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class="vector-toc-link" href="#The_Alexandrian_school"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>The Alexandrian school</span> </div> </a> <ul id="toc-The_Alexandrian_school-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sextus_Julius_Frontinus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sextus_Julius_Frontinus"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Sextus Julius Frontinus</span> </div> </a> <ul id="toc-Sextus_Julius_Frontinus-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Middle_Ages" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Middle_Ages"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Middle Ages</span> </div> </a> <button aria-controls="toc-Middle_Ages-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Middle Ages subsection</span> </button> <ul id="toc-Middle_Ages-sublist" class="vector-toc-list"> <li id="toc-Islamicate_physicists" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Islamicate_physicists"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Islamicate physicists</span> </div> </a> <ul id="toc-Islamicate_physicists-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Islamicate_engineers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Islamicate_engineers"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Islamicate engineers</span> </div> </a> <ul id="toc-Islamicate_engineers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sixteenth_and_seventeenth_century" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Sixteenth_and_seventeenth_century"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Sixteenth and seventeenth century</span> </div> </a> <button aria-controls="toc-Sixteenth_and_seventeenth_century-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Sixteenth and seventeenth century subsection</span> </button> <ul id="toc-Sixteenth_and_seventeenth_century-sublist" class="vector-toc-list"> <li id="toc-Leonardo_da_Vinci" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Leonardo_da_Vinci"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Leonardo da Vinci</span> </div> </a> <ul id="toc-Leonardo_da_Vinci-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simon_Stevin" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simon_Stevin"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Simon Stevin</span> </div> </a> <ul id="toc-Simon_Stevin-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Castelli_and_Torricelli" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Castelli_and_Torricelli"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Castelli and Torricelli</span> </div> </a> <ul id="toc-Castelli_and_Torricelli-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Blaise_Pascal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Blaise_Pascal"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Blaise Pascal</span> </div> </a> <ul id="toc-Blaise_Pascal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mariotte_and_Guglielmini" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mariotte_and_Guglielmini"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Mariotte and Guglielmini</span> </div> </a> <ul id="toc-Mariotte_and_Guglielmini-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Eighteenth_century" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Eighteenth_century"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Eighteenth century</span> </div> </a> <button aria-controls="toc-Eighteenth_century-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Eighteenth century subsection</span> </button> <ul id="toc-Eighteenth_century-sublist" class="vector-toc-list"> <li id="toc-Studies_by_Isaac_Newton" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Studies_by_Isaac_Newton"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Studies by Isaac Newton</span> </div> </a> <ul id="toc-Studies_by_Isaac_Newton-sublist" class="vector-toc-list"> <li id="toc-Friction_and_viscosity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Friction_and_viscosity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Friction and viscosity</span> </div> </a> <ul id="toc-Friction_and_viscosity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Orifices" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Orifices"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2</span> <span>Orifices</span> </div> </a> <ul id="toc-Orifices-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Waves" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Waves"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.3</span> <span>Waves</span> </div> </a> <ul id="toc-Waves-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Daniel_Bernoulli" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Daniel_Bernoulli"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Daniel Bernoulli</span> </div> </a> <ul id="toc-Daniel_Bernoulli-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jean_le_Rond_d'Alembert" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Jean_le_Rond_d'Alembert"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Jean le Rond d'Alembert</span> </div> </a> <ul id="toc-Jean_le_Rond_d'Alembert-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Leonhard_Euler" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Leonhard_Euler"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Leonhard Euler</span> </div> </a> <ul id="toc-Leonhard_Euler-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pierre_Louis_Georges_Dubuat" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pierre_Louis_Georges_Dubuat"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Pierre Louis Georges Dubuat</span> </div> </a> <ul id="toc-Pierre_Louis_Georges_Dubuat-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Nineteenth_century" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Nineteenth_century"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Nineteenth century</span> </div> </a> <button aria-controls="toc-Nineteenth_century-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Nineteenth century subsection</span> </button> <ul id="toc-Nineteenth_century-sublist" class="vector-toc-list"> <li id="toc-Claude-Louis_Navier_and_George_Gabriel_Stokes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Claude-Louis_Navier_and_George_Gabriel_Stokes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Claude-Louis Navier and George Gabriel Stokes</span> </div> </a> <ul id="toc-Claude-Louis_Navier_and_George_Gabriel_Stokes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hermann_von_Helmholtz" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hermann_von_Helmholtz"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Hermann von Helmholtz</span> </div> </a> <ul id="toc-Hermann_von_Helmholtz-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gaspard_Riche_de_Prony" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gaspard_Riche_de_Prony"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Gaspard Riche de Prony</span> </div> </a> <ul id="toc-Gaspard_Riche_de_Prony-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Johann_Albert_Eytelwein" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Johann_Albert_Eytelwein"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Johann Albert Eytelwein</span> </div> </a> <ul id="toc-Johann_Albert_Eytelwein-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jean_Nicolas_Pierre_Hachette_and_others" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Jean_Nicolas_Pierre_Hachette_and_others"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Jean Nicolas Pierre Hachette and others</span> </div> </a> <ul id="toc-Jean_Nicolas_Pierre_Hachette_and_others-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Andreas_Rudolf_Harlacher_and_others" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Andreas_Rudolf_Harlacher_and_others"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Andreas Rudolf Harlacher and others</span> </div> </a> <ul id="toc-Andreas_Rudolf_Harlacher_and_others-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Twentieth_century" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Twentieth_century"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Twentieth century</span> </div> </a> <button aria-controls="toc-Twentieth_century-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Twentieth century subsection</span> </button> <ul id="toc-Twentieth_century-sublist" class="vector-toc-list"> <li id="toc-Ludwig_Prandtl" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ludwig_Prandtl"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Ludwig Prandtl</span> </div> </a> <ul id="toc-Ludwig_Prandtl-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Developments_in_vortex_dynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Developments_in_vortex_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Developments in vortex dynamics</span> </div> </a> <ul id="toc-Developments_in_vortex_dynamics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" 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.tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:242px;max-width:242px"><div class="trow"><div class="theader" style="text-align:center">Pioneers of fluid mechanics</div></div><div class="trow"><div class="tsingle" style="width:120px;max-width:120px"><div class="thumbimage" style="height:155px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Retrato_de_un_erudito_(%C2%BFArqu%C3%ADmedes%3F),_por_Domenico_Fetti.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Retrato_de_un_erudito_%28%C2%BFArqu%C3%ADmedes%3F%29%2C_por_Domenico_Fetti.jpg/118px-Retrato_de_un_erudito_%28%C2%BFArqu%C3%ADmedes%3F%29%2C_por_Domenico_Fetti.jpg" decoding="async" width="118" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Retrato_de_un_erudito_%28%C2%BFArqu%C3%ADmedes%3F%29%2C_por_Domenico_Fetti.jpg/177px-Retrato_de_un_erudito_%28%C2%BFArqu%C3%ADmedes%3F%29%2C_por_Domenico_Fetti.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Retrato_de_un_erudito_%28%C2%BFArqu%C3%ADmedes%3F%29%2C_por_Domenico_Fetti.jpg/236px-Retrato_de_un_erudito_%28%C2%BFArqu%C3%ADmedes%3F%29%2C_por_Domenico_Fetti.jpg 2x" data-file-width="756" data-file-height="1000" /></a></span></div><div class="thumbcaption text-align-center"><a href="/wiki/Archimedes" title="Archimedes">Archimedes</a></div></div><div class="tsingle" style="width:118px;max-width:118px"><div class="thumbimage" style="height:155px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Evangelista_Torricelli_by_Lorenzo_Lippi_(circa_1647,_Galleria_Silvano_Lodi_%26_Due).jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Evangelista_Torricelli_by_Lorenzo_Lippi_%28circa_1647%2C_Galleria_Silvano_Lodi_%26_Due%29.jpg/116px-Evangelista_Torricelli_by_Lorenzo_Lippi_%28circa_1647%2C_Galleria_Silvano_Lodi_%26_Due%29.jpg" decoding="async" width="116" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Evangelista_Torricelli_by_Lorenzo_Lippi_%28circa_1647%2C_Galleria_Silvano_Lodi_%26_Due%29.jpg/174px-Evangelista_Torricelli_by_Lorenzo_Lippi_%28circa_1647%2C_Galleria_Silvano_Lodi_%26_Due%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Evangelista_Torricelli_by_Lorenzo_Lippi_%28circa_1647%2C_Galleria_Silvano_Lodi_%26_Due%29.jpg/232px-Evangelista_Torricelli_by_Lorenzo_Lippi_%28circa_1647%2C_Galleria_Silvano_Lodi_%26_Due%29.jpg 2x" data-file-width="2685" data-file-height="3608" /></a></span></div><div class="thumbcaption text-align-center"><a href="/wiki/Evangelista_Torricelli" title="Evangelista Torricelli">Evangelista Torricelli</a></div></div></div><div class="trow"><div class="tsingle" style="width:123px;max-width:123px"><div class="thumbimage" style="height:144px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Blaise_Pascal_Versailles.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Blaise_Pascal_Versailles.JPG/121px-Blaise_Pascal_Versailles.JPG" decoding="async" width="121" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Blaise_Pascal_Versailles.JPG/182px-Blaise_Pascal_Versailles.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Blaise_Pascal_Versailles.JPG/242px-Blaise_Pascal_Versailles.JPG 2x" data-file-width="2365" data-file-height="2817" /></a></span></div><div class="thumbcaption text-align-center"><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Blaise Pascal</a></div></div><div class="tsingle" style="width:115px;max-width:115px"><div class="thumbimage" style="height:144px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Portr%C3%A4t_des_Daniel_Bernoulli.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Portr%C3%A4t_des_Daniel_Bernoulli.jpg/113px-Portr%C3%A4t_des_Daniel_Bernoulli.jpg" decoding="async" width="113" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Portr%C3%A4t_des_Daniel_Bernoulli.jpg/170px-Portr%C3%A4t_des_Daniel_Bernoulli.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Portr%C3%A4t_des_Daniel_Bernoulli.jpg/226px-Portr%C3%A4t_des_Daniel_Bernoulli.jpg 2x" data-file-width="2289" data-file-height="2916" /></a></span></div><div class="thumbcaption text-align-center"><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a></div></div></div></div></div> <p>The <b>history of <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a></b> is a fundamental strand of the <a href="/wiki/History_of_physics" title="History of physics">history of physics</a> and <a href="/wiki/Engineering" title="Engineering">engineering</a>. The study of the movement of <a href="/wiki/Fluid" title="Fluid">fluids</a> (liquids and gases) and the <a href="/wiki/Force" title="Force">forces</a> that act upon them dates back to pre-history. The field has undergone a continuous evolution, driven by human dependence on water, <a href="/wiki/Meteorology" title="Meteorology">meteorological conditions</a>, and internal biological processes. </p><p>The success of early <a href="/wiki/Civilization" title="Civilization">civilizations</a>, can be attributed to developments in the understanding of water dynamics, allowing for the construction of canals and aqueducts for water distribution and farm irrigation, as well as maritime transport. Due to its conceptual complexity, most discoveries in this field relied almost entirely on experiments, at least until the development of advanced understanding of <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a> and computational methods. Significant theoretical contributions were made by notables figures like <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a>, <a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a> and his son <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a>, <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>, <a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Claude-Louis Navier</a> and <a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">Stokes</a>, who developed the fundamental equations to describe fluid mechanics. Advancements in experimentation and computational methods have further propelled the field, leading to practical applications in more specialized industries ranging from aerospace to environmental engineering. Fluid mechanics has also been important for the study of <a href="/wiki/Astronomical_object" title="Astronomical object">astronomical bodies</a> and the dynamics of galaxies. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Antiquity">Antiquity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=1" title="Edit section: Antiquity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Pre-history">Pre-history</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=2" title="Edit section: Pre-history"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A pragmatic, if not scientific, knowledge of fluid flow was exhibited by ancient civilizations, such as in the design of arrows, spears, boats, and particularly hydraulic engineering projects for flood protection, irrigation, drainage, and water supply.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The earliest human <a href="/wiki/Cradle_of_Civilization" class="mw-redirect" title="Cradle of Civilization">civilizations</a> began near the shores of rivers, and consequently coincided with the dawn of <a href="/wiki/Hydrology" title="Hydrology">hydrology</a>, <a href="/wiki/Hydraulics" title="Hydraulics">hydraulics</a>, and <a href="/wiki/Hydraulic_engineering" title="Hydraulic engineering">hydraulic engineering</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Ancient_China">Ancient China</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=3" title="Edit section: Ancient China"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Observations of specific gravity and <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> were recorded by ancient Chinese philosophers. In the 4th century BCE <a href="/wiki/Mencius" title="Mencius">Mencius</a> describes the weight of the gold is equivalent to the feathers. In 3rd century CE, <a href="/wiki/Cao_Chong" title="Cao Chong">Cao Chong</a> describes the story of weighing the elephant by observing displacement of the boats loaded with different weights.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Archimedes">Archimedes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=4" title="Edit section: Archimedes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Buoyancy.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Buoyancy.svg/220px-Buoyancy.svg.png" decoding="async" width="220" height="276" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Buoyancy.svg/330px-Buoyancy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Buoyancy.svg/440px-Buoyancy.svg.png 2x" data-file-width="300" data-file-height="376" /></a><figcaption>The forces at work in <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> as discovered by Archimedes. Note that the object is floating because the upward force of buoyancy is equal to the downward force of <a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">gravity</a>.</figcaption></figure> <p>The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work <i><a href="/wiki/On_Floating_Bodies" title="On Floating Bodies">On Floating Bodies</a></i> (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: <span lang="grc">Περὶ τῶν ὀχουμένων</span>), around 250 BC. In it, Archimedes develops the law of buoyancy, also known as <a href="/wiki/Archimedes%27_Principle" class="mw-redirect" title="Archimedes' Principle">Archimedes' principle</a>. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Archimedes maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direction; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium.<sup id="cite_ref-EB1911_4-0" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="The_Alexandrian_school">The Alexandrian school</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=5" title="Edit section: The Alexandrian school"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the Greek school at <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>, which flourished under the auspices of the <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemies</a>, attempts were made at the construction of hydraulic machinery, and about 120 BC the fountain of compression, the <a href="/wiki/Siphon" title="Siphon">siphon</a>, and the <a href="/wiki/Force_pump" class="mw-redirect" title="Force pump">forcing-pump</a> were invented by <a href="/wiki/Ctesibius" title="Ctesibius">Ctesibius</a> and <a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Hero</a>. The siphon is a simple instrument; but the forcing-pump is a complicated invention, which could scarcely have been expected in the infancy of hydraulics. It was probably suggested to Ctesibius by the <a href="/wiki/Egyptian_wheel" class="mw-redirect" title="Egyptian wheel">Egyptian wheel</a> or <a href="/wiki/Noria" title="Noria">Noria</a>, which was common at that time, and which was a kind of chain pump, consisting of a number of earthen pots carried round by a wheel. In some of these machines the pots have a valve in the bottom which enables them to descend without much resistance, and diminishes greatly the load upon the wheel; and, if we suppose that this valve was introduced so early as the time of Ctesibius, it is not difficult to perceive how such a machine might have led to the invention of the forcing-pump.<sup id="cite_ref-EB1911_4-1" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Sextus_Julius_Frontinus">Sextus Julius Frontinus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=6" title="Edit section: Sextus Julius Frontinus"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Notwithstanding these inventions of the Alexandrian school, its attention does not seem to have been directed to the motion of fluids; and the first attempt to investigate this subject was made by <a href="/wiki/Sextus_Julius_Frontinus" class="mw-redirect" title="Sextus Julius Frontinus">Sextus Julius Frontinus</a>, inspector of the public fountains at <a href="/wiki/Rome" title="Rome">Rome</a> in the reigns of <a href="/wiki/Nerva" title="Nerva">Nerva</a> and <a href="/wiki/Trajan" title="Trajan">Trajan</a>. In his work <i>De aquaeductibus urbis Romae commentarius</i>, he considers the methods which were at that time employed for ascertaining the quantity of water discharged from ajutages (tubes), and the mode of distributing the waters of an <a href="/wiki/Aqueduct_(water_supply)" title="Aqueduct (water supply)">aqueduct</a> or a <a href="/wiki/Fountain" title="Fountain">fountain</a>. He remarked that the flow of water from an orifice depends not only on the magnitude of the orifice itself, but also on the height of the water in the reservoir; and that a pipe employed to carry off a portion of water from an aqueduct should, as circumstances required, have a position more or less inclined to the original direction of the current. But as he was unacquainted with the law of the velocities of running water as depending upon the depth of the orifice, the want of precision which appears in his results is not surprising.<sup id="cite_ref-EB1911_4-2" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Middle_Ages">Middle Ages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=7" title="Edit section: Middle Ages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Cite_check plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>may contain <a href="/wiki/Wikipedia:CITE" class="mw-redirect" title="Wikipedia:CITE">citations</a> that do not <a href="/wiki/Wikipedia:V" class="mw-redirect" title="Wikipedia:V">verify</a> the text</b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=History_of_fluid_mechanics&action=edit">check for citation inaccuracies</a>.</span> <span class="date-container"><i>(<span class="date">September 2010</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Islamicate_physicists">Islamicate physicists</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=8" title="Edit section: Islamicate physicists"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Physics_in_the_medieval_Islamic_world" title="Physics in the medieval Islamic world">Physics in the medieval Islamic world</a></div> <p><a href="/wiki/Science_in_medieval_Islam" class="mw-redirect" title="Science in medieval Islam">Islamicate scientists</a>, particularly <a href="/wiki/Abu_Rayhan_Biruni" class="mw-redirect" title="Abu Rayhan Biruni">Abu Rayhan Biruni</a> (973–1048) and later <a href="/wiki/Al-Khazini" title="Al-Khazini">Al-Khazini</a> (fl. 1115–1130), were the first to apply <a href="/wiki/Experiment" title="Experiment">experimental</a> <a href="/wiki/Scientific_method" title="Scientific method">scientific methods</a> to fluid mechanics, especially in the field of <a href="/wiki/Fluid_statics" class="mw-redirect" title="Fluid statics">fluid statics</a>, such as for determining <a href="/wiki/Specific_weight" title="Specific weight">specific weights</a>. They applied the mathematical theories of <a href="/wiki/Ratio" title="Ratio">ratios</a> and <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimal</a> techniques, and introduced <a href="/wiki/Algebra" title="Algebra">algebraic</a> and fine <a href="/wiki/Calculation" title="Calculation">calculation</a> techniques into the field of fluid statics.<sup id="cite_ref-Rozhanskaya-642_5-0" class="reference"><a href="#cite_note-Rozhanskaya-642-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Biruni introduced the method of <a href="/wiki/Test_method" title="Test method">checking tests</a> during experiments and measured the <a href="/wiki/Weight" title="Weight">weights</a> of various liquids. He also recorded the differences in weight between <a href="/wiki/Freshwater" class="mw-redirect" title="Freshwater">freshwater</a> and <a href="/wiki/Saline_water" title="Saline water">saline water</a>, and between hot water and cold water.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2010)">citation needed</span></a></i>]</sup> During his experiments on fluid mechanics, Biruni invented the <a href="/wiki/Conical_measure" title="Conical measure">conical measure</a>,<sup id="cite_ref-Marshall_Clagett_1961_p._64_6-0" class="reference"><a href="#cite_note-Marshall_Clagett_1961_p._64-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> in order to find the ratio between the <a href="/wiki/Weight" title="Weight">weight</a> of a substance in air and the weight of water displaced.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2010)">citation needed</span></a></i>]</sup> </p><p>Al-Khazini, in <i>The Book of the Balance of Wisdom</i> (1121), invented a <a href="/wiki/Hydrostatic_equilibrium" title="Hydrostatic equilibrium">hydrostatic balance</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Islamicate_engineers">Islamicate engineers</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=9" title="Edit section: Islamicate engineers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_inventions_in_the_medieval_Islamic_world" title="List of inventions in the medieval Islamic world">List of inventions in the medieval Islamic world</a></div> <p>In the 9th century, <a href="/wiki/Ban%C5%AB_M%C5%ABs%C4%81" class="mw-redirect" title="Banū Mūsā">Banū Mūsā</a> brothers' <i><a href="/wiki/Book_of_Ingenious_Devices" title="Book of Ingenious Devices">Book of Ingenious Devices</a></i> described a number of early <a href="/wiki/Automatic_control" class="mw-redirect" title="Automatic control">automatic controls</a> in fluid mechanics.<sup id="cite_ref-Hassan_8-0" class="reference"><a href="#cite_note-Hassan-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Two-step level controls for fluids, an early form of discontinuous <a href="/wiki/Variable_structure_control" title="Variable structure control">variable structure controls</a>, was developed by the Banu Musa brothers.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> They also described an early <a href="/wiki/Control_theory" title="Control theory">feedback controller</a> for fluids.<sup id="cite_ref-Mayr_10-0" class="reference"><a href="#cite_note-Mayr-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> According to <a href="/wiki/Donald_Routledge_Hill" class="mw-redirect" title="Donald Routledge Hill">Donald Routledge Hill</a>, the Banu Musa brothers were "masters in the exploitation of small variations" in <a href="/wiki/Fluid_statics" class="mw-redirect" title="Fluid statics">hydrostatic</a> pressures and in using conical <a href="/wiki/Valve" title="Valve">valves</a> as "in-line" components in flow systems, "the first known use of conical valves as automatic controllers."<sup id="cite_ref-Hill_11-0" class="reference"><a href="#cite_note-Hill-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> They also described the use of other valves, including a <a href="/wiki/Plug_valve" title="Plug valve">plug valve</a>,<sup id="cite_ref-Mayr_10-1" class="reference"><a href="#cite_note-Mayr-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hill_11-1" class="reference"><a href="#cite_note-Hill-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Float_valve" class="mw-redirect" title="Float valve">float valve</a><sup id="cite_ref-Mayr_10-2" class="reference"><a href="#cite_note-Mayr-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Tap_(valve)" title="Tap (valve)">tap</a>.<sup id="cite_ref-Hill-1979_12-0" class="reference"><a href="#cite_note-Hill-1979-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 74–77">: 74–77 </span></sup> The Banu Musa also developed an early <a href="/wiki/Fail-safe" title="Fail-safe">fail-safe</a> system where "one can withdraw small quantities of liquid repeatedly, but if one withdraws a large quantity, no further extractions are possible."<sup id="cite_ref-Hill_11-2" class="reference"><a href="#cite_note-Hill-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The double-concentric <a href="/wiki/Siphon" title="Siphon">siphon</a> and the <a href="/wiki/Funnel" title="Funnel">funnel</a> with bent end for pouring in different liquids, neither of which appear in any earlier Greek works, were also original inventions by the Banu Musa brothers.<sup id="cite_ref-Hill-1979_12-1" class="reference"><a href="#cite_note-Hill-1979-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 21">: 21 </span></sup> Some of the other mechanisms they described include a <a href="/wiki/Float_chamber" title="Float chamber">float chamber</a><sup id="cite_ref-Hassan_8-1" class="reference"><a href="#cite_note-Hassan-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and an early <a href="/wiki/Pressure_sensor" class="mw-redirect" title="Pressure sensor">differential pressure</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>In 1206, <a href="/wiki/Al-Jazari" class="mw-redirect" title="Al-Jazari">Al-Jazari</a>'s <i>Book of Knowledge of Ingenious Mechanical Devices</i> described many hydraulic machines. Of particular importance were his water-raising <a href="/wiki/Pump" title="Pump">pumps</a>. The first known use of a <a href="/wiki/Crankshaft" title="Crankshaft">crankshaft</a> in a <a href="/wiki/Chain_pump" title="Chain pump">chain pump</a> was in one of al-Jazari's <a href="/wiki/Sakia" class="mw-redirect" title="Sakia">saqiya</a> machines. The concept of minimizing <a href="/wiki/Intermittency" title="Intermittency">intermittent working</a> is also first implied in one of al-Jazari's saqiya chain pumps, which was for the purpose of maximising the efficiency of the saqiya chain pump.<sup id="cite_ref-Hill-776_14-0" class="reference"><a href="#cite_note-Hill-776-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Al-Jazari also invented a <a href="/wiki/Straight-twin_engine" title="Straight-twin engine">twin-cylinder</a> <a href="/wiki/Reciprocating_engine" title="Reciprocating engine">reciprocating</a> <a href="/wiki/Piston" title="Piston">piston</a> suction pump, which included the first <a href="/wiki/Suction" title="Suction">suction</a> pipes, suction pumping, <a href="/wiki/Double-acting_cylinder" class="mw-redirect" title="Double-acting cylinder">double-action</a> pumping, and made early uses of valves and a <a href="/wiki/Crankshaft" title="Crankshaft">crankshaft</a>-<a href="/wiki/Connecting_rod" title="Connecting rod">connecting rod</a> mechanism. This pump is remarkable for three reasons: the first known use of a true suction pipe (which sucks fluids into a <a href="/wiki/Partial_vacuum" class="mw-redirect" title="Partial vacuum">partial vacuum</a>) in a pump, the first application of the <a href="/wiki/Double-acting_cylinder" class="mw-redirect" title="Double-acting cylinder">double-acting</a> principle, and the conversion of <a href="/wiki/Rotary_engine" title="Rotary engine">rotary</a> to <a href="/wiki/Reciprocating_motion" title="Reciprocating motion">reciprocating motion</a>, via the crankshaft-connecting rod mechanism.<sup id="cite_ref-Hill2_15-0" class="reference"><a href="#cite_note-Hill2-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hill-1996_17-0" class="reference"><a href="#cite_note-Hill-1996-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Sixteenth_and_seventeenth_century">Sixteenth and seventeenth century</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=10" title="Edit section: Sixteenth and seventeenth century"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Leonardo_da_Vinci">Leonardo da Vinci</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=11" title="Edit section: Leonardo da Vinci"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>During the <a href="/wiki/Renaissance" title="Renaissance">Renaissance</a>, <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> was well known for his experimental skills. His notes provide precise depictions of various phenomena, including vessels, jets, hydraulic jumps, eddy formation, tides, as well as designs for both low drag (streamlined) and high drag (parachute) configurations. Da Vinci is also credited for formulating the conservation of mass in one-dimensional steady flow.<sup id="cite_ref-:0_18-0" class="reference"><a href="#cite_note-:0-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Simon_Stevin">Simon Stevin</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=12" title="Edit section: Simon Stevin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1586, the Flemish engineer and mathematician <a href="/wiki/Simon_Stevin" title="Simon Stevin">Simon Stevin</a> published <i>De Beghinselen des Waterwichts</i> (<i>Principles on the Weight of Water</i>), a study of hydrostatics that, among other things, extensively discussed the hydrostatic paradox.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Castelli_and_Torricelli">Castelli and Torricelli</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=13" title="Edit section: Castelli and Torricelli"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Benedetto_Castelli" title="Benedetto Castelli">Benedetto Castelli</a>, and <a href="/wiki/Evangelista_Torricelli" title="Evangelista Torricelli">Evangelista Torricelli</a>, two of the disciples of <a href="/wiki/Galileo" class="mw-redirect" title="Galileo">Galileo</a>, applied the discoveries of their master to the science of hydrodynamics. In 1628 Castelli published a small work, <i>Della misura dell' acque correnti</i>, in which he satisfactorily explained several phenomena in the motion of fluids in rivers and <a href="/wiki/Canal" title="Canal">canals</a>; but he committed a great <a href="/wiki/Paralogism" class="mw-redirect" title="Paralogism">paralogism</a> in supposing the velocity of the water proportional to the depth of the orifice below the surface of the vessel. Torricelli, observing that in a jet where the water rushed through a small ajutage it rose to nearly the same height with the reservoir from which it was supplied, imagined that it ought to move with the same velocity as if it had fallen through that height by the <a href="/wiki/Force_of_gravity" class="mw-redirect" title="Force of gravity">force of gravity</a>, and hence he deduced the proposition that the velocities of liquids are as the <a href="/wiki/Square_root" title="Square root">square root</a> of the <a href="/wiki/Hydraulic_head" title="Hydraulic head">head</a>, apart from the resistance of the air and the <a href="/wiki/Friction" title="Friction">friction</a> of the orifice. This theorem was published in 1643, at the end of his treatise <i>De motu gravium projectorum</i>, and it was confirmed by the experiments of <a href="/wiki/Raffaello_Magiotti" title="Raffaello Magiotti">Raffaello Magiotti</a> on the quantities of water discharged from different ajutages under different pressures (1648).<sup id="cite_ref-EB1911_4-3" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Blaise_Pascal">Blaise Pascal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=14" title="Edit section: Blaise Pascal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the hands of <a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Blaise Pascal</a> hydrostatics assumed the dignity of a science, and in a treatise on the equilibrium of liquids (<i>Sur l’équilibre des liqueurs</i>), found among his manuscripts after his death and published in 1663, the laws of the equilibrium of liquids were demonstrated in the most simple manner, and amply confirmed by experiments.<sup id="cite_ref-EB1911_4-4" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Mariotte_and_Guglielmini">Mariotte and Guglielmini</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=15" title="Edit section: Mariotte and Guglielmini"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The theorem of Torricelli was employed by many succeeding writers, but particularly by <a href="/wiki/Edme_Mariotte" title="Edme Mariotte">Edme Mariotte</a> (1620–1684), whose <i>Traité du mouvement des eaux</i>, published after his death in the year 1686, is founded on a great variety of well-conducted experiments on the motion of fluids, performed at <a href="/wiki/Versailles_(city)" class="mw-redirect" title="Versailles (city)">Versailles</a> and <a href="/wiki/Chantilly,_Oise" title="Chantilly, Oise">Chantilly</a>. In the discussion of some points he committed considerable mistakes. Others he treated very superficially, and in none of his experiments apparently did he attend to the diminution of efflux arising from the contraction of the liquid vein, when the orifice is merely a perforation in a thin plate; but he appears to have been the first who attempted to ascribe the discrepancy between theory and experiment to the retardation of the water's velocity through friction. His contemporary <a href="/wiki/Domenico_Guglielmini" title="Domenico Guglielmini">Domenico Guglielmini</a> (1655–1710), who was inspector of the rivers and canals at <a href="/wiki/Bologna" title="Bologna">Bologna</a>, had ascribed this diminution of velocity in rivers to transverse motions arising from inequalities in their bottom. But as Mariotte observed similar obstructions even in glass pipes where no transverse currents could exist, the cause assigned by Guglielmini seemed destitute of foundation. The French philosopher, therefore, regarded these obstructions as the effects of friction. He supposed that the filaments of water which graze along the sides of the pipe lose a portion of their velocity; that the contiguous filaments, having on this account a greater velocity, rub upon the former, and suffer a diminution of their celerity; and that the other filaments are affected with similar retardations proportional to their distance from the axis of the pipe. In this way the medium velocity of the current may be diminished, and consequently the quantity of water discharged in a given time must, from the effects of friction, be considerably less than that which is computed from theory.<sup id="cite_ref-EB1911_4-5" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Eighteenth_century">Eighteenth century</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=16" title="Edit section: Eighteenth century"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Studies_by_Isaac_Newton">Studies by Isaac Newton</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=17" title="Edit section: Studies by Isaac Newton"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Friction_and_viscosity">Friction and viscosity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=18" title="Edit section: Friction and viscosity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The effects of friction and viscosity in diminishing the velocity of running water were noticed in the <i><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia</a></i> of <a href="/wiki/Sir_Isaac_Newton" class="mw-redirect" title="Sir Isaac Newton">Sir Isaac Newton</a>, who threw much light upon several branches of hydromechanics. At a time when the <a href="/wiki/Mechanical_explanations_of_gravitation#Vortex" title="Mechanical explanations of gravitation">Cartesian system of vortices</a> universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it. Taking advantage of these results, <a href="/wiki/France" title="France">French</a> engineer <a href="/wiki/Henri_Pitot" title="Henri Pitot">Henri Pitot</a> afterwards showed that the retardations arising from friction are inversely as the diameters of the pipes in which the fluid moves.<sup id="cite_ref-EB1911_4-6" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Orifices">Orifices</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=19" title="Edit section: Orifices"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The attention of Newton was also directed to the discharge of water from orifices in the bottom of vessels. He supposed a cylindrical vessel full of water to be perforated in its bottom with a small hole by which the water escaped, and the vessel to be supplied with water in such a manner that it always remained full at the same height. He then supposed this cylindrical column of water to be divided into two parts – the first, which he called the "cataract," being an hyperboloid generated by the revolution of an <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a> of the fifth degree around the axis of the cylinder which should pass through the orifice, and the second the remainder of the water in the cylindrical vessel. He considered the horizontal strata of this hyperboloid as always in motion, while the remainder of the water was in a state of rest, and imagined that there was a kind of cataract in the middle of the fluid.<sup id="cite_ref-EB1911_4-7" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>When the results of this theory were compared with the quantity of water actually discharged, Newton concluded that the velocity with which the water issued from the orifice was equal to that which a falling body would receive by descending through half the height of water in the reservoir. This conclusion, however, is absolutely irreconcilable with the known fact that jets of water rise nearly to the same height as their reservoirs, and Newton seems to have been aware of this objection. Accordingly, in the second edition of his <i>Principia</i>, which appeared in 1713, he reconsidered his theory. He had discovered a contraction in the vein of fluid (<i><a href="/wiki/Vena_contracta" title="Vena contracta">vena contracta</a></i>) which issued from the orifice, and found that, at the distance of about a diameter of the aperture, the section of the vein was contracted in the subduplicate ratio of two to one. He regarded, therefore, the section of the contracted vein as the true orifice from which the discharge of water ought to be deduced, and the velocity of the effluent water as due to the whole height of water in the reservoir; and by this means his theory became more conformable to the results of experience, though still open to serious objections.<sup id="cite_ref-EB1911_4-8" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Waves">Waves</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=20" title="Edit section: Waves"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Newton was also the first to investigate the difficult subject of the motion of <a href="/wiki/Wave" title="Wave">waves</a>.<sup id="cite_ref-EB1911_4-9" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Daniel_Bernoulli">Daniel Bernoulli</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=21" title="Edit section: Daniel Bernoulli"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1738 Daniel Bernoulli published his <i>Hydrodynamica seu de viribus et motibus fluidorum commentarii</i>. His theory of the motion of fluids, the germ of which was first published in his memoir entitled <i>Theoria nova de motu aquarum per canales quocunque fluentes</i>, communicated to the academy of <a href="/wiki/St_Petersburg" class="mw-redirect" title="St Petersburg">St Petersburg</a> as early as 1726, was founded on two suppositions, which appeared to him conformable to experience. He supposed that the surface of the fluid, contained in a vessel which is emptying itself by an orifice, remains always horizontal; and, if the fluid mass is conceived to be divided into an infinite number of horizontal strata of the same bulk, that these strata remain contiguous to each other, and that all their points descend vertically, with velocities inversely proportional to their breadth, or to the horizontal sections of the reservoir. In order to determine the motion of each stratum, he employed the principle of the <i>conservatio virium vivarum</i>, and obtained very elegant solutions. But in the absence of a general demonstration of that principle, his results did not command the confidence which they would otherwise have deserved, and it became desirable to have a theory more certain, and depending solely on the fundamental laws of mechanics. <a href="/wiki/Colin_Maclaurin" title="Colin Maclaurin">Colin Maclaurin</a> and <a href="/wiki/John_Bernoulli" class="mw-redirect" title="John Bernoulli">John Bernoulli</a>, who were of this opinion, resolved the problem by more direct methods, the one in his <i>Fluxions</i>, published in 1742, and the other in his <i>Hydraulica nunc primum detecta</i>, <i>et demonstrata directe ex fundamentis pure mechanicis</i>, which forms the fourth volume of his works. The method employed by Maclaurin has been thought not sufficiently rigorous; and that of John Bernoulli is, in the opinion of <a href="/wiki/Joseph_Louis_Lagrange" class="mw-redirect" title="Joseph Louis Lagrange">Lagrange</a>, defective in clearness and precision.<sup id="cite_ref-EB1911_4-10" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Jean_le_Rond_d'Alembert"><span id="Jean_le_Rond_d.27Alembert"></span>Jean le Rond d'Alembert</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=22" title="Edit section: Jean le Rond d'Alembert"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The theory of Daniel Bernoulli was opposed also by <a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">Jean le Rond d'Alembert</a>. When generalizing the theory of <a href="/wiki/Pendulum" title="Pendulum">pendulums</a> of <a href="/wiki/Jacob_Bernoulli" title="Jacob Bernoulli">Jacob Bernoulli</a> he discovered a principle of dynamics so simple and general that it reduced the laws of the motions of bodies to that of their <a href="/wiki/Mechanical_equilibrium" title="Mechanical equilibrium">equilibrium</a>. He applied this principle to the motion of fluids, and gave a specimen of its application at the end of his <i>Dynamics</i> in 1743. It was more fully developed in his <i>Traité des fluides</i>, published in 1744, in which he gave simple and elegant solutions of problems relating to the equilibrium and motion of fluids. He made use of the same suppositions as Daniel Bernoulli, though his calculus was established in a very different manner. He considered, at every instant, the actual motion of a stratum as composed of a motion which it had in the preceding instant and of a motion which it had lost; and the laws of equilibrium between the motions lost furnished him with <a href="/wiki/Equation" title="Equation">equations</a> representing the motion of the fluid. It remained a desideratum to express by equations the motion of a particle of the fluid in any assigned direction. These equations were found by d'Alembert from two principles – that a rectangular canal, taken in a mass of fluid in equilibrium, is itself in equilibrium, and that a portion of the fluid, in passing from one place to another, preserves the same volume when the fluid is incompressible, or dilates itself according to a given law when the fluid is elastic. His ingenious method, published in 1752, in his <i>Essai sur la résistance des fluides</i>, was brought to perfection in his <i>Opuscules mathématiques</i>, and was adopted by <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>.<sup id="cite_ref-EB1911_4-11" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Leonhard_Euler">Leonhard Euler</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=23" title="Edit section: Leonhard Euler"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b>. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=History_of_fluid_mechanics&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">October 2024</span>)</i></span></div></td></tr></tbody></table> <p>The resolution of the questions concerning the motion of fluids was effected by means of Leonhard Euler's <a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial differential coefficients</a>. This calculus was first applied to the motion of water by d'Alembert, and enabled both him and Euler to represent the theory of fluids in formulae restricted by no particular hypothesis.<sup id="cite_ref-EB1911_4-12" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pierre_Louis_Georges_Dubuat">Pierre Louis Georges Dubuat</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=24" title="Edit section: Pierre Louis Georges Dubuat"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One of the most successful labourers in the science of hydrodynamics at this period was <a href="/wiki/Pierre-Louis-Georges_du_Buat" title="Pierre-Louis-Georges du Buat">Pierre-Louis-Georges du Buat</a>. Following in the steps of the Abbé <a href="/wiki/Charles_Bossut" title="Charles Bossut">Charles Bossut</a> (<i>Nouvelles Experiences sur la résistance des fluides</i>, 1777), he published, in 1786, a revised edition of his <i>Principes d'hydraulique</i>, which contains a satisfactory theory of the motion of fluids, founded solely upon experiments. Dubuat considered that if water were a perfect fluid, and the channels in which it flowed infinitely smooth, its motion would be continually accelerated, like that of bodies descending in an inclined plane. But as the motion of rivers is not continually accelerated, and soon arrives at a state of uniformity, it is evident that the viscosity of the water, and the friction of the channel in which it descends, must equal the accelerating force. Dubuat, therefore, assumed it as a proposition of fundamental importance that, when water flows in any channel or bed, the accelerating force which obliges it to move is equal to the sum of all the resistances which it meets with, whether they arise from its own <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> or from the friction of its bed. This principle was employed by him in the first edition of his work, which appeared in 1779. The theory contained in that edition was founded on the experiments of others, but he soon saw that a theory so new, and leading to results so different from the ordinary theory, should be founded on new experiments more direct than the former, and he was employed in the performance of these from 1780 to 1783. The experiments of Bossut were made only on pipes of a moderate declivity, but Dubuat used declivities of every kind, and made his experiments upon channels of various sizes.<sup id="cite_ref-EB1911_4-13" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Nineteenth_century">Nineteenth century</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=25" title="Edit section: Nineteenth century"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Claude-Louis_Navier_and_George_Gabriel_Stokes">Claude-Louis Navier and George Gabriel Stokes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=26" title="Edit section: Claude-Louis Navier and George Gabriel Stokes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b>. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=History_of_fluid_mechanics&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">June 2023</span>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Hermann_von_Helmholtz">Hermann von Helmholtz</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=27" title="Edit section: Hermann von Helmholtz"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1858 <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> published his seminal paper "Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen," in <i><a href="/wiki/Journal_f%C3%BCr_die_reine_und_angewandte_Mathematik" class="mw-redirect" title="Journal für die reine und angewandte Mathematik">Journal für die reine und angewandte Mathematik</a></i>, vol. 55, pp. 25–55. So important was the paper that a few years later <a href="/wiki/P._G._Tait" class="mw-redirect" title="P. G. Tait">P. G. Tait</a> published an English translation, "On integrals of the hydrodynamical equations which express vortex motion", in <i><a href="/wiki/Philosophical_Magazine" title="Philosophical Magazine">Philosophical Magazine</a></i>, vol. 33, pp. 485–512 (1867). In his paper Helmholtz established his three "laws of vortex motion" in much the same way one finds them in any advanced textbook of <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a> today. This work established the significance of <a href="/wiki/Vorticity" title="Vorticity">vorticity</a> to fluid mechanics and science in general. </p><p>For the next century or so <i>vortex dynamics</i> matured as a subfield of fluid mechanics, always commanding at least a major chapter in treatises on the subject. Thus, <a href="/wiki/Horace_Lamb" title="Horace Lamb">H. Lamb's</a> well known <i>Hydrodynamics</i> (6th ed., 1932) devotes a full chapter to <a href="/wiki/Vorticity" title="Vorticity">vorticity</a> and vortex dynamics as does <a href="/wiki/George_Batchelor" title="George Batchelor">G. K. Batchelor's</a> <i><a rel="nofollow" class="external text" href="https://archive.today/20130112165003/http://www.cambridge.org/uk/series/sSeries.asp?code=CML&srt=T">Introduction to Fluid Dynamics</a></i> (1967). In due course entire treatises were devoted to vortex motion. <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">H. Poincaré's</a> <i>Théorie des Tourbillons</i> (1893), <a rel="nofollow" class="external text" href="http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=80970">H. Villat's</a> <i>Leçons sur la Théorie des Tourbillons</i> (1930), <a href="/wiki/Clifford_Truesdell" title="Clifford Truesdell">C. Truesdell's</a> <i>The Kinematics of Vorticity</i> (1954), and <a href="/wiki/P._G._Saffman" class="mw-redirect" title="P. G. Saffman">P. G. Saffman's</a> <i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070314022441/http://www.cambridge.org/us/catalogue/email.asp?isbn=0521477395">Vortex Dynamics</a></i> (1992) may be mentioned. Early on individual sessions at scientific conferences were devoted to <a href="/wiki/Vortices" class="mw-redirect" title="Vortices">vortices</a>, vortex motion, vortex dynamics and vortex flows. Later, entire meetings were devoted to the subject. </p><p>The range of applicability of Helmholtz's work grew to encompass <a href="/wiki/Atmospheric_science" title="Atmospheric science">atmospheric</a> and <a href="/wiki/Oceanographic" class="mw-redirect" title="Oceanographic">oceanographic</a> flows, to all branches of <a href="/wiki/Engineering" title="Engineering">engineering</a> and <a href="/wiki/Applied_Science" class="mw-redirect" title="Applied Science">applied science</a> and, ultimately, to <a href="/wiki/Superfluid" class="mw-redirect" title="Superfluid">superfluids</a> (today including <a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensates</a>). In modern fluid mechanics the role of vortex dynamics in explaining flow phenomena is firmly established. Well known vortices have acquired names and are regularly depicted in the popular media: <a href="/wiki/Hurricane" class="mw-redirect" title="Hurricane">hurricanes</a>, <a href="/wiki/Tornado" title="Tornado">tornadoes</a>, <a href="/wiki/Waterspout" title="Waterspout">waterspouts</a>, aircraft trailing vortices (e.g., <a href="/wiki/Wingtip_vortices" title="Wingtip vortices">wingtip vortices</a>), drainhole vortices (including the bathtub vortex), <a href="/wiki/Smoke_ring" title="Smoke ring">smoke rings</a>, underwater bubble air rings, cavitation vortices behind ship propellers, and so on. In the technical literature a number of vortices that arise under special conditions also have names: the <a href="/wiki/Von_K%C3%A1rm%C3%A1n_vortex_street" class="mw-redirect" title="Von Kármán vortex street">Kármán vortex street</a> wake behind a bluff body, <a href="/wiki/Taylor_vortex" class="mw-redirect" title="Taylor vortex">Taylor vortices</a> between rotating cylinders, <a href="/wiki/G%C3%B6rtler_vortices" title="Görtler vortices">Görtler vortices</a> in flow along a curved wall, etc. </p> <div class="mw-heading mw-heading3"><h3 id="Gaspard_Riche_de_Prony">Gaspard Riche de Prony</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=28" title="Edit section: Gaspard Riche de Prony"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The theory of running water was greatly advanced by the researches of <a href="/wiki/Gaspard_Riche_de_Prony" class="mw-redirect" title="Gaspard Riche de Prony">Gaspard Riche de Prony</a> (1755–1839). From a collection of the best experiments by previous workers he selected eighty-two (fifty-one on the velocity of water in conduit pipes, and thirty-one on its velocity in open canals); and, discussing these on physical and mechanical principles, he succeeded in drawing up general formulae, which afforded a simple expression for the velocity of running water.<sup id="cite_ref-EB1911_4-14" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Johann_Albert_Eytelwein">Johann Albert Eytelwein</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=29" title="Edit section: Johann Albert Eytelwein"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Johann_Albert_Eytelwein" title="Johann Albert Eytelwein">J. A. Eytelwein</a> of <a href="/wiki/Berlin" title="Berlin">Berlin</a>, who published in 1801 a valuable compendium of hydraulics entitled <i>Handbuch der Mechanik und der Hydraulik</i>, investigated the subject of the discharge of water by compound pipes, the motions of jets and their impulses against plane and oblique surfaces; and he showed theoretically that a <a href="/wiki/Water_wheel" title="Water wheel">water-wheel</a> will have its maximum effect when its circumference moves with half the velocity of the stream.<sup id="cite_ref-EB1911_4-15" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Jean_Nicolas_Pierre_Hachette_and_others">Jean Nicolas Pierre Hachette and others</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=30" title="Edit section: Jean Nicolas Pierre Hachette and others"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Jean_Nicolas_Pierre_Hachette" title="Jean Nicolas Pierre Hachette">JNP Hachette</a> in 1816–1817 published memoirs containing the results of experiments on the spouting of fluids and the discharge of vessels. His object was to measure the contracted part of a fluid vein, to examine the phenomena attendant on additional tubes, and to investigate the form of the fluid vein and the results obtained when different forms of orifices are employed. Extensive experiments on the discharge of water from orifices (<i>Expériences hydrauliques</i>, Paris, 1832) were conducted under the direction of the French government by J. V. Poncelet (1788–1867) and <a href="/w/index.php?title=Joseph_Aim%C3%A9_Lesbros&action=edit&redlink=1" class="new" title="Joseph Aimé Lesbros (page does not exist)">J. A. Lesbros</a> (1790–1860).<sup id="cite_ref-EB1911_4-16" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>P. P. Boileau (1811–1891) discussed their results and added experiments of his own (<i>Traité de la mesure des eaux courantes</i>, Paris, 1854). K. R. Bornemann re-examined all these results with great care, and gave formulae expressing the variation of the coefficients of discharge in different conditions (<i>Civil Ingénieur,</i> 1880). <a href="/wiki/Julius_Weisbach" title="Julius Weisbach">Julius Weisbach</a> (1806–1871) also made many experimental investigations on the discharge of fluids.<sup id="cite_ref-EB1911_4-17" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The experiments of <a href="/wiki/James_Bicheno_Francis" class="mw-redirect" title="James Bicheno Francis">J. B. Francis</a> (<i>Lowell Hydraulic Experiments</i>, Boston, Mass., 1855) led him to propose variations in the accepted formulae for the discharge over weirs, and a generation later a very complete investigation of this subject was carried out by <a href="/wiki/Henri-%C3%89mile_Bazin" title="Henri-Émile Bazin">Henri-Émile Bazin</a>. An elaborate inquiry on the flow of water in pipes and channels was conducted by <a href="/wiki/Henry_Darcy" title="Henry Darcy">Henry G. P. Darcy</a> (1803–1858) and continued by Bazin, at the expense of the French government (<i>Recherches hydrauliques</i>, Paris, 1866).<sup id="cite_ref-EB1911_4-18" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Andreas_Rudolf_Harlacher_and_others">Andreas Rudolf Harlacher and others</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=31" title="Edit section: Andreas Rudolf Harlacher and others"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>German engineers have also devoted special attention to the measurement of the flow in rivers; the <i>Beiträge zur Hydrographie des Königreiches Böhmen</i> (Prague, 1872–1875) of <a href="/w/index.php?title=Andreas_Rudolf_Harlacher&action=edit&redlink=1" class="new" title="Andreas Rudolf Harlacher (page does not exist)">Andreas Rudolf Harlacher</a> contained valuable measurements of this kind, together with a comparison of the experimental results with the formulae of flow that had been proposed up to the date of its publication, and important data were yielded by the gaugings of the <a href="/wiki/Mississippi" title="Mississippi">Mississippi</a> made for the United States government by <a href="/wiki/Andrew_Atkinson_Humphreys" class="mw-redirect" title="Andrew Atkinson Humphreys">Andrew Atkinson Humphreys</a> and <a href="/wiki/Henry_Larcom_Abbot" title="Henry Larcom Abbot">Henry Larcom Abbot</a>, by Robert Gordon's gaugings of the <a href="/wiki/Irrawaddy_River" title="Irrawaddy River">Irrawaddy River</a>, and by Allen J. C. Cunningham's experiments on the <a href="/wiki/Ganges" title="Ganges">Ganges</a> canal.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> The friction of water, investigated for slow speeds by <a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a>, was measured for higher speeds by <a href="/wiki/William_Froude" title="William Froude">William Froude</a> (1810–1879), whose work is of great value in the theory of ship resistance (<i>Brit. Assoc. Report.</i>, 1869), and stream line motion was studied by <a href="/wiki/Osborne_Reynolds" title="Osborne Reynolds">Professor Osborne Reynolds</a> and by <a href="/wiki/Henry_Selby_Hele-Shaw" title="Henry Selby Hele-Shaw">Professor Henry S. Hele-Shaw</a>.<sup id="cite_ref-EB1911_4-19" class="reference"><a href="#cite_note-EB1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Twentieth_century">Twentieth century</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=32" title="Edit section: Twentieth century"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ludwig_Prandtl">Ludwig Prandtl</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=33" title="Edit section: Ludwig Prandtl"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1904, German scientist <a href="/wiki/Ludwig_Prandtl" title="Ludwig Prandtl">Ludwig Prandtl</a> pioneered boundary layer theory. He pointed out that fluids with small viscosity can be divided into a thin viscous layer (boundary layer) near solid surfaces and interfaces, and an outer layer where <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a> and <a href="/wiki/Euler_equations_(fluid_dynamics)" title="Euler equations (fluid dynamics)">Euler equations</a> apply.<sup id="cite_ref-:0_18-1" class="reference"><a href="#cite_note-:0-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Developments_in_vortex_dynamics">Developments in vortex dynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=34" title="Edit section: Developments in vortex dynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Vortex dynamics</b> is a vibrant subfield of fluid dynamics, commanding attention at major scientific conferences and precipitating workshops and symposia that focus fully on the subject. </p><p>A curious diversion in the history of vortex dynamics was the <a href="/wiki/Vortex_theory_of_the_atom" title="Vortex theory of the atom">Vortex theory of the atom</a> of <a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">William Thomson</a>, later <a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Lord Kelvin</a>. His basic idea was that atoms were to be represented as vortex motions in the ether. This theory predated the <a href="/wiki/Bohr_model" title="Bohr model">quantum theory</a> by several decades and because of the scientific standing of its originator received considerable attention. Many profound insights into vortex dynamics were generated during the pursuit of this theory. Other interesting corollaries were the first counting of simple knots by <a href="/wiki/P._G._Tait" class="mw-redirect" title="P. G. Tait">P. G. Tait</a>, today considered a pioneering effort in <a href="/wiki/Graph_theory" title="Graph theory">graph theory</a>, <a href="/wiki/Topology" title="Topology">topology</a> and <a href="/wiki/Knot_theory" title="Knot theory">knot theory</a>. Ultimately, <a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin's</a> vortex atom was seen to be wrong-headed but the many results in vortex dynamics that it precipitated have stood the test of time. Kelvin himself originated the notion of <a href="/wiki/Circulation_(fluid_dynamics)" class="mw-redirect" title="Circulation (fluid dynamics)">circulation</a> and proved that in an <a href="/wiki/Euler_equations" class="mw-redirect" title="Euler equations">inviscid fluid</a> circulation around a material contour would be conserved. This result — singled out by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a> in "Zum hundertjährigen Gedenktag von Lord Kelvins Geburt, Naturwissenschaften, 12 (1924), 601–602," (title translation: "On the 100th Anniversary of Lord Kelvin's Birth"), as one of the most significant results of Kelvin's work provided an early link between fluid dynamics and topology. </p><p>The history of vortex dynamics seems particularly rich in discoveries and re-discoveries of important results, because results obtained were entirely forgotten after their discovery and then were re-discovered decades later. Thus, the integrability of the problem of three point vortices on the plane was solved in the 1877 thesis of a young Swiss applied mathematician named <a href="/wiki/Walter_Gr%C3%B6bli" title="Walter Gröbli">Walter Gröbli</a>. In spite of having been written in <a href="/wiki/G%C3%B6ttingen" title="Göttingen">Göttingen</a> in the general circle of scientists surrounding <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a> and <a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Kirchhoff</a>, and in spite of having been mentioned in Kirchhoff's well known lectures on <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a> and in other major texts such as Lamb's <i>Hydrodynamics</i>, this solution was largely forgotten. A 1949 paper by the noted applied mathematician <a href="/wiki/John_Lighton_Synge" title="John Lighton Synge">J. L. Synge</a> created a brief revival, but Synge's paper was in turn forgotten. A quarter century later a 1975 paper by <a href="/w/index.php?title=E._A._Novikov&action=edit&redlink=1" class="new" title="E. A. Novikov (page does not exist)">E. A. Novikov</a> and a 1979 paper by <a href="/wiki/Hassan_Aref" title="Hassan Aref">H. Aref</a> on <a href="/wiki/Chaotic_advection" class="mw-redirect" title="Chaotic advection">chaotic advection</a> finally brought this important earlier work to light. The subsequent elucidation of chaos in the four-vortex problem, and in the advection of a passive particle by three vortices, made Gröbli's work part of "modern science". </p><p>Another example of this kind is the so-called "localized induction approximation" (LIA) for three-dimensional vortex filament motion, which gained favor in the mid-1960s through the work of Arms, Hama, Betchov and others, but turns out to date from the early years of the 20th century in the work of Da Rios, a gifted student of the noted Italian mathematician <a href="/wiki/Tullio_Levi-Civita" title="Tullio Levi-Civita">T. Levi-Civita</a>. Da Rios published his results in several forms but they were never assimilated into the fluid mechanics literature of his time. In 1972 H. Hasimoto used Da Rios' "intrinsic equations" (later re-discovered independently by R. Betchov) to show how the motion of a vortex filament under LIA could be related to the non-linear <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a>. This immediately made the problem part of "modern science" since it was then realized that vortex filaments can support solitary twist waves of large amplitude. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=35" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Timeline_of_fluid_and_continuum_mechanics" title="Timeline of fluid and continuum mechanics">Timeline of fluid and continuum mechanics</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=36" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>J. D. Anderson Jr. (1997). <i>A History of Aerodynamics</i> (Cambridge University Press). <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-45435-2" title="Special:BookSources/0-521-45435-2">0-521-45435-2</a></li> <li>J. D. Anderson Jr. (1998). <i>Some Reflections on the History of Fluid Dynamics,</i> in <i>The Handbook of Fluid Dynamics</i> (ed. by R.W. Johnson, CRC Press) Ch. 2.</li> <li>J. S. Calero (2008). <i>The Genesis of Fluid Mechanics, 1640–1780</i> (Springer). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-6414-2" title="Special:BookSources/978-1-4020-6414-2">978-1-4020-6414-2</a></li> <li>O. Darrigol (2005). <i>Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl</i> (Oxford University Press). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-856843-6" title="Special:BookSources/0-19-856843-6">0-19-856843-6</a></li> <li>P. A. Davidson, Y. Kaneda, K. Moffatt, and K. R. Sreenivasan (eds, 2011). <i>A Voyage Through Turbulence</i> (Cambridge University Press). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-19868-4" title="Special:BookSources/978-0-521-19868-4">978-0-521-19868-4</a></li> <li>M. Eckert (2006). <i>The Dawn of Fluid Dynamics: A Discipline Between Science and Technology</i> (Wiley-VCH). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-40513-8" title="Special:BookSources/978-3-527-40513-8">978-3-527-40513-8</a></li> <li>G. Garbrecht (ed., 1987). <i>Hydraulics and Hydraulic Research: A Historical Review</i> (A.A. Balkema). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/90-6191-621-6" title="Special:BookSources/90-6191-621-6">90-6191-621-6</a></li> <li>M. J. Lighthill (1995). <i>Fluid mechanics</i>, in <i>Twentieth Century Physics</i> ed. by L.M. Brown, A. Pais, and B. Pippard (IOP/AIP), Vol. 2, pp. 795–912.</li> <li>H. Rouse and S. Ince (1957). <i>History of Hydraulics</i> (Iowa Institute of Hydraulic Research, State University of Iowa).</li> <li>G. A. Tokaty (1994). <i>A History and Philosophy of Fluid Mechanics</i> (Dover). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-68103-3" title="Special:BookSources/0-486-68103-3">0-486-68103-3</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_fluid_mechanics&action=edit&section=37" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">G. Garbrecht (1987). <i>Hydrologic and hydraulic concepts in antiquity</i> in <i>Hydraulics and Hydraulic Research: A Historical Review</i> (A.A. Balkema).</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeedham1978" class="citation journal cs1">Needham, Joseph (1978). <a rel="nofollow" class="external text" href="https://archive.org/details/shorterscienceci0000need/page/336/mode/1up">"Science and civilization in china"</a>. <i>Cambridge University Press</i>. <b>2</b> (336): 476 – via Internet Archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Cambridge+University+Press&rft.atitle=Science+and+civilization+in+china&rft.volume=2&rft.issue=336&rft.pages=476&rft.date=1978&rft.aulast=Needham&rft.aufirst=Joseph&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fshorterscienceci0000need%2Fpage%2F336%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarroll" class="citation web cs1">Carroll, Bradley W. <a rel="nofollow" class="external text" href="http://www.physics.weber.edu/carroll/Archimedes/principle.htm">"<i>Archimedes' Principle</i>"</a>. <a href="/wiki/Weber_State_University" title="Weber State University">Weber State University</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2007-07-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedes%27+Principle&rft.pub=Weber+State+University&rft.aulast=Carroll&rft.aufirst=Bradley+W&rft_id=http%3A%2F%2Fwww.physics.weber.edu%2Fcarroll%2FArchimedes%2Fprinciple.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-EB1911-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-EB1911_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-EB1911_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-EB1911_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-EB1911_4-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-EB1911_4-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-EB1911_4-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-EB1911_4-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-EB1911_4-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-EB1911_4-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-EB1911_4-9"><sup><i><b>j</b></i></sup></a> <a href="#cite_ref-EB1911_4-10"><sup><i><b>k</b></i></sup></a> <a href="#cite_ref-EB1911_4-11"><sup><i><b>l</b></i></sup></a> <a href="#cite_ref-EB1911_4-12"><sup><i><b>m</b></i></sup></a> <a href="#cite_ref-EB1911_4-13"><sup><i><b>n</b></i></sup></a> <a href="#cite_ref-EB1911_4-14"><sup><i><b>o</b></i></sup></a> <a href="#cite_ref-EB1911_4-15"><sup><i><b>p</b></i></sup></a> <a href="#cite_ref-EB1911_4-16"><sup><i><b>q</b></i></sup></a> <a href="#cite_ref-EB1911_4-17"><sup><i><b>r</b></i></sup></a> <a href="#cite_ref-EB1911_4-18"><sup><i><b>s</b></i></sup></a> <a href="#cite_ref-EB1911_4-19"><sup><i><b>t</b></i></sup></a></span> <span class="reference-text"><span class="noprint"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/18px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span> </span>One or more of the preceding sentences incorporates text from a publication now in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenhill1911" class="citation encyclopaedia cs1">Greenhill, Alfred George (1911). "<a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Hydromechanics" class="extiw" title="s:1911 Encyclopædia Britannica/Hydromechanics">Hydromechanics</a>". In <a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a> (ed.). <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 14 (11th ed.). Cambridge University Press. pp. 115–116.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hydromechanics&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=115-116&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rft.aulast=Greenhill&rft.aufirst=Alfred+George&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Rozhanskaya-642-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Rozhanskaya-642_5-0">^</a></b></span> <span class="reference-text">Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", p. 642, in (<a href="#CITEREFRashedMorelon1996">Rashed & Morelon 1996</a>, pp. 614–642): <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>Using a whole body of mathematical methods (not only those inherited from the antique theory of ratios and infinitesimal techniques, but also the methods of the contemporary algebra and fine calculation techniques), Arabic scientists raised statics to a new, higher level. The classical results of Archimedes in the theory of the centre of gravity were generalized and applied to three-dimensional bodies, the theory of ponderable lever was founded and the 'science of gravity' was created and later further developed in medieval Europe. The phenomena of statics were studied by using the dynamic approach so that two trends – statics and dynamics – turned out to be inter-related within a single science, mechanics. The combination of the dynamic approach with Archimedean hydrostatics gave birth to a direction in science which may be called medieval hydrodynamics. Archimedean statics formed the basis for creating the fundamentals of the science on specific weight. Numerous fine experimental methods were developed for determining the specific weight, which were based, in particular, on the theory of balances and weighing. The classical works of al-Biruni and al-Khazini can by right be considered as the beginning of the application of experimental methods in medieval science. Arabic statics was an essential link in the progress of world science. It played an important part in the prehistory of classical mechanics in medieval Europe. Without it classical mechanics proper could probably not have been created.</p></blockquote></span> </li> <li id="cite_note-Marshall_Clagett_1961_p._64-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Marshall_Clagett_1961_p._64_6-0">^</a></b></span> <span class="reference-text">Marshall Clagett (1961), <i>The Science of Mechanics in the Middle Ages</i>, p. 64, <a href="/wiki/University_of_Wisconsin_Press" title="University of Wisconsin Press">University of Wisconsin Press</a></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Robert E. Hall (1973), "Al-Biruni", <i><a href="/wiki/Dictionary_of_Scientific_Biography" title="Dictionary of Scientific Biography">Dictionary of Scientific Biography</a></i>, Vol. VII, p. 336</span> </li> <li id="cite_note-Hassan-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hassan_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hassan_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Ahmad_Y_Hassan" class="mw-redirect" title="Ahmad Y Hassan">Ahmad Y Hassan</a>, <a rel="nofollow" class="external text" href="http://www.history-science-technology.com/Articles/articles%2071.htm">Transfer Of Islamic Technology To The West, Part II: Transmission Of Islamic Engineering</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080218171021/http://www.history-science-technology.com/Articles/articles%2071.htm">Archived</a> 2008-02-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ._Adamy_&_A._Flemming2004" class="citation cs2">J. Adamy & A. Flemming (November 2004), <a rel="nofollow" class="external text" href="http://tubiblio.ulb.tu-darmstadt.de/24577/">"Soft variable-structure controls: a survey"</a>, <i>Automatica</i>, <b>40</b> (11), <a href="/wiki/Elsevier" title="Elsevier">Elsevier</a>: 1821–1844, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.automatica.2004.05.017">10.1016/j.automatica.2004.05.017</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Automatica&rft.atitle=Soft+variable-structure+controls%3A+a+survey&rft.volume=40&rft.issue=11&rft.pages=1821-1844&rft.date=2004-11&rft_id=info%3Adoi%2F10.1016%2Fj.automatica.2004.05.017&rft.au=J.+Adamy+%26+A.+Flemming&rft_id=http%3A%2F%2Ftubiblio.ulb.tu-darmstadt.de%2F24577%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Mayr-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-Mayr_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Mayr_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Mayr_10-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Otto_Mayr" title="Otto Mayr">Otto Mayr</a> (1970). <i>The Origins of Feedback Control</i>, <a href="/wiki/MIT_Press" title="MIT Press">MIT Press</a>.</span> </li> <li id="cite_note-Hill-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hill_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hill_11-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Hill_11-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Donald_Routledge_Hill" class="mw-redirect" title="Donald Routledge Hill">Donald Routledge Hill</a>, "Mechanical Engineering in the Medieval Near East", <i>Scientific American</i>, May 1991, pp. 64–69. (<a href="/wiki/Cf." title="Cf.">cf.</a> Donald Routledge Hill, <a rel="nofollow" class="external text" href="http://home.swipnet.se/islam/articles/HistoryofSciences.htm">Mechanical Engineering</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071225091836/http://home.swipnet.se/islam/articles/HistoryofSciences.htm">Archived</a> 2007-12-25 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>)</span> </li> <li id="cite_note-Hill-1979-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hill-1979_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hill-1979_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBanu_Musa1979" class="citation cs2"><a href="/wiki/Banu_Musa" class="mw-redirect" title="Banu Musa">Banu Musa</a> (1979), <i>The book of ingenious devices (Kitāb al-ḥiyal)</i>, translated by <a href="/wiki/Donald_Routledge_Hill" class="mw-redirect" title="Donald Routledge Hill">Donald Routledge Hill</a>, <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/90-277-0833-9" title="Special:BookSources/90-277-0833-9"><bdi>90-277-0833-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+book+of+ingenious+devices+%28Kit%C4%81b+al-%E1%B8%A5iyal%29&rft.pub=Springer&rft.date=1979&rft.isbn=90-277-0833-9&rft.au=Banu+Musa&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=n6gdknoXww8"><i>Ancient Discoveries, Episode 12: Machines of the East</i></a>, <a href="/wiki/History_(U.S._TV_channel)" class="mw-redirect" title="History (U.S. TV channel)">History Channel</a>, 26 July 2008, <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211221/n6gdknoXww8">archived</a> from the original on 2021-12-21<span class="reference-accessdate">, retrieved <span class="nowrap">2008-09-06</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ancient+Discoveries%2C+Episode+12%3A+Machines+of+the+East&rft.pub=History+Channel&rft.date=2008-07-26&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dn6gdknoXww8&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Hill-776-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hill-776_14-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Donald_Routledge_Hill" class="mw-redirect" title="Donald Routledge Hill">Donald Routledge Hill</a>, "Engineering", in Roshdi Rashed, ed., <i><a href="/wiki/Encyclopedia_of_the_History_of_Arabic_Science" title="Encyclopedia of the History of Arabic Science">Encyclopedia of the History of Arabic Science</a></i>, Vol. 2, pp. 751–795 [776]. <a href="/wiki/Routledge" title="Routledge">Routledge</a>, London and New York.</span> </li> <li id="cite_note-Hill2-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hill2_15-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Donald_Routledge_Hill" class="mw-redirect" title="Donald Routledge Hill">Donald Routledge Hill</a>, "Mechanical Engineering in the Medieval Near East", <i><a href="/wiki/Scientific_American" title="Scientific American">Scientific American</a></i>, May 1991, pp. 64–69 (<a href="/wiki/Cf." title="Cf.">cf.</a> <a href="/wiki/Donald_Routledge_Hill" class="mw-redirect" title="Donald Routledge Hill">Donald Routledge Hill</a>, <a rel="nofollow" class="external text" href="http://home.swipnet.se/islam/articles/HistoryofSciences.htm">Mechanical Engineering</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071225091836/http://home.swipnet.se/islam/articles/HistoryofSciences.htm">Archived</a> 2007-12-25 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>)</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAhmad_Y_Hassan" class="citation web cs1"><a href="/wiki/Ahmad_Y_Hassan" class="mw-redirect" title="Ahmad Y Hassan">Ahmad Y Hassan</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080226102543/http://www.history-science-technology.com/Notes/Notes%202.htm">"The Origin of the Suction Pump: Al-Jazari 1206 A.D."</a> Archived from <a rel="nofollow" class="external text" href="http://www.history-science-technology.com/Notes/Notes%202.htm">the original</a> on 2008-02-26<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-07-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Origin+of+the+Suction+Pump%3A+Al-Jazari+1206+A.D.&rft.au=Ahmad+Y+Hassan&rft_id=http%3A%2F%2Fwww.history-science-technology.com%2FNotes%2FNotes%25202.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-Hill-1996-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hill-1996_17-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Donald_Routledge_Hill" class="mw-redirect" title="Donald Routledge Hill">Donald Routledge Hill</a> (1996), <i>A History of Engineering in Classical and Medieval Times</i>, <a href="/wiki/Routledge" title="Routledge">Routledge</a>, pp. 143, 150–152</span> </li> <li id="cite_note-:0-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_18-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhite1999" class="citation book cs1">White, Frank M. (1999). <i>Fluid mechanics</i>. McGraw-Hill International Editions (4th ed.). 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Martinus Nijhoff.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Simon+Stevin%3A+Science+in+the+Netherlands+Around+1600&rft.pub=Martinus+Nijhoff&rft.date=1970&rft.aulast=Dijksterhuis&rft.aufirst=E.J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVernon-Harcourt2015" class="citation book cs1">Vernon-Harcourt, Leveson Francis (2 July 2015). <i>Rivers and canals, Volume 1, Rivers : with statistics of the traffic on inland waterways</i>. Cambridge. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1108080590" title="Special:BookSources/978-1108080590"><bdi>978-1108080590</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/967596679">967596679</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rivers+and+canals%2C+Volume+1%2C+Rivers+%3A+with+statistics+of+the+traffic+on+inland+waterways&rft.place=Cambridge&rft.date=2015-07-02&rft_id=info%3Aoclcnum%2F967596679&rft.isbn=978-1108080590&rft.aulast=Vernon-Harcourt&rft.aufirst=Leveson+Francis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> </ol></div></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRashedMorelon1996" class="citation book cs1">Rashed, Roshdi; Morelon, Régis, eds. (1996). <a href="/wiki/Encyclopedia_of_the_History_of_Arabic_Science" title="Encyclopedia of the History of Arabic Science"><i>Encyclopedia of the History of Arabic Science</i></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Encyclopedia+of+the+History+of+Arabic+Science&rft.date=1996&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+fluid+mechanics" class="Z3988"></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output 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href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">Electromagnetism</a> <ul><li><a href="/wiki/Timeline_of_electromagnetism_and_classical_optics" title="Timeline of electromagnetism and classical optics">timeline</a></li> <li><a href="/wiki/History_of_electrical_engineering" title="History of electrical engineering">Electrical engineering</a></li> <li><a href="/wiki/History_of_Maxwell%27s_equations" title="History of Maxwell's equations">Maxwell's equations</a></li></ul></li> <li><a class="mw-selflink selflink">Fluid mechanics</a> <ul><li><a href="/wiki/Timeline_of_fluid_and_continuum_mechanics" title="Timeline of fluid and continuum mechanics">timeline</a></li> <li><a href="/wiki/History_of_aerodynamics" title="History of aerodynamics">Aerodynamics</a></li></ul></li> <li><a href="/wiki/History_of_classical_field_theory" title="History of classical field theory">Field theory</a></li> <li><a href="/wiki/History_of_gravitational_theory" title="History of gravitational theory">Gravitational theory</a> <ul><li><a href="/wiki/Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">timeline</a></li></ul></li> <li><a href="/wiki/History_of_materials_science" title="History of materials science">Material science</a> <ul><li><a href="/wiki/Timeline_of_materials_technology" title="Timeline of materials technology">timeline</a></li> <li><a href="/wiki/History_of_metamaterials" title="History of metamaterials">Metamaterials</a></li></ul></li> <li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">Mechanics</a> <ul><li><a href="/wiki/Timeline_of_classical_mechanics" title="Timeline of classical mechanics">timeline</a></li> <li><a href="/wiki/History_of_variational_principles_in_physics" title="History of variational principles in physics">Variational principles</a></li></ul></li> <li><a href="/wiki/History_of_optics" title="History of optics">Optics</a> <ul><li><a href="/wiki/History_of_spectroscopy" title="History of spectroscopy">Spectroscopy</a></li></ul></li> <li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">timeline</a></li> <li><a href="/wiki/History_of_energy" title="History of energy">Energy</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">Perpetual motion</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern physics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Computational physics <ul><li><a href="/wiki/Timeline_of_computational_physics" title="Timeline of computational physics">timeline</a></li></ul></li> <li>Condensed matter <ul><li><a href="/wiki/Timeline_of_condensed_matter_physics" title="Timeline of condensed matter physics">timeline</a></li> <li><a href="/wiki/History_of_superconductivity" title="History of superconductivity">Superconductivity</a></li></ul></li> <li>Cosmology <ul><li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">timeline</a></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">Big Bang theory</a></li></ul></li> <li><a href="/wiki/History_of_general_relativity" title="History of general relativity">General relativity</a> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">tests</a></li></ul></li> <li><a href="/wiki/History_of_geophysics" title="History of geophysics">Geophysics</a></li> <li>Nuclear physics <ul><li><a href="/wiki/Discovery_of_nuclear_fission" title="Discovery of nuclear fission">Fission</a></li> <li><a href="/wiki/History_of_nuclear_fusion" title="History of nuclear fusion">Fusion</a></li> <li><a href="/wiki/History_of_nuclear_power" title="History of nuclear power">Power</a></li> <li><a href="/wiki/History_of_nuclear_weapons" title="History of nuclear weapons">Weapons</a></li></ul></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">Quantum mechanics</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">timeline</a></li> <li><a href="/wiki/History_of_atomic_theory" title="History of atomic theory">Atoms</a></li> <li><a href="/wiki/History_of_molecular_theory" title="History of molecular theory">Molecules</a></li> <li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">Quantum field theory</a></li></ul></li> <li><a href="/wiki/History_of_subatomic_physics" title="History of subatomic physics">Subatomic physics</a> <ul><li><a href="/wiki/Timeline_of_atomic_and_subatomic_physics" title="Timeline of atomic and subatomic physics">timeline</a></li></ul></li> <li><a href="/wiki/History_of_special_relativity" title="History of special relativity">Special relativity</a> <ul><li><a href="/wiki/Timeline_of_special_relativity_and_the_speed_of_light" title="Timeline of special relativity and the speed of light">timeline</a></li> <li><a href="/wiki/History_of_Lorentz_transformations" title="History of Lorentz transformations">Lorentz transformations</a></li> <li><a href="/wiki/Tests_of_special_relativity" title="Tests of special relativity">tests</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Recent developments</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Quantum information <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">timeline</a></li></ul></li> <li><a href="/wiki/History_of_loop_quantum_gravity" title="History of loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/History_of_nanotechnology" title="History of nanotechnology">Nanotechnology</a></li> <li><a href="/wiki/History_of_string_theory" title="History of string theory">String theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">On specific discoveries</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Cosmic microwave background</a></li> <li><a href="/wiki/Discovery_of_graphene" title="Discovery of graphene">Graphene</a></li> <li><a href="/wiki/First_observation_of_gravitational_waves" title="First observation of gravitational waves">Gravitational waves</a></li> <li>Subatomic particles <ul><li><a href="/wiki/Timeline_of_particle_discoveries" title="Timeline of particle discoveries">timeline</a></li> <li><a href="/wiki/Search_for_the_Higgs_boson" title="Search for the Higgs boson">Higgs boson</a></li> <li><a href="/wiki/Discovery_of_the_neutron" title="Discovery of the neutron">Neutron</a></li></ul></li> <li><a href="/wiki/R%C3%B8mer%27s_determination_of_the_speed_of_light" title="Rømer's determination of the speed of light">Speed of light</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By periods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Copernican_Revolution" title="Copernican Revolution">Copernican Revolution</a></li> <li><a href="/wiki/Golden_age_of_physics" title="Golden age of physics">Golden age of physics</a></li> <li><a href="/wiki/Golden_age_of_cosmology" title="Golden age of cosmology">Golden age of cosmology</a></li> <li><a href="/wiki/Physics_in_the_medieval_Islamic_world" title="Physics in the medieval Islamic world">Medieval Islamic world</a> <ul><li><a href="/wiki/Astronomy_in_the_medieval_Islamic_world" title="Astronomy in the medieval Islamic world">Astronomy</a></li></ul></li> <li><a href="/wiki/Noisy_intermediate-scale_quantum_era" title="Noisy intermediate-scale quantum era">Noisy intermediate-scale quantum era</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By groups</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Harvard_Computers" title="Harvard Computers">Harvard Computers</a></li> <li><a href="/wiki/The_Martians_(scientists)" title="The Martians (scientists)">The Martians</a></li> <li><a href="/wiki/Oxford_Calculators" title="Oxford Calculators">Oxford Calculators</a></li> <li><a href="/wiki/Via_Panisperna_boys" title="Via Panisperna boys">Via Panisperna boys</a></li> <li><a href="/wiki/Women_in_physics" title="Women in physics">Women in physics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Scientific disputes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bohr%E2%80%93Einstein_debates" title="Bohr–Einstein debates">Bohr–Einstein</a></li> <li><a href="/wiki/Chandrasekhar%E2%80%93Eddington_dispute" title="Chandrasekhar–Eddington dispute">Chandrasekhar–Eddington</a></li> <li><a href="/wiki/Galileo_affair" title="Galileo affair">Galileo affair</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton</a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Joule–von Mayer</a></li> <li><a href="/wiki/Great_Debate_(astronomy)" title="Great Debate (astronomy)">Shapley–Curtis</a></li> <li>Relativity priority <ul><li><a href="/wiki/Relativity_priority_dispute" title="Relativity priority dispute">Special relativity</a></li> <li><a href="/wiki/General_relativity_priority_dispute" title="General relativity priority dispute">General relativity</a></li></ul></li> <li><a href="/wiki/Transfermium_Wars" title="Transfermium Wars">Transfermium Wars</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" 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