wikipedia.org\/wiki\/Plasticity_\\(physics\\) \"Plasticity (physics)\") [Hooke's law](https:\/\/en.wikipedia.org\/wiki\/Hooke%27s_law \"Hooke's law\") [Stress](https:\/\/en.wikipedia.org\/wiki\/Stress_\\(mechanics\\) \"Stress (mechanics)\") [Strain](https:\/\/en.wikipedia.org\/wiki\/Strain_\\(mechanics\\) \"Strain (mechanics)\") [Finite strain](https:\/\/en.wikipedia.org\/wiki\/Finite_strain_theory \"Finite strain theory\") [Infinitesimal strain](https:\/\/en.wikipedia.org\/wiki\/Infinitesimal_strain_theory \"Infinitesimal strain theory\") [Compatibility](https:\/\/en.wikipedia.org\/wiki\/Compatibility_\\(mechanics\\) \"Compatibility (mechanics)\") [Bending](https:\/\/en.wikipedia.org\/wiki\/Bending \"Bending\") [Contact mechanics](https:\/\/en.wikipedia.org\/wiki\/Contact_mechanics \"Contact mechanics\") [frictional](https:\/\/en.wikipedia.org\/wiki\/Frictional_contact_mechanics \"Frictional contact mechanics\") [Material failure theory](https:\/\/en.wikipedia.org\/wiki\/Material_failure_theory \"Material failure theory\") [Fracture mechanics](https:\/\/en.wikipedia.org\/wiki\/Fracture_mechanics \"Fracture mechanics\") |\n| [Fluids](https:\/\/en.wikipedia.org\/wiki\/Fluid \"Fluid\") |\n| [Statics]() **·** [Dynamics](https:\/\/en.wikipedia.org\/wiki\/Fluid_dynamics \"Fluid dynamics\") [Archimedes' principle](https:\/\/en.wikipedia.org\/wiki\/Archimedes%27_principle \"Archimedes' principle\") **·** [Bernoulli's principle](https:\/\/en.wikipedia.org\/wiki\/Bernoulli%27s_principle \"Bernoulli's principle\") [Navier–Stokes equations](https:\/\/en.wikipedia.org\/wiki\/Navier%E2%80%93Stokes_equations \"Navier–Stokes equations\") [Poiseuille equation](https:\/\/en.wikipedia.org\/wiki\/Hagen%E2%80%93Poiseuille_equation \"Hagen–Poiseuille equation\") **·** [Pascal's law](https:\/\/en.wikipedia.org\/wiki\/Pascal%27s_law \"Pascal's law\") [Viscosity](https:\/\/en.wikipedia.org\/wiki\/Viscosity \"Viscosity\") ([Newtonian](https:\/\/en.wikipedia.org\/wiki\/Newtonian_fluid \"Newtonian fluid\") **·** [non-Newtonian](https:\/\/en.wikipedia.org\/wiki\/Non-Newtonian_fluid \"Non-Newtonian fluid\")) [Buoyancy](https:\/\/en.wikipedia.org\/wiki\/Buoyancy \"Buoyancy\") **·** [Mixing](https:\/\/en.wikipedia.org\/wiki\/Mixing_\\(process_engineering\\) \"Mixing (process engineering)\") **·** [Pressure](https:\/\/en.wikipedia.org\/wiki\/Fluid_pressure \"Fluid pressure\") |\n| [Liquids](https:\/\/en.wikipedia.org\/wiki\/Liquid \"Liquid\") |\n| [Adhesion](https:\/\/en.wikipedia.org\/wiki\/Adhesion \"Adhesion\") [Capillary action](https:\/\/en.wikipedia.org\/wiki\/Capillary_action \"Capillary action\") [Chromatography](https:\/\/en.wikipedia.org\/wiki\/Chromatography \"Chromatography\") [Cohesion (chemistry)](https:\/\/en.wikipedia.org\/wiki\/Cohesion_\\(chemistry\\) \"Cohesion (chemistry)\") [Surface tension](https:\/\/en.wikipedia.org\/wiki\/Surface_tension \"Surface tension\") |\n| [Gases](https:\/\/en.wikipedia.org\/wiki\/Gas \"Gas\") |\n| [Atmosphere](https:\/\/en.wikipedia.org\/wiki\/Atmosphere \"Atmosphere\") [Boyle's law](https:\/\/en.wikipedia.org\/wiki\/Boyle%27s_law \"Boyle's law\") [Charles's law](https:\/\/en.wikipedia.org\/wiki\/Charles%27s_law \"Charles's law\") [Combined gas law](https:\/\/en.wikipedia.org\/wiki\/Combined_gas_law \"Combined gas law\") [Fick's law](https:\/\/en.wikipedia.org\/wiki\/Fick%27s_law \"Fick's law\") [Gay-Lussac's law](https:\/\/en.wikipedia.org\/wiki\/Gay-Lussac%27s_law \"Gay-Lussac's law\") [Graham's law](https:\/\/en.wikipedia.org\/wiki\/Graham%27s_law \"Graham's law\") |\n| [Plasma](https:\/\/en.wikipedia.org\/wiki\/Plasma_\\(physics\\) \"Plasma (physics)\") |\n|   |\n| [Viscoelasticity](https:\/\/en.wikipedia.org\/wiki\/Viscoelasticity \"Viscoelasticity\") [Rheometry](https:\/\/en.wikipedia.org\/wiki\/Rheometry \"Rheometry\") [Rheometer](https:\/\/en.wikipedia.org\/wiki\/Rheometer \"Rheometer\") |\n| [Smart fluids](https:\/\/en.wikipedia.org\/wiki\/Smart_fluid \"Smart fluid\") |\n| [Electrorheological](https:\/\/en.wikipedia.org\/wiki\/Electrorheological_fluid \"Electrorheological fluid\") [Magnetorheological](https:\/\/en.wikipedia.org\/wiki\/Magnetorheological_fluid \"Magnetorheological fluid\") [Ferrofluids](https:\/\/en.wikipedia.org\/wiki\/Ferrofluid \"Ferrofluid\") |\n| Scientists [Bernoulli](https:\/\/en.wikipedia.org\/wiki\/Daniel_Bernoulli \"Daniel Bernoulli\") [Boyle](https:\/\/en.wikipedia.org\/wiki\/Robert_Boyle \"Robert Boyle\") [Cauchy](https:\/\/en.wikipedia.org\/wiki\/Augustin-Louis_Cauchy \"Augustin-Louis Cauchy\") [Charles](https:\/\/en.wikipedia.org\/wiki\/Jacques_Charles \"Jacques Charles\") [Euler](https:\/\/en.wikipedia.org\/wiki\/Leonhard_Euler \"Leonhard Euler\") [Fick](https:\/\/en.wikipedia.org\/wiki\/Adolf_Eugen_Fick \"Adolf Eugen Fick\") [Gay-Lussac](https:\/\/en.wikipedia.org\/wiki\/Joseph_Louis_Gay-Lussac \"Joseph Louis Gay-Lussac\") [Graham](https:\/\/en.wikipedia.org\/wiki\/Thomas_Graham_\\(chemist\\) \"Thomas Graham (chemist)\") [Hooke](https:\/\/en.wikipedia.org\/wiki\/Robert_Hooke \"Robert Hooke\") [Newton](https:\/\/en.wikipedia.org\/wiki\/Isaac_Newton \"Isaac Newton\") [Navier](https:\/\/en.wikipedia.org\/wiki\/Claude-Louis_Navier \"Claude-Louis Navier\") [Noll](https:\/\/en.wikipedia.org\/wiki\/Walter_Noll \"Walter Noll\") [Pascal](https:\/\/en.wikipedia.org\/wiki\/Blaise_Pascal \"Blaise Pascal\") [Stokes](https:\/\/en.wikipedia.org\/wiki\/Sir_George_Stokes,_1st_Baronet \"Sir George Stokes, 1st Baronet\") [Truesdell](https:\/\/en.wikipedia.org\/wiki\/Clifford_Truesdell \"Clifford Truesdell\") |\n| [v](https:\/\/en.wikipedia.org\/wiki\/Template:Continuum_mechanics \"Template:Continuum mechanics\") [t](https:\/\/en.wikipedia.org\/wiki\/Template_talk:Continuum_mechanics \"Template talk:Continuum mechanics\") [e](https:\/\/en.wikipedia.org\/wiki\/Special:EditPage\/Template:Continuum_mechanics \"Special:EditPage\/Template:Continuum mechanics\") |\n\n**Hydrostatics** is the branch of [fluid mechanics](https:\/\/en.wikipedia.org\/wiki\/Fluid_mechanics \"Fluid mechanics\") that studies [fluids](https:\/\/en.wikipedia.org\/wiki\/Fluid \"Fluid\") at [hydrostatic equilibrium](https:\/\/en.wikipedia.org\/wiki\/Hydrostatic_equilibrium \"Hydrostatic equilibrium\")[\\[1\\]](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_note-1) and \"the pressure in a fluid or exerted by a fluid on an immersed body\".[\\[2\\]](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_note-MW_dictionary_def-2) The word \"hydrostatics\" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether [compressible](https:\/\/en.wikipedia.org\/wiki\/Compressible_flow \"Compressible flow\") or [incompressible](https:\/\/en.wikipedia.org\/wiki\/Incompressible_flow \"Incompressible flow\"). It encompasses the study of the conditions under which fluids are at rest in [stable equilibrium](https:\/\/en.wikipedia.org\/wiki\/Mechanical_equilibrium \"Mechanical equilibrium\"). It is opposed to *[fluid dynamics](https:\/\/en.wikipedia.org\/wiki\/Fluid_dynamics \"Fluid dynamics\")*, the study of fluids in motion.\n\nHydrostatics is fundamental to *[hydraulics](https:\/\/en.wikipedia.org\/wiki\/Hydraulics \"Hydraulics\")*, the [engineering](https:\/\/en.wikipedia.org\/wiki\/Engineering \"Engineering\") of equipment for storing, transporting and using fluids. It is also relevant to [geophysics](https:\/\/en.wikipedia.org\/wiki\/Geophysics \"Geophysics\") and [astrophysics](https:\/\/en.wikipedia.org\/wiki\/Astrophysics \"Astrophysics\") (for example, in understanding [plate tectonics](https:\/\/en.wikipedia.org\/wiki\/Plate_tectonics \"Plate tectonics\") and the anomalies of the [Earth's gravitational field](https:\/\/en.wikipedia.org\/wiki\/Gravity_of_Earth \"Gravity of Earth\")), to [meteorology](https:\/\/en.wikipedia.org\/wiki\/Meteorology \"Meteorology\"), to [medicine](https:\/\/en.wikipedia.org\/wiki\/Medicine \"Medicine\") (in the context of [blood pressure](https:\/\/en.wikipedia.org\/wiki\/Blood_pressure \"Blood pressure\")), and many other fields.\n\nHydrostatics offers physical explanations for many phenomena of everyday life, such as why [atmospheric pressure](https:\/\/en.wikipedia.org\/wiki\/Atmospheric_pressure \"Atmospheric pressure\") changes with [altitude](https:\/\/en.wikipedia.org\/wiki\/Altitude \"Altitude\"), why wood and oil float on water, and why the surface of still water is always [level](https:\/\/en.wikipedia.org\/wiki\/Water_level \"Water level\") according to the [curvature of the earth](https:\/\/en.wikipedia.org\/wiki\/Spherical_Earth \"Spherical Earth\").\n\n## History\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=1 \"Edit section: History\")\\]\n\nSome principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, [cisterns](https:\/\/en.wikipedia.org\/wiki\/Cistern \"Cistern\"), [aqueducts](https:\/\/en.wikipedia.org\/wiki\/Aqueduct_\\(water_supply\\) \"Aqueduct (water supply)\") and [fountains](https:\/\/en.wikipedia.org\/wiki\/Fountain \"Fountain\"). [Archimedes](https:\/\/en.wikipedia.org\/wiki\/Archimedes \"Archimedes\") is credited with the discovery of [Archimedes' Principle](https:\/\/en.wikipedia.org\/wiki\/Archimedes%27_Principle \"Archimedes' Principle\"), which relates the [buoyancy](https:\/\/en.wikipedia.org\/wiki\/Buoyancy \"Buoyancy\") force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The [Roman](https:\/\/en.wikipedia.org\/wiki\/Roman_Empire \"Roman Empire\") engineer [Vitruvius](https:\/\/en.wikipedia.org\/wiki\/Vitruvius \"Vitruvius\") warned readers about [lead](https:\/\/en.wikipedia.org\/wiki\/Lead \"Lead\") pipes bursting under hydrostatic pressure.[\\[3\\]](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_note-VitruviusVIII.6-3)\n\nThe concept of pressure and the way it is transmitted by fluids was formulated by the [French](https:\/\/en.wikipedia.org\/wiki\/France \"France\") [mathematician](https:\/\/en.wikipedia.org\/wiki\/Mathematician \"Mathematician\") and [philosopher](https:\/\/en.wikipedia.org\/wiki\/Philosopher \"Philosopher\") [Blaise Pascal](https:\/\/en.wikipedia.org\/wiki\/Blaise_Pascal \"Blaise Pascal\") in 1647.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\n## Hydrostatics in ancient Greece and Rome\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=2 \"Edit section: Hydrostatics in ancient Greece and Rome\")\\]\n\n### Pythagorean Cup\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=3 \"Edit section: Pythagorean Cup\")\\]\n\nMain article: [Pythagorean cup](https:\/\/en.wikipedia.org\/wiki\/Pythagorean_cup \"Pythagorean cup\")\n\nThe \"fair cup\" or [Pythagorean cup](https:\/\/en.wikipedia.org\/wiki\/Pythagorean_cup \"Pythagorean cup\"), which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\nThe cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied.\n\n### Heron's fountain\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=4 \"Edit section: Heron's fountain\")\\]\n\nMain article: [Heron's fountain](https:\/\/en.wikipedia.org\/wiki\/Heron%27s_fountain \"Heron's fountain\")\n\n[Heron's fountain](https:\/\/en.wikipedia.org\/wiki\/Heron%27s_fountain \"Heron's fountain\") is a device invented by [Heron of Alexandria](https:\/\/en.wikipedia.org\/wiki\/Heron_of_Alexandria \"Heron of Alexandria\") that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several [cannula](https:\/\/en.wikipedia.org\/wiki\/Cannula \"Cannula\") (a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\n## Pascal's contribution in hydrostatics\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=5 \"Edit section: Pascal's contribution in hydrostatics\")\\]\n\nMain article: [Pascal's law](https:\/\/en.wikipedia.org\/wiki\/Pascal%27s_law \"Pascal's law\")\n\nPascal made contributions to developments in both hydrostatics and hydrodynamics. [Pascal's law](https:\/\/en.wikipedia.org\/wiki\/Pascal%27s_law \"Pascal's law\") is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed.\n\n## Liquids (fluids with free surfaces)\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=6 \"Edit section: Liquids (fluids with free surfaces)\")\\]\n\nLiquids can have [free surfaces](https:\/\/en.wikipedia.org\/wiki\/Free_surface \"Free surface\") at which they interface with gases, or with a [vacuum](https:\/\/en.wikipedia.org\/wiki\/Vacuum \"Vacuum\"). In general, the lack of the ability to sustain a [shear stress](https:\/\/en.wikipedia.org\/wiki\/Shear_stress \"Shear stress\") entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from [surface tension](https:\/\/en.wikipedia.org\/wiki\/Surface_tension \"Surface tension\").\n\n### Capillary action\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=7 \"Edit section: Capillary action\")\\]\n\nWhen liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, [surface tension](https:\/\/en.wikipedia.org\/wiki\/Surface_tension \"Surface tension\") effects become important leading to the formation of a [meniscus](https:\/\/en.wikipedia.org\/wiki\/Meniscus_\\(liquid\\) \"Meniscus (liquid)\") through [capillary action](https:\/\/en.wikipedia.org\/wiki\/Capillary_action \"Capillary action\"). This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in [plant](https:\/\/en.wikipedia.org\/wiki\/Plant \"Plant\") [xylem](https:\/\/en.wikipedia.org\/wiki\/Xylem \"Xylem\"), the [transpirational pull](https:\/\/en.wikipedia.org\/wiki\/Transpirational_pull \"Transpirational pull\").\n\n### Hanging drops\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=8 \"Edit section: Hanging drops\")\\]\n\nWithout surface tension, [drops](https:\/\/en.wikipedia.org\/wiki\/Drop_\\(liquid\\) \"Drop (liquid)\") would not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid.\n\n## See also\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=9 \"Edit section: See also\")\\]\n\n- [Communicating vessels](https:\/\/en.wikipedia.org\/wiki\/Communicating_vessels \"Communicating vessels\") – Set of internally connected containers containing a homogeneous fluid\n- [D-DIA](https:\/\/en.wikipedia.org\/wiki\/D-DIA \"D-DIA\") – Apparatus used for high pressure and high temperature deformation experiments\n- [Hydrostatic pressure](https:\/\/en.wikipedia.org\/wiki\/Hydrostatic_pressure \"Hydrostatic pressure\") – Physical quantity\n- [Hydrostatic test](https:\/\/en.wikipedia.org\/wiki\/Hydrostatic_test \"Hydrostatic test\") – Non-destructive test of pressure vessels\n- [Triaxial shear test](https:\/\/en.wikipedia.org\/wiki\/Triaxial_shear_test \"Triaxial shear test\") – Stress test with different levels of stress in each perpendicular direction\n\n## References\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=10 \"Edit section: References\")\\]\n\n1. **[^](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_ref-1)**\n   [\"Fluid Mechanics\/Fluid Statics\/Fundamentals of Fluid Statics - Wikibooks, open books for an open world\"](https:\/\/en.wikibooks.org\/wiki\/Fluid_Mechanics\/Fluid_Statics\/Fundamentals_of_Fluid_Statics#Hydrostatic_Equilibrium). *en.wikibooks.org*. Retrieved 2021-04-01.\n2. **[^](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_ref-MW_dictionary_def_2-0)**\n   [\"Hydrostatics\"](https:\/\/www.merriam-webster.com\/dictionary\/hydrostatics). *Merriam-Webster*. Retrieved 11 September 2018.\n3. **[^](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_ref-VitruviusVIII.6_3-0)** Marcus Vitruvius Pollio (ca. 15 BCE), [\"The Ten Books of Architecture\"](https:\/\/penelope.uchicago.edu\/Thayer\/E\/Roman\/Texts\/Vitruvius\/8*.html), Book VIII, Chapter 6. At the University of Chicago's Penelope site. Accessed on 2013-02-25.\n\n## Further reading\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=11 \"Edit section: Further reading\")\\]\n\n- Batchelor, George K. (1967). *An Introduction to Fluid Dynamics*. Cambridge University Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [0-521-66396-2](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-521-66396-2 \"Special:BookSources\/0-521-66396-2\")\n  \n  .\n- Falkovich, Gregory (2011). *Fluid Mechanics (A short course for physicists)*. Cambridge University Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-1-107-00575-4](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-1-107-00575-4 \"Special:BookSources\/978-1-107-00575-4\")\n  \n  .\n- Kundu, Pijush K.; Cohen, Ira M. (2008). *Fluid Mechanics* (4th rev. ed.). Academic Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-0-12-373735-9](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-0-12-373735-9 \"Special:BookSources\/978-0-12-373735-9\")\n  \n  .\n- Currie, I. G. (1974). *Fundamental Mechanics of Fluids*. McGraw-Hill. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [0-07-015000-1](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-07-015000-1 \"Special:BookSources\/0-07-015000-1\")\n  \n  .\n- Massey, B.; Ward-Smith, J. (2005). *Mechanics of Fluids* (8th ed.). Taylor & Francis. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-0-415-36206-1](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-0-415-36206-1 \"Special:BookSources\/978-0-415-36206-1\")\n  \n  .\n- White, Frank M. (2003). *Fluid Mechanics*. McGraw–Hill. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [0-07-240217-2](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-07-240217-2 \"Special:BookSources\/0-07-240217-2\")\n  \n  .\n\n## External links\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=12 \"Edit section: External links\")\\]\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/9\/99\/Wiktionary-logo-en-v2.svg\/40px-Wiktionary-logo-en-v2.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Wiktionary-logo-en-v2.svg)\n\nLook up ***[hydrostatics](https:\/\/en.wiktionary.org\/wiki\/hydrostatics \"wiktionary:hydrostatics\")*** in Wiktionary, the free dictionary.\n\n- [The Flow of Dry Water - The Feynman Lectures on Physics](https:\/\/www.feynmanlectures.caltech.edu\/II_40.html)\n\n| [v](https:\/\/en.wikipedia.org\/wiki\/Template:Branches_of_physics \"Template:Branches of physics\") 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Wikipedia® is a registered trademark of the [Wikimedia Foundation, Inc.](https:\/\/wikimediafoundation.org\/), a non-profit organization.\n\n- [Privacy policy](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Privacy_policy)\n- [About Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:About)\n- [Disclaimers](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:General_disclaimer)\n- [Contact Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contact_us)\n- [Legal & safety contacts](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Legal:Wikimedia_Foundation_Legal_and_Safety_Contact_Information)\n- [Code of Conduct](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Universal_Code_of_Conduct)\n- [Developers](https:\/\/developer.wikimedia.org\/)\n- [Statistics](https:\/\/stats.wikimedia.org\/#\/en.wikipedia.org)\n- [Cookie statement](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Cookie_statement)\n- [Mobile view](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&mobileaction=toggle_view_mobile)\n\n- [![Wikimedia Foundation](https:\/\/en.wikipedia.org\/static\/images\/footer\/wikimedia.svg)](https:\/\/www.wikimedia.org\/)\n- [![Powered by MediaWiki](https:\/\/en.wikipedia.org\/w\/resources\/assets\/mediawiki_compact.svg)](https:\/\/www.mediawiki.org\/)\n\nSearch\n\nToggle the table of contents\n\nHydrostatics\n\n65 languages\n\n[Add topic](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics)","attrs_readable_markdown":"From Wikipedia, the free encyclopedia\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e4\/Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg\/250px-Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg)](https:\/\/en.wikipedia.org\/wiki\/File:Table_of_Hydraulics_and_Hydrostatics,_Cyclopaedia,_Volume_1.jpg)\n\nTable of Hydraulics and Hydrostatics, from the 1728 *[Cyclopædia](https:\/\/en.wikipedia.org\/wiki\/Cyclop%C3%A6dia,_or_an_Universal_Dictionary_of_Arts_and_Sciences \"Cyclopædia, or an Universal Dictionary of Arts and Sciences\")*\n\n**Hydrostatics** is the branch of [fluid mechanics](https:\/\/en.wikipedia.org\/wiki\/Fluid_mechanics \"Fluid mechanics\") that studies [fluids](https:\/\/en.wikipedia.org\/wiki\/Fluid \"Fluid\") at [hydrostatic equilibrium](https:\/\/en.wikipedia.org\/wiki\/Hydrostatic_equilibrium \"Hydrostatic equilibrium\")[\\[1\\]](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_note-1) and \"the pressure in a fluid or exerted by a fluid on an immersed body\".[\\[2\\]](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_note-MW_dictionary_def-2) The word \"hydrostatics\" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether [compressible](https:\/\/en.wikipedia.org\/wiki\/Compressible_flow \"Compressible flow\") or [incompressible](https:\/\/en.wikipedia.org\/wiki\/Incompressible_flow \"Incompressible flow\"). It encompasses the study of the conditions under which fluids are at rest in [stable equilibrium](https:\/\/en.wikipedia.org\/wiki\/Mechanical_equilibrium \"Mechanical equilibrium\"). It is opposed to *[fluid dynamics](https:\/\/en.wikipedia.org\/wiki\/Fluid_dynamics \"Fluid dynamics\")*, the study of fluids in motion.\n\nHydrostatics is fundamental to *[hydraulics](https:\/\/en.wikipedia.org\/wiki\/Hydraulics \"Hydraulics\")*, the [engineering](https:\/\/en.wikipedia.org\/wiki\/Engineering \"Engineering\") of equipment for storing, transporting and using fluids. It is also relevant to [geophysics](https:\/\/en.wikipedia.org\/wiki\/Geophysics \"Geophysics\") and [astrophysics](https:\/\/en.wikipedia.org\/wiki\/Astrophysics \"Astrophysics\") (for example, in understanding [plate tectonics](https:\/\/en.wikipedia.org\/wiki\/Plate_tectonics \"Plate tectonics\") and the anomalies of the [Earth's gravitational field](https:\/\/en.wikipedia.org\/wiki\/Gravity_of_Earth \"Gravity of Earth\")), to [meteorology](https:\/\/en.wikipedia.org\/wiki\/Meteorology \"Meteorology\"), to [medicine](https:\/\/en.wikipedia.org\/wiki\/Medicine \"Medicine\") (in the context of [blood pressure](https:\/\/en.wikipedia.org\/wiki\/Blood_pressure \"Blood pressure\")), and many other fields.\n\nHydrostatics offers physical explanations for many phenomena of everyday life, such as why [atmospheric pressure](https:\/\/en.wikipedia.org\/wiki\/Atmospheric_pressure \"Atmospheric pressure\") changes with [altitude](https:\/\/en.wikipedia.org\/wiki\/Altitude \"Altitude\"), why wood and oil float on water, and why the surface of still water is always [level](https:\/\/en.wikipedia.org\/wiki\/Water_level \"Water level\") according to the [curvature of the earth](https:\/\/en.wikipedia.org\/wiki\/Spherical_Earth \"Spherical Earth\").\n\nSome principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, [cisterns](https:\/\/en.wikipedia.org\/wiki\/Cistern \"Cistern\"), [aqueducts](https:\/\/en.wikipedia.org\/wiki\/Aqueduct_\\(water_supply\\) \"Aqueduct (water supply)\") and [fountains](https:\/\/en.wikipedia.org\/wiki\/Fountain \"Fountain\"). [Archimedes](https:\/\/en.wikipedia.org\/wiki\/Archimedes \"Archimedes\") is credited with the discovery of [Archimedes' Principle](https:\/\/en.wikipedia.org\/wiki\/Archimedes%27_Principle \"Archimedes' Principle\"), which relates the [buoyancy](https:\/\/en.wikipedia.org\/wiki\/Buoyancy \"Buoyancy\") force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The [Roman](https:\/\/en.wikipedia.org\/wiki\/Roman_Empire \"Roman Empire\") engineer [Vitruvius](https:\/\/en.wikipedia.org\/wiki\/Vitruvius \"Vitruvius\") warned readers about [lead](https:\/\/en.wikipedia.org\/wiki\/Lead \"Lead\") pipes bursting under hydrostatic pressure.[\\[3\\]](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_note-VitruviusVIII.6-3)\n\nThe concept of pressure and the way it is transmitted by fluids was formulated by the [French](https:\/\/en.wikipedia.org\/wiki\/France \"France\") [mathematician](https:\/\/en.wikipedia.org\/wiki\/Mathematician \"Mathematician\") and [philosopher](https:\/\/en.wikipedia.org\/wiki\/Philosopher \"Philosopher\") [Blaise Pascal](https:\/\/en.wikipedia.org\/wiki\/Blaise_Pascal \"Blaise Pascal\") in 1647.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\n## Hydrostatics in ancient Greece and Rome\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=2 \"Edit section: Hydrostatics in ancient Greece and Rome\")\\]\n\nThe \"fair cup\" or [Pythagorean cup](https:\/\/en.wikipedia.org\/wiki\/Pythagorean_cup \"Pythagorean cup\"), which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\nThe cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied.\n\n[Heron's fountain](https:\/\/en.wikipedia.org\/wiki\/Heron%27s_fountain \"Heron's fountain\") is a device invented by [Heron of Alexandria](https:\/\/en.wikipedia.org\/wiki\/Heron_of_Alexandria \"Heron of Alexandria\") that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several [cannula](https:\/\/en.wikipedia.org\/wiki\/Cannula \"Cannula\") (a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir.\\[*[citation needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Citation_needed \"Wikipedia:Citation needed\")*\\]\n\n## Pascal's contribution in hydrostatics\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=5 \"Edit section: Pascal's contribution in hydrostatics\")\\]\n\nPascal made contributions to developments in both hydrostatics and hydrodynamics. [Pascal's law](https:\/\/en.wikipedia.org\/wiki\/Pascal%27s_law \"Pascal's law\") is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed.\n\n## Liquids (fluids with free surfaces)\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Hydrostatics&action=edit&section=6 \"Edit section: Liquids (fluids with free surfaces)\")\\]\n\nLiquids can have [free surfaces](https:\/\/en.wikipedia.org\/wiki\/Free_surface \"Free surface\") at which they interface with gases, or with a [vacuum](https:\/\/en.wikipedia.org\/wiki\/Vacuum \"Vacuum\"). In general, the lack of the ability to sustain a [shear stress](https:\/\/en.wikipedia.org\/wiki\/Shear_stress \"Shear stress\") entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from [surface tension](https:\/\/en.wikipedia.org\/wiki\/Surface_tension \"Surface tension\").\n\nWhen liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, [surface tension](https:\/\/en.wikipedia.org\/wiki\/Surface_tension \"Surface tension\") effects become important leading to the formation of a [meniscus](https:\/\/en.wikipedia.org\/wiki\/Meniscus_\\(liquid\\) \"Meniscus (liquid)\") through [capillary action](https:\/\/en.wikipedia.org\/wiki\/Capillary_action \"Capillary action\"). This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in [plant](https:\/\/en.wikipedia.org\/wiki\/Plant \"Plant\") [xylem](https:\/\/en.wikipedia.org\/wiki\/Xylem \"Xylem\"), the [transpirational pull](https:\/\/en.wikipedia.org\/wiki\/Transpirational_pull \"Transpirational pull\").\n\nWithout surface tension, [drops](https:\/\/en.wikipedia.org\/wiki\/Drop_\\(liquid\\) \"Drop (liquid)\") would not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid.\n\n- [Communicating vessels](https:\/\/en.wikipedia.org\/wiki\/Communicating_vessels \"Communicating vessels\") – Set of internally connected containers containing a homogeneous fluid\n- [D-DIA](https:\/\/en.wikipedia.org\/wiki\/D-DIA \"D-DIA\") – Apparatus used for high pressure and high temperature deformation experiments\n- [Hydrostatic pressure](https:\/\/en.wikipedia.org\/wiki\/Hydrostatic_pressure \"Hydrostatic pressure\") – Physical quantity\n- [Hydrostatic test](https:\/\/en.wikipedia.org\/wiki\/Hydrostatic_test \"Hydrostatic test\") – Non-destructive test of pressure vessels\n- [Triaxial shear test](https:\/\/en.wikipedia.org\/wiki\/Triaxial_shear_test \"Triaxial shear test\") – Stress test with different levels of stress in each perpendicular direction\n\n1. **[^](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_ref-1)**\n   [\"Fluid Mechanics\/Fluid Statics\/Fundamentals of Fluid Statics - Wikibooks, open books for an open world\"](https:\/\/en.wikibooks.org\/wiki\/Fluid_Mechanics\/Fluid_Statics\/Fundamentals_of_Fluid_Statics#Hydrostatic_Equilibrium). *en.wikibooks.org*. Retrieved 2021-04-01.\n2. **[^](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_ref-MW_dictionary_def_2-0)**\n   [\"Hydrostatics\"](https:\/\/www.merriam-webster.com\/dictionary\/hydrostatics). *Merriam-Webster*. Retrieved 11 September 2018.\n3. **[^](https:\/\/en.wikipedia.org\/wiki\/Hydrostatics#cite_ref-VitruviusVIII.6_3-0)** Marcus Vitruvius Pollio (ca. 15 BCE), [\"The Ten Books of Architecture\"](https:\/\/penelope.uchicago.edu\/Thayer\/E\/Roman\/Texts\/Vitruvius\/8*.html), Book VIII, Chapter 6. At the University of Chicago's Penelope site. Accessed on 2013-02-25.\n\n- Batchelor, George K. (1967). *An Introduction to Fluid Dynamics*. Cambridge University Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [0-521-66396-2](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-521-66396-2 \"Special:BookSources\/0-521-66396-2\")\n  \n  .\n- Falkovich, Gregory (2011). *Fluid Mechanics (A short course for physicists)*. Cambridge University Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-1-107-00575-4](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-1-107-00575-4 \"Special:BookSources\/978-1-107-00575-4\")\n  \n  .\n- Kundu, Pijush K.; Cohen, Ira M. (2008). *Fluid Mechanics* (4th rev. ed.). Academic Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-0-12-373735-9](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-0-12-373735-9 \"Special:BookSources\/978-0-12-373735-9\")\n  \n  .\n- Currie, I. G. (1974). *Fundamental Mechanics of Fluids*. McGraw-Hill. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [0-07-015000-1](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-07-015000-1 \"Special:BookSources\/0-07-015000-1\")\n  \n  .\n- Massey, B.; Ward-Smith, J. (2005). *Mechanics of Fluids* (8th ed.). Taylor & Francis. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-0-415-36206-1](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-0-415-36206-1 \"Special:BookSources\/978-0-415-36206-1\")\n  \n  .\n- White, Frank M. (2003). *Fluid Mechanics*. McGraw–Hill. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [0-07-240217-2](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-07-240217-2 \"Special:BookSources\/0-07-240217-2\")\n  \n  .\n\n- [The Flow of Dry Water - The Feynman Lectures on Physics](https:\/\/www.feynmanlectures.caltech.edu\/II_40.html)","meta_canonical":null}

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Boilerpipe Text	From Wikipedia, the free encyclopedia Table of Hydraulics and Hydrostatics, from the 1728 Cyclopædia Hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium [ 1 ] and "the pressure in a fluid or exerted by a fluid on an immersed body". [ 2 ] The word "hydrostatics" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether compressible or incompressible . It encompasses the study of the conditions under which fluids are at rest in stable equilibrium . It is opposed to fluid dynamics , the study of fluids in motion. Hydrostatics is fundamental to hydraulics , the engineering of equipment for storing, transporting and using fluids. It is also relevant to geophysics and astrophysics (for example, in understanding plate tectonics and the anomalies of the Earth's gravitational field ), to meteorology , to medicine (in the context of blood pressure ), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude , why wood and oil float on water, and why the surface of still water is always level according to the curvature of the earth . Some principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, cisterns , aqueducts and fountains . Archimedes is credited with the discovery of Archimedes' Principle , which relates the buoyancy force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The Roman engineer Vitruvius warned readers about lead pipes bursting under hydrostatic pressure. [ 3 ] The concept of pressure and the way it is transmitted by fluids was formulated by the French mathematician and philosopher Blaise Pascal in 1647. [ citation needed ] Hydrostatics in ancient Greece and Rome [ edit ] The "fair cup" or Pythagorean cup , which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool. [ citation needed ] The cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied. Heron's fountain is a device invented by Heron of Alexandria that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several cannula (a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir. [ citation needed ] Pascal's contribution in hydrostatics [ edit ] Pascal made contributions to developments in both hydrostatics and hydrodynamics. Pascal's law is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed. Liquids (fluids with free surfaces) [ edit ] Liquids can have free surfaces at which they interface with gases, or with a vacuum . In general, the lack of the ability to sustain a shear stress entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from surface tension . When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, surface tension effects become important leading to the formation of a meniscus through capillary action . This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in plant xylem , the transpirational pull . Without surface tension, drops would not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid. Communicating vessels – Set of internally connected containers containing a homogeneous fluid D-DIA – Apparatus used for high pressure and high temperature deformation experiments Hydrostatic pressure – Physical quantity Hydrostatic test – Non-destructive test of pressure vessels Triaxial shear test – Stress test with different levels of stress in each perpendicular direction ^ "Fluid Mechanics/Fluid Statics/Fundamentals of Fluid Statics - Wikibooks, open books for an open world" . en.wikibooks.org . Retrieved 2021-04-01 . ^ "Hydrostatics" . Merriam-Webster . Retrieved 11 September 2018 . ^ Marcus Vitruvius Pollio (ca. 15 BCE), "The Ten Books of Architecture" , Book VIII, Chapter 6. At the University of Chicago's Penelope site. Accessed on 2013-02-25. Batchelor, George K. (1967). An Introduction to Fluid Dynamics . Cambridge University Press. ISBN 0-521-66396-2 . Falkovich, Gregory (2011). Fluid Mechanics (A short course for physicists) . Cambridge University Press. ISBN 978-1-107-00575-4 . Kundu, Pijush K.; Cohen, Ira M. (2008). Fluid Mechanics (4th rev. ed.). Academic Press. ISBN 978-0-12-373735-9 . Currie, I. G. (1974). Fundamental Mechanics of Fluids . McGraw-Hill. ISBN 0-07-015000-1 . Massey, B.; Ward-Smith, J. (2005). Mechanics of Fluids (8th ed.). Taylor & Francis. ISBN 978-0-415-36206-1 . White, Frank M. (2003). Fluid Mechanics . McGraw–Hill. ISBN 0-07-240217-2 . The Flow of Dry Water - The Feynman Lectures on Physics
Markdown	[Jump to content](https://en.wikipedia.org/wiki/Hydrostatics#bodyContent) Main menu Main menu move to sidebar hide Navigation - [Main page](https://en.wikipedia.org/wiki/Main_Page "Visit the main page [z]") - [Contents](https://en.wikipedia.org/wiki/Wikipedia:Contents "Guides to browsing Wikipedia") - [Current events](https://en.wikipedia.org/wiki/Portal:Current_events "Articles related to current events") - [Random article](https://en.wikipedia.org/wiki/Special:Random "Visit a randomly selected article [x]") - [About Wikipedia](https://en.wikipedia.org/wiki/Wikipedia:About "Learn about Wikipedia and how it works") - [Contact us](https://en.wikipedia.org/wiki/Wikipedia:Contact_us "How to contact Wikipedia") Contribute - [Help](https://en.wikipedia.org/wiki/Help:Contents "Guidance on how to use and edit Wikipedia") - [Learn to edit](https://en.wikipedia.org/wiki/Help:Introduction "Learn how to edit Wikipedia") - [Community portal](https://en.wikipedia.org/wiki/Wikipedia:Community_portal "The hub for editors") - [Recent changes](https://en.wikipedia.org/wiki/Special:RecentChanges "A list of recent changes to Wikipedia [r]") - [Upload file](https://en.wikipedia.org/wiki/Wikipedia:File_upload_wizard "Add images or other media for use on Wikipedia") - [Special pages](https://en.wikipedia.org/wiki/Special:SpecialPages "A list of all special pages [q]") [![](https://en.wikipedia.org/static/images/icons/enwiki-25.svg) ![Wikipedia](https://en.wikipedia.org/static/images/mobile/copyright/wikipedia-wordmark-en-25.svg) ![The Free Encyclopedia](https://en.wikipedia.org/static/images/mobile/copyright/wikipedia-tagline-en-25.svg)](https://en.wikipedia.org/wiki/Main_Page) [Search](https://en.wikipedia.org/wiki/Special:Search "Search Wikipedia [f]") Appearance - [Donate](https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en) - [Create account](https://en.wikipedia.org/w/index.php?title=Special:CreateAccount&returnto=Hydrostatics "You are encouraged to create an account and log in; however, it is not mandatory") - [Log in](https://en.wikipedia.org/w/index.php?title=Special:UserLogin&returnto=Hydrostatics "You're encouraged to log in; however, it's not mandatory. [o]") Personal tools - [Donate](https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en) - [Create account](https://en.wikipedia.org/w/index.php?title=Special:CreateAccount&returnto=Hydrostatics "You are encouraged to create an account and log in; however, it is not mandatory") - [Log in](https://en.wikipedia.org/w/index.php?title=Special:UserLogin&returnto=Hydrostatics "You're encouraged to log in; however, it's not mandatory. [o]") ## Contents move to sidebar hide - [(Top)](https://en.wikipedia.org/wiki/Hydrostatics) - [1 History](https://en.wikipedia.org/wiki/Hydrostatics#History) - [2 Hydrostatics in ancient Greece and Rome](https://en.wikipedia.org/wiki/Hydrostatics#Hydrostatics_in_ancient_Greece_and_Rome) Toggle Hydrostatics in ancient Greece and Rome subsection - [2\.1 Pythagorean Cup](https://en.wikipedia.org/wiki/Hydrostatics#Pythagorean_Cup) - [2\.2 Heron's fountain](https://en.wikipedia.org/wiki/Hydrostatics#Heron's_fountain) - [3 Pascal's contribution in hydrostatics](https://en.wikipedia.org/wiki/Hydrostatics#Pascal's_contribution_in_hydrostatics) - [4 Liquids (fluids with free surfaces)](https://en.wikipedia.org/wiki/Hydrostatics#Liquids_\(fluids_with_free_surfaces\)) Toggle Liquids (fluids with free surfaces) subsection - [4\.1 Capillary action](https://en.wikipedia.org/wiki/Hydrostatics#Capillary_action) - [4\.2 Hanging drops](https://en.wikipedia.org/wiki/Hydrostatics#Hanging_drops) - [5 See also](https://en.wikipedia.org/wiki/Hydrostatics#See_also) - 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[Get shortened URL](https://en.wikipedia.org/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FHydrostatics) Print/export - [Download as PDF](https://en.wikipedia.org/w/index.php?title=Special:DownloadAsPdf&page=Hydrostatics&action=show-download-screen "Download this page as a PDF file") - [Printable version](https://en.wikipedia.org/w/index.php?title=Hydrostatics&printable=yes "Printable version of this page [p]") In other projects - [Wikimedia Commons](https://commons.wikimedia.org/wiki/Category:Fluid_statics) - [Wikiversity](https://en.wikiversity.org/wiki/Fluid_statics) - [Wikidata item](https://www.wikidata.org/wiki/Special:EntityPage/Q177807 "Structured data on this page hosted by Wikidata [g]") Appearance move to sidebar hide From Wikipedia, the free encyclopedia Branch of fluid mechanics that studies fluids at rest This article is about the discipline branch. For the concept, see [Hydrostatic equilibrium](https://en.wikipedia.org/wiki/Hydrostatic_equilibrium "Hydrostatic equilibrium"). [![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg/250px-Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg)](https://en.wikipedia.org/wiki/File:Table_of_Hydraulics_and_Hydrostatics,_Cyclopaedia,_Volume_1.jpg) Table of Hydraulics and Hydrostatics, from the 1728 [Cyclopædia](https://en.wikipedia.org/wiki/Cyclop%C3%A6dia,_or_an_Universal_Dictionary_of_Arts_and_Sciences "Cyclopædia, or an Universal Dictionary of Arts and Sciences") \| \| \|---\| \| Part of a series on \| \| [Continuum mechanics](https://en.wikipedia.org/wiki/Continuum_mechanics "Continuum mechanics") \| \| J \= − D d φ d x {\\displaystyle J=-D{\\frac {d\\varphi }{dx}}} ![{\\displaystyle J=-D{\\frac {d\\varphi }{dx}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1856f88def2056f28ed27c7d31180a6240820ea6)[Fick's laws of diffusion](https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion "Fick's laws of diffusion") \| \| [Solid mechanics](https://en.wikipedia.org/wiki/Solid_mechanics "Solid mechanics") [Deformation](https://en.wikipedia.org/wiki/Deformation_\(physics\) "Deformation (physics)") [Elasticity](https://en.wikipedia.org/wiki/Elasticity_\(physics\) "Elasticity (physics)") [linear](https://en.wikipedia.org/wiki/Linear_elasticity "Linear elasticity") [Plasticity](https://en.wikipedia.org/wiki/Plasticity_\(physics\) "Plasticity (physics)") [Hooke's law](https://en.wikipedia.org/wiki/Hooke%27s_law "Hooke's law") [Stress](https://en.wikipedia.org/wiki/Stress_\(mechanics\) "Stress (mechanics)") [Strain](https://en.wikipedia.org/wiki/Strain_\(mechanics\) "Strain (mechanics)") [Finite strain](https://en.wikipedia.org/wiki/Finite_strain_theory "Finite strain theory") [Infinitesimal strain](https://en.wikipedia.org/wiki/Infinitesimal_strain_theory "Infinitesimal strain theory") [Compatibility](https://en.wikipedia.org/wiki/Compatibility_\(mechanics\) "Compatibility (mechanics)") [Bending](https://en.wikipedia.org/wiki/Bending "Bending") [Contact mechanics](https://en.wikipedia.org/wiki/Contact_mechanics "Contact mechanics") [frictional](https://en.wikipedia.org/wiki/Frictional_contact_mechanics "Frictional contact mechanics") [Material failure theory](https://en.wikipedia.org/wiki/Material_failure_theory "Material failure theory") [Fracture mechanics](https://en.wikipedia.org/wiki/Fracture_mechanics "Fracture mechanics") \| \| [Fluids](https://en.wikipedia.org/wiki/Fluid "Fluid") \| \| [Statics]() · [Dynamics](https://en.wikipedia.org/wiki/Fluid_dynamics "Fluid dynamics") [Archimedes' principle](https://en.wikipedia.org/wiki/Archimedes%27_principle "Archimedes' principle") · [Bernoulli's principle](https://en.wikipedia.org/wiki/Bernoulli%27s_principle "Bernoulli's principle") [Navier–Stokes equations](https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations "Navier–Stokes equations") [Poiseuille equation](https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation "Hagen–Poiseuille equation") · [Pascal's law](https://en.wikipedia.org/wiki/Pascal%27s_law "Pascal's law") [Viscosity](https://en.wikipedia.org/wiki/Viscosity "Viscosity") ([Newtonian](https://en.wikipedia.org/wiki/Newtonian_fluid "Newtonian fluid") · [non-Newtonian](https://en.wikipedia.org/wiki/Non-Newtonian_fluid "Non-Newtonian fluid")) [Buoyancy](https://en.wikipedia.org/wiki/Buoyancy "Buoyancy") · [Mixing](https://en.wikipedia.org/wiki/Mixing_\(process_engineering\) "Mixing (process engineering)") · [Pressure](https://en.wikipedia.org/wiki/Fluid_pressure "Fluid pressure") \| \| [Liquids](https://en.wikipedia.org/wiki/Liquid "Liquid") \| \| [Adhesion](https://en.wikipedia.org/wiki/Adhesion "Adhesion") [Capillary action](https://en.wikipedia.org/wiki/Capillary_action "Capillary action") [Chromatography](https://en.wikipedia.org/wiki/Chromatography "Chromatography") [Cohesion (chemistry)](https://en.wikipedia.org/wiki/Cohesion_\(chemistry\) "Cohesion (chemistry)") [Surface tension](https://en.wikipedia.org/wiki/Surface_tension "Surface tension") \| \| [Gases](https://en.wikipedia.org/wiki/Gas "Gas") \| \| [Atmosphere](https://en.wikipedia.org/wiki/Atmosphere "Atmosphere") [Boyle's law](https://en.wikipedia.org/wiki/Boyle%27s_law "Boyle's law") [Charles's law](https://en.wikipedia.org/wiki/Charles%27s_law "Charles's law") [Combined gas law](https://en.wikipedia.org/wiki/Combined_gas_law "Combined gas law") [Fick's law](https://en.wikipedia.org/wiki/Fick%27s_law "Fick's law") [Gay-Lussac's law](https://en.wikipedia.org/wiki/Gay-Lussac%27s_law "Gay-Lussac's law") [Graham's law](https://en.wikipedia.org/wiki/Graham%27s_law "Graham's law") \| \| [Plasma](https://en.wikipedia.org/wiki/Plasma_\(physics\) "Plasma (physics)") \| \| \| \| [Viscoelasticity](https://en.wikipedia.org/wiki/Viscoelasticity "Viscoelasticity") [Rheometry](https://en.wikipedia.org/wiki/Rheometry "Rheometry") [Rheometer](https://en.wikipedia.org/wiki/Rheometer "Rheometer") \| \| [Smart fluids](https://en.wikipedia.org/wiki/Smart_fluid "Smart fluid") \| \| [Electrorheological](https://en.wikipedia.org/wiki/Electrorheological_fluid "Electrorheological fluid") [Magnetorheological](https://en.wikipedia.org/wiki/Magnetorheological_fluid "Magnetorheological fluid") [Ferrofluids](https://en.wikipedia.org/wiki/Ferrofluid "Ferrofluid") \| \| Scientists [Bernoulli](https://en.wikipedia.org/wiki/Daniel_Bernoulli "Daniel Bernoulli") [Boyle](https://en.wikipedia.org/wiki/Robert_Boyle "Robert Boyle") [Cauchy](https://en.wikipedia.org/wiki/Augustin-Louis_Cauchy "Augustin-Louis Cauchy") [Charles](https://en.wikipedia.org/wiki/Jacques_Charles "Jacques Charles") [Euler](https://en.wikipedia.org/wiki/Leonhard_Euler "Leonhard Euler") [Fick](https://en.wikipedia.org/wiki/Adolf_Eugen_Fick "Adolf Eugen Fick") [Gay-Lussac](https://en.wikipedia.org/wiki/Joseph_Louis_Gay-Lussac "Joseph Louis Gay-Lussac") [Graham](https://en.wikipedia.org/wiki/Thomas_Graham_\(chemist\) "Thomas Graham (chemist)") [Hooke](https://en.wikipedia.org/wiki/Robert_Hooke "Robert Hooke") [Newton](https://en.wikipedia.org/wiki/Isaac_Newton "Isaac Newton") [Navier](https://en.wikipedia.org/wiki/Claude-Louis_Navier "Claude-Louis Navier") [Noll](https://en.wikipedia.org/wiki/Walter_Noll "Walter Noll") [Pascal](https://en.wikipedia.org/wiki/Blaise_Pascal "Blaise Pascal") [Stokes](https://en.wikipedia.org/wiki/Sir_George_Stokes,_1st_Baronet "Sir George Stokes, 1st Baronet") [Truesdell](https://en.wikipedia.org/wiki/Clifford_Truesdell "Clifford Truesdell") \| \| [v](https://en.wikipedia.org/wiki/Template:Continuum_mechanics "Template:Continuum mechanics") [t](https://en.wikipedia.org/wiki/Template_talk:Continuum_mechanics "Template talk:Continuum mechanics") [e](https://en.wikipedia.org/wiki/Special:EditPage/Template:Continuum_mechanics "Special:EditPage/Template:Continuum mechanics") \| Hydrostatics is the branch of [fluid mechanics](https://en.wikipedia.org/wiki/Fluid_mechanics "Fluid mechanics") that studies [fluids](https://en.wikipedia.org/wiki/Fluid "Fluid") at [hydrostatic equilibrium](https://en.wikipedia.org/wiki/Hydrostatic_equilibrium "Hydrostatic equilibrium")[\[1\]](https://en.wikipedia.org/wiki/Hydrostatics#cite_note-1) and "the pressure in a fluid or exerted by a fluid on an immersed body".[\[2\]](https://en.wikipedia.org/wiki/Hydrostatics#cite_note-MW_dictionary_def-2) The word "hydrostatics" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether [compressible](https://en.wikipedia.org/wiki/Compressible_flow "Compressible flow") or [incompressible](https://en.wikipedia.org/wiki/Incompressible_flow "Incompressible flow"). It encompasses the study of the conditions under which fluids are at rest in [stable equilibrium](https://en.wikipedia.org/wiki/Mechanical_equilibrium "Mechanical equilibrium"). It is opposed to [fluid dynamics](https://en.wikipedia.org/wiki/Fluid_dynamics "Fluid dynamics"), the study of fluids in motion. Hydrostatics is fundamental to [hydraulics](https://en.wikipedia.org/wiki/Hydraulics "Hydraulics"), the [engineering](https://en.wikipedia.org/wiki/Engineering "Engineering") of equipment for storing, transporting and using fluids. It is also relevant to [geophysics](https://en.wikipedia.org/wiki/Geophysics "Geophysics") and [astrophysics](https://en.wikipedia.org/wiki/Astrophysics "Astrophysics") (for example, in understanding [plate tectonics](https://en.wikipedia.org/wiki/Plate_tectonics "Plate tectonics") and the anomalies of the [Earth's gravitational field](https://en.wikipedia.org/wiki/Gravity_of_Earth "Gravity of Earth")), to [meteorology](https://en.wikipedia.org/wiki/Meteorology "Meteorology"), to [medicine](https://en.wikipedia.org/wiki/Medicine "Medicine") (in the context of [blood pressure](https://en.wikipedia.org/wiki/Blood_pressure "Blood pressure")), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why [atmospheric pressure](https://en.wikipedia.org/wiki/Atmospheric_pressure "Atmospheric pressure") changes with [altitude](https://en.wikipedia.org/wiki/Altitude "Altitude"), why wood and oil float on water, and why the surface of still water is always [level](https://en.wikipedia.org/wiki/Water_level "Water level") according to the [curvature of the earth](https://en.wikipedia.org/wiki/Spherical_Earth "Spherical Earth"). ## History \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=1 "Edit section: History")\] Some principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, [cisterns](https://en.wikipedia.org/wiki/Cistern "Cistern"), [aqueducts](https://en.wikipedia.org/wiki/Aqueduct_\(water_supply\) "Aqueduct (water supply)") and [fountains](https://en.wikipedia.org/wiki/Fountain "Fountain"). [Archimedes](https://en.wikipedia.org/wiki/Archimedes "Archimedes") is credited with the discovery of [Archimedes' Principle](https://en.wikipedia.org/wiki/Archimedes%27_Principle "Archimedes' Principle"), which relates the [buoyancy](https://en.wikipedia.org/wiki/Buoyancy "Buoyancy") force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The [Roman](https://en.wikipedia.org/wiki/Roman_Empire "Roman Empire") engineer [Vitruvius](https://en.wikipedia.org/wiki/Vitruvius "Vitruvius") warned readers about [lead](https://en.wikipedia.org/wiki/Lead "Lead") pipes bursting under hydrostatic pressure.[\[3\]](https://en.wikipedia.org/wiki/Hydrostatics#cite_note-VitruviusVIII.6-3) The concept of pressure and the way it is transmitted by fluids was formulated by the [French](https://en.wikipedia.org/wiki/France "France") [mathematician](https://en.wikipedia.org/wiki/Mathematician "Mathematician") and [philosopher](https://en.wikipedia.org/wiki/Philosopher "Philosopher") [Blaise Pascal](https://en.wikipedia.org/wiki/Blaise_Pascal "Blaise Pascal") in 1647.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] ## Hydrostatics in ancient Greece and Rome \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=2 "Edit section: Hydrostatics in ancient Greece and Rome")\] ### Pythagorean Cup \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=3 "Edit section: Pythagorean Cup")\] Main article: [Pythagorean cup](https://en.wikipedia.org/wiki/Pythagorean_cup "Pythagorean cup") The "fair cup" or [Pythagorean cup](https://en.wikipedia.org/wiki/Pythagorean_cup "Pythagorean cup"), which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] The cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied. ### Heron's fountain \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=4 "Edit section: Heron's fountain")\] Main article: [Heron's fountain](https://en.wikipedia.org/wiki/Heron%27s_fountain "Heron's fountain") [Heron's fountain](https://en.wikipedia.org/wiki/Heron%27s_fountain "Heron's fountain") is a device invented by [Heron of Alexandria](https://en.wikipedia.org/wiki/Heron_of_Alexandria "Heron of Alexandria") that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several [cannula](https://en.wikipedia.org/wiki/Cannula "Cannula") (a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] ## Pascal's contribution in hydrostatics \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=5 "Edit section: Pascal's contribution in hydrostatics")\] Main article: [Pascal's law](https://en.wikipedia.org/wiki/Pascal%27s_law "Pascal's law") Pascal made contributions to developments in both hydrostatics and hydrodynamics. [Pascal's law](https://en.wikipedia.org/wiki/Pascal%27s_law "Pascal's law") is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed. ## Liquids (fluids with free surfaces) \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=6 "Edit section: Liquids (fluids with free surfaces)")\] Liquids can have [free surfaces](https://en.wikipedia.org/wiki/Free_surface "Free surface") at which they interface with gases, or with a [vacuum](https://en.wikipedia.org/wiki/Vacuum "Vacuum"). In general, the lack of the ability to sustain a [shear stress](https://en.wikipedia.org/wiki/Shear_stress "Shear stress") entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from [surface tension](https://en.wikipedia.org/wiki/Surface_tension "Surface tension"). ### Capillary action \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=7 "Edit section: Capillary action")\] When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, [surface tension](https://en.wikipedia.org/wiki/Surface_tension "Surface tension") effects become important leading to the formation of a [meniscus](https://en.wikipedia.org/wiki/Meniscus_\(liquid\) "Meniscus (liquid)") through [capillary action](https://en.wikipedia.org/wiki/Capillary_action "Capillary action"). This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in [plant](https://en.wikipedia.org/wiki/Plant "Plant") [xylem](https://en.wikipedia.org/wiki/Xylem "Xylem"), the [transpirational pull](https://en.wikipedia.org/wiki/Transpirational_pull "Transpirational pull"). ### Hanging drops \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=8 "Edit section: Hanging drops")\] Without surface tension, [drops](https://en.wikipedia.org/wiki/Drop_\(liquid\) "Drop (liquid)") would not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid. ## See also \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=9 "Edit section: See also")\] - [Communicating vessels](https://en.wikipedia.org/wiki/Communicating_vessels "Communicating vessels") – Set of internally connected containers containing a homogeneous fluid - [D-DIA](https://en.wikipedia.org/wiki/D-DIA "D-DIA") – Apparatus used for high pressure and high temperature deformation experiments - [Hydrostatic pressure](https://en.wikipedia.org/wiki/Hydrostatic_pressure "Hydrostatic pressure") – Physical quantity - [Hydrostatic test](https://en.wikipedia.org/wiki/Hydrostatic_test "Hydrostatic test") – Non-destructive test of pressure vessels - [Triaxial shear test](https://en.wikipedia.org/wiki/Triaxial_shear_test "Triaxial shear test") – Stress test with different levels of stress in each perpendicular direction ## References \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=10 "Edit section: References")\] 1. [^](https://en.wikipedia.org/wiki/Hydrostatics#cite_ref-1) ["Fluid Mechanics/Fluid Statics/Fundamentals of Fluid Statics - Wikibooks, open books for an open world"](https://en.wikibooks.org/wiki/Fluid_Mechanics/Fluid_Statics/Fundamentals_of_Fluid_Statics#Hydrostatic_Equilibrium). en.wikibooks.org. Retrieved 2021-04-01. 2. [^](https://en.wikipedia.org/wiki/Hydrostatics#cite_ref-MW_dictionary_def_2-0) ["Hydrostatics"](https://www.merriam-webster.com/dictionary/hydrostatics). Merriam-Webster. Retrieved 11 September 2018. 3. [^](https://en.wikipedia.org/wiki/Hydrostatics#cite_ref-VitruviusVIII.6_3-0) Marcus Vitruvius Pollio (ca. 15 BCE), ["The Ten Books of Architecture"](https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/8.html), Book VIII, Chapter 6. At the University of Chicago's Penelope site. Accessed on 2013-02-25. ## Further reading \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=11 "Edit section: Further reading")\] - Batchelor, George K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-521-66396-2](https://en.wikipedia.org/wiki/Special:BookSources/0-521-66396-2 "Special:BookSources/0-521-66396-2") . - Falkovich, Gregory (2011). Fluid Mechanics (A short course for physicists). Cambridge University Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-1-107-00575-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-107-00575-4 "Special:BookSources/978-1-107-00575-4") . - Kundu, Pijush K.; Cohen, Ira M. (2008). Fluid Mechanics* (4th rev. ed.). Academic Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-0-12-373735-9](https://en.wikipedia.org/wiki/Special:BookSources/978-0-12-373735-9 "Special:BookSources/978-0-12-373735-9") . - Currie, I. G. (1974). Fundamental Mechanics of Fluids. McGraw-Hill. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-07-015000-1](https://en.wikipedia.org/wiki/Special:BookSources/0-07-015000-1 "Special:BookSources/0-07-015000-1") . - Massey, B.; Ward-Smith, J. (2005). Mechanics of Fluids (8th ed.). Taylor & Francis. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-0-415-36206-1](https://en.wikipedia.org/wiki/Special:BookSources/978-0-415-36206-1 "Special:BookSources/978-0-415-36206-1") . - White, Frank M. (2003). Fluid Mechanics. McGraw–Hill. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-07-240217-2](https://en.wikipedia.org/wiki/Special:BookSources/0-07-240217-2 "Special:BookSources/0-07-240217-2") . ## External links \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=12 "Edit section: External links")\] [![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png)](https://en.wikipedia.org/wiki/File:Wiktionary-logo-en-v2.svg) Look up *[hydrostatics](https://en.wiktionary.org/wiki/hydrostatics "wiktionary:hydrostatics")* in Wiktionary, the free dictionary. - [The Flow of Dry Water - The Feynman Lectures on Physics](https://www.feynmanlectures.caltech.edu/II_40.html) \| [v](https://en.wikipedia.org/wiki/Template:Branches_of_physics "Template:Branches of physics") [t](https://en.wikipedia.org/wiki/Template_talk:Branches_of_physics "Template talk:Branches of physics") 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Readable Markdown	From Wikipedia, the free encyclopedia [![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg/250px-Table_of_Hydraulics_and_Hydrostatics%2C_Cyclopaedia%2C_Volume_1.jpg)](https://en.wikipedia.org/wiki/File:Table_of_Hydraulics_and_Hydrostatics,_Cyclopaedia,_Volume_1.jpg) Table of Hydraulics and Hydrostatics, from the 1728 [Cyclopædia](https://en.wikipedia.org/wiki/Cyclop%C3%A6dia,_or_an_Universal_Dictionary_of_Arts_and_Sciences "Cyclopædia, or an Universal Dictionary of Arts and Sciences") Hydrostatics is the branch of [fluid mechanics](https://en.wikipedia.org/wiki/Fluid_mechanics "Fluid mechanics") that studies [fluids](https://en.wikipedia.org/wiki/Fluid "Fluid") at [hydrostatic equilibrium](https://en.wikipedia.org/wiki/Hydrostatic_equilibrium "Hydrostatic equilibrium")[\[1\]](https://en.wikipedia.org/wiki/Hydrostatics#cite_note-1) and "the pressure in a fluid or exerted by a fluid on an immersed body".[\[2\]](https://en.wikipedia.org/wiki/Hydrostatics#cite_note-MW_dictionary_def-2) The word "hydrostatics" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether [compressible](https://en.wikipedia.org/wiki/Compressible_flow "Compressible flow") or [incompressible](https://en.wikipedia.org/wiki/Incompressible_flow "Incompressible flow"). It encompasses the study of the conditions under which fluids are at rest in [stable equilibrium](https://en.wikipedia.org/wiki/Mechanical_equilibrium "Mechanical equilibrium"). It is opposed to [fluid dynamics](https://en.wikipedia.org/wiki/Fluid_dynamics "Fluid dynamics"), the study of fluids in motion. Hydrostatics is fundamental to [hydraulics](https://en.wikipedia.org/wiki/Hydraulics "Hydraulics"), the [engineering](https://en.wikipedia.org/wiki/Engineering "Engineering") of equipment for storing, transporting and using fluids. It is also relevant to [geophysics](https://en.wikipedia.org/wiki/Geophysics "Geophysics") and [astrophysics](https://en.wikipedia.org/wiki/Astrophysics "Astrophysics") (for example, in understanding [plate tectonics](https://en.wikipedia.org/wiki/Plate_tectonics "Plate tectonics") and the anomalies of the [Earth's gravitational field](https://en.wikipedia.org/wiki/Gravity_of_Earth "Gravity of Earth")), to [meteorology](https://en.wikipedia.org/wiki/Meteorology "Meteorology"), to [medicine](https://en.wikipedia.org/wiki/Medicine "Medicine") (in the context of [blood pressure](https://en.wikipedia.org/wiki/Blood_pressure "Blood pressure")), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why [atmospheric pressure](https://en.wikipedia.org/wiki/Atmospheric_pressure "Atmospheric pressure") changes with [altitude](https://en.wikipedia.org/wiki/Altitude "Altitude"), why wood and oil float on water, and why the surface of still water is always [level](https://en.wikipedia.org/wiki/Water_level "Water level") according to the [curvature of the earth](https://en.wikipedia.org/wiki/Spherical_Earth "Spherical Earth"). Some principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, [cisterns](https://en.wikipedia.org/wiki/Cistern "Cistern"), [aqueducts](https://en.wikipedia.org/wiki/Aqueduct_\(water_supply\) "Aqueduct (water supply)") and [fountains](https://en.wikipedia.org/wiki/Fountain "Fountain"). [Archimedes](https://en.wikipedia.org/wiki/Archimedes "Archimedes") is credited with the discovery of [Archimedes' Principle](https://en.wikipedia.org/wiki/Archimedes%27_Principle "Archimedes' Principle"), which relates the [buoyancy](https://en.wikipedia.org/wiki/Buoyancy "Buoyancy") force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The [Roman](https://en.wikipedia.org/wiki/Roman_Empire "Roman Empire") engineer [Vitruvius](https://en.wikipedia.org/wiki/Vitruvius "Vitruvius") warned readers about [lead](https://en.wikipedia.org/wiki/Lead "Lead") pipes bursting under hydrostatic pressure.[\[3\]](https://en.wikipedia.org/wiki/Hydrostatics#cite_note-VitruviusVIII.6-3) The concept of pressure and the way it is transmitted by fluids was formulated by the [French](https://en.wikipedia.org/wiki/France "France") [mathematician](https://en.wikipedia.org/wiki/Mathematician "Mathematician") and [philosopher](https://en.wikipedia.org/wiki/Philosopher "Philosopher") [Blaise Pascal](https://en.wikipedia.org/wiki/Blaise_Pascal "Blaise Pascal") in 1647.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] ## Hydrostatics in ancient Greece and Rome \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=2 "Edit section: Hydrostatics in ancient Greece and Rome")\] The "fair cup" or [Pythagorean cup](https://en.wikipedia.org/wiki/Pythagorean_cup "Pythagorean cup"), which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] The cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied. [Heron's fountain](https://en.wikipedia.org/wiki/Heron%27s_fountain "Heron's fountain") is a device invented by [Heron of Alexandria](https://en.wikipedia.org/wiki/Heron_of_Alexandria "Heron of Alexandria") that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several [cannula](https://en.wikipedia.org/wiki/Cannula "Cannula") (a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir.\[[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed "Wikipedia:Citation needed")\] ## Pascal's contribution in hydrostatics \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=5 "Edit section: Pascal's contribution in hydrostatics")\] Pascal made contributions to developments in both hydrostatics and hydrodynamics. [Pascal's law](https://en.wikipedia.org/wiki/Pascal%27s_law "Pascal's law") is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed. ## Liquids (fluids with free surfaces) \[[edit](https://en.wikipedia.org/w/index.php?title=Hydrostatics&action=edit&section=6 "Edit section: Liquids (fluids with free surfaces)")\] Liquids can have [free surfaces](https://en.wikipedia.org/wiki/Free_surface "Free surface") at which they interface with gases, or with a [vacuum](https://en.wikipedia.org/wiki/Vacuum "Vacuum"). In general, the lack of the ability to sustain a [shear stress](https://en.wikipedia.org/wiki/Shear_stress "Shear stress") entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from [surface tension](https://en.wikipedia.org/wiki/Surface_tension "Surface tension"). When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, [surface tension](https://en.wikipedia.org/wiki/Surface_tension "Surface tension") effects become important leading to the formation of a [meniscus](https://en.wikipedia.org/wiki/Meniscus_\(liquid\) "Meniscus (liquid)") through [capillary action](https://en.wikipedia.org/wiki/Capillary_action "Capillary action"). This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in [plant](https://en.wikipedia.org/wiki/Plant "Plant") [xylem](https://en.wikipedia.org/wiki/Xylem "Xylem"), the [transpirational pull](https://en.wikipedia.org/wiki/Transpirational_pull "Transpirational pull"). Without surface tension, [drops](https://en.wikipedia.org/wiki/Drop_\(liquid\) "Drop (liquid)") would not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid. - [Communicating vessels](https://en.wikipedia.org/wiki/Communicating_vessels "Communicating vessels") – Set of internally connected containers containing a homogeneous fluid - [D-DIA](https://en.wikipedia.org/wiki/D-DIA "D-DIA") – Apparatus used for high pressure and high temperature deformation experiments - [Hydrostatic pressure](https://en.wikipedia.org/wiki/Hydrostatic_pressure "Hydrostatic pressure") – Physical quantity - [Hydrostatic test](https://en.wikipedia.org/wiki/Hydrostatic_test "Hydrostatic test") – Non-destructive test of pressure vessels - [Triaxial shear test](https://en.wikipedia.org/wiki/Triaxial_shear_test "Triaxial shear test") – Stress test with different levels of stress in each perpendicular direction 1. [^](https://en.wikipedia.org/wiki/Hydrostatics#cite_ref-1) ["Fluid Mechanics/Fluid Statics/Fundamentals of Fluid Statics - Wikibooks, open books for an open world"](https://en.wikibooks.org/wiki/Fluid_Mechanics/Fluid_Statics/Fundamentals_of_Fluid_Statics#Hydrostatic_Equilibrium). en.wikibooks.org. Retrieved 2021-04-01. 2. [^](https://en.wikipedia.org/wiki/Hydrostatics#cite_ref-MW_dictionary_def_2-0) ["Hydrostatics"](https://www.merriam-webster.com/dictionary/hydrostatics). Merriam-Webster. Retrieved 11 September 2018. 3. [^](https://en.wikipedia.org/wiki/Hydrostatics#cite_ref-VitruviusVIII.6_3-0) Marcus Vitruvius Pollio (ca. 15 BCE), ["The Ten Books of Architecture"](https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/8.html), Book VIII, Chapter 6. At the University of Chicago's Penelope site. Accessed on 2013-02-25. - Batchelor, George K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-521-66396-2](https://en.wikipedia.org/wiki/Special:BookSources/0-521-66396-2 "Special:BookSources/0-521-66396-2") . - Falkovich, Gregory (2011). Fluid Mechanics (A short course for physicists). Cambridge University Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-1-107-00575-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-107-00575-4 "Special:BookSources/978-1-107-00575-4") . - Kundu, Pijush K.; Cohen, Ira M. (2008). Fluid Mechanics* (4th rev. ed.). Academic Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-0-12-373735-9](https://en.wikipedia.org/wiki/Special:BookSources/978-0-12-373735-9 "Special:BookSources/978-0-12-373735-9") . - Currie, I. G. (1974). Fundamental Mechanics of Fluids. McGraw-Hill. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-07-015000-1](https://en.wikipedia.org/wiki/Special:BookSources/0-07-015000-1 "Special:BookSources/0-07-015000-1") . - Massey, B.; Ward-Smith, J. (2005). Mechanics of Fluids (8th ed.). Taylor & Francis. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-0-415-36206-1](https://en.wikipedia.org/wiki/Special:BookSources/978-0-415-36206-1 "Special:BookSources/978-0-415-36206-1") . - White, Frank M. (2003). Fluid Mechanics. McGraw–Hill. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-07-240217-2](https://en.wikipedia.org/wiki/Special:BookSources/0-07-240217-2 "Special:BookSources/0-07-240217-2") . - [The Flow of Dry Water - The Feynman Lectures on Physics](https://www.feynmanlectures.caltech.edu/II_40.html)
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