{"id":8267,"date":"2018-11-13T11:47:16","date_gmt":"2018-11-13T11:47:16","guid":{"rendered":"https:\/\/www.experimentoscientificos.es\/?page_id=8267"},"modified":"2018-11-19T09:49:05","modified_gmt":"2018-11-19T09:49:05","slug":"principio-de-bernoulli","status":"publish","type":"page","link":"https:\/\/www.experimentoscientificos.es\/en\/principio-de-bernoulli\/","title":{"rendered":"Bernoulli's Principle - Statement and Examples"},"content":{"rendered":"<p>Bernoulli's principle (<b>Bernoulli's equation or Bernoulli's trinomial)<\/b>describes the behaviour of a liquid or gas in a closed system. Bernoulli's principle describes the law of the <strong>conservation of energy<\/strong>in an ideal fluid (moving without friction and without viscosity), its energy remains constant along its entire length when it flows through a closed conduit.<\/p>\n<h2>BERNOULLI PRINCIPLE EQUATION<\/h2>\n<p>Bernoulli's equation describes the <strong>law of conservation of energy in a fluid<\/strong>. For this we need the energy components that a fluid in motion can have. In a <strong>ideal situation<\/strong>without friction and viscosity, the 3 components of the energy would be:<\/p>\n<ul>\n<li>Kinetic energy: The kinetic energy is due to the velocity of the fluid.<\/li>\n<li>Potential energy: The potential energy is due to the height of the fluid.<\/li>\n<li>Pressure energy: The energy due to the pressure that a fluid possesses.<\/li>\n<\/ul>\n<p>The 3 parts of energy, in formula would look like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8269\" src=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/Ecuacion-de-bernoulli.jpg\" alt=\"\" width=\"215\" height=\"65\" \/><\/p>\n<p>The first part corresponds to the kinetic energy, the second to the pressure energy and the third to the potential energy due to the height jumps it may have.<\/p>\n<ul>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/af0f6064540e84211d0ffe4dac72098adfa52845\" alt=\"V\" aria-hidden=\"true\" \/><\/span>\u00a0= fluid velocity.<\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/1f7d439671d1289b6a816e6af7a304be40608d64\" alt=\"\\rho \" aria-hidden=\"true\" \/><\/span>\u00a0=\u00a0<a href=\"https:\/\/www.experimentoscientificos.es\/en\/densidad\/\">density<\/a>\u00a0of the liquid or gas.<\/li>\n<li><span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b4dc73bf40314945ff376bd363916a738548d40a\" alt=\"P\" aria-hidden=\"true\" \/><\/span><\/span>= fluid pressure along the streamline.<\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d3556280e66fe2c0d0140df20935a6f057381d77\" alt=\"g\" aria-hidden=\"true\" \/><\/span>\u00a0=\u00a0<a class=\"mw-redirect\" title=\"Intensity of gravity\" href=\"https:\/\/es.wikipedia.org\/wiki\/Intensidad_de_la_gravedad\">gravitational acceleration<\/a><\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/bf368e72c009decd9b6686ee84a375632e11de98\" alt=\"z\" aria-hidden=\"true\" \/><\/span>\u00a0= height in the direction of the\u00a0<a title=\"Gravity\" href=\"https:\/\/www.experimentoscientificos.es\/en\/gravedad\/\">gravity<\/a>.<\/li>\n<\/ul>\n<p>The fact that the sum of the 3 energies remains constant means that if there is a variation in any one of them, there must necessarily be a variation in another to maintain the constant.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8281\" src=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/principio-de-bernoulli.png\" alt=\"\" width=\"450\" height=\"221\" srcset=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/principio-de-bernoulli.png 450w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/principio-de-bernoulli-300x147.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>For example, if the velocity of a fluid changes without changing its height, the pressure must change. If we increase the velocity (e.g. by passing it through a narrower section - see next section), the pressure exerted by the fluid will be lower. If we decrease the velocity, the pressure will be higher. This simple approach, explained by Bernoulli's principle, gives the reason for the <a href=\"https:\/\/www.experimentoscientificos.es\/en\/experimento-vuelan-los-aviones\/\">elevation of aircraft wings<\/a>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8303\" src=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/aerodinamica-2.jpg\" alt=\"Experimento Vuelo de Avi\u00f3n\" width=\"675\" height=\"300\" srcset=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/aerodinamica-2.jpg 727w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/aerodinamica-2-300x133.jpg 300w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/aerodinamica-2-660x293.jpg 660w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/p>\n<p>The velocity at the top of the wing increases due to the law of continuity of mass, where the flow rate at the inlet must be equal to the flow rate at the outlet (see next section). As the velocity at the top increases, the kinetic energy of the fluid increases and according to Bernoulli's principle, for the sum of energies to remain constant, either its head or its pressure varies. The height does not change, so the fluid pressure is lower.<\/p>\n<p>Lower pressure in the upper wing area and higher pressure below causes the wing to hover.<\/p>\n<h2>LAW OF CONTINUITY OF MASS IN FLUIDS<\/h2>\n<p>Complementary to Bernoulli's law is the <strong>law of continuity of mass in fluids<\/strong>The same amount of mass that enters a section, exits the section. This law is also important when applying Bernoulli's principle. According to the law of continuity, the flow in the wide section will be the same as the flow in the narrow section, and for the same flow per unit time, the velocity in the narrow section will be greater.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8273\" src=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/ecuacion-de-continuidad-4-638.jpg\" alt=\"ecuacion de continuidad\" width=\"323\" height=\"242\" srcset=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/ecuacion-de-continuidad-4-638.jpg 638w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/ecuacion-de-continuidad-4-638-300x225.jpg 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2>APPLICATIONS OF THE BERNOULLI PRINCIPLE<\/h2>\n<h3><b>Pipe<\/b><\/h3>\n<p>Bernoulli's equation and the continuity equation tell us that reducing the cross-sectional area of a pipe will increase its velocity and reduce the fluid pressure.<\/p>\n<p>The increase in velocity is by the mass continuity equation. Where the flow rate in all sections must be constant. The flow rate is the mass per unit time. If the section is reduced the velocity must increase so that the amount of mass is the same.<\/p>\n<p>According to Bernoulli's principle of conservation of energy, when the velocity is reduced, either the pressure or the height must change in order to comply with Bernoulli's constant. If there is no change in height, there must be a change in pressure. If the velocity increases, the pressure decreases and vice versa.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8281\" src=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/principio-de-bernoulli.png\" alt=\"\" width=\"450\" height=\"221\" srcset=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/principio-de-bernoulli.png 450w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/principio-de-bernoulli-300x147.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>According to the picture, there is less velocity in the wider section than in the narrow section. By placing a tube and comparing the pressures you can see that there is more pressure where there is less velocity. This corresponds to Bernoulli's principle or conservation of energy.<\/p>\n<h3><b>Automotive carburettor<\/b><\/h3>\n<p>In an automotive carburettor, the pressure of the air passing through the carburettor body decreases as it passes through a choke. As the pressure decreases, the gasoline flows, vaporises and mixes with the air stream.<\/p>\n<h3><b>Aircraft<\/b><\/h3>\n<p>The geometry of aeroplane wings takes advantage of Bernoulli's principle for their lift. You can see here the <a href=\"https:\/\/www.experimentoscientificos.es\/en\/experimento-vuelan-los-aviones\/\">experiment why aeroplanes fly.<\/a><\/p>\n<h3>Sailing Boat<\/h3>\n<p>Sailing boats, when sailing upwind, are also doing so thanks to Bernoulli's principle. When sailing upwind (at most 45\u00b0 upwind with a smaller angle you cannot sail), it is the lower pressure on the outboard side of the sail that causes the boat to push. This force, together with the resistance of the keel, is what causes the force in the direction of movement.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8286\" src=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos1.-bernoulli.jpg\" alt=\"barcos1. bernoulli\" width=\"606\" height=\"322\" srcset=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos1.-bernoulli.jpg 640w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos1.-bernoulli-300x159.jpg 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8285\" src=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos.-bernoulli-888x1024.jpg\" alt=\"\" width=\"408\" height=\"470\" srcset=\"https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos.-bernoulli-888x1024.jpg 888w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos.-bernoulli-260x300.jpg 260w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos.-bernoulli-768x885.jpg 768w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos.-bernoulli-660x761.jpg 660w, https:\/\/www.experimentoscientificos.es\/wp-content\/uploads\/2018\/11\/barcos.-bernoulli.jpg 1388w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<h2>RELATED EXPERIMENTS<\/h2>\n<div class=\"facetwp-template\" data-name=\"dinamica\">\n<div style=\"margin-top: 20px\">\n\n\n<div style=\"float: left; width: 18%\">\n<\/div>\n<div style=\"float:left; width: 78%; margin-left: 2%\">\n<div>\n\n<div><h3 class=\"entry-title\" style=\"\"><a href=\"https:\/\/www.experimentoscientificos.es\/en\/experimento-vuelan-los-aviones\/\">How Planes Fly Experiment. Bernoulli's Principle<\/a><\/h3><\/div>\n\n<strong><\/strong> In this experiment, carried out at the Alcobendas Science Museum, we are going to see how the lift of an aeroplane wing is produced following Bernoulli's principle.<\/div>\n\n<\/div>\n<div class=\"clear\"><\/div>\n<\/div>\n<div class=\"clear\"><\/div>\n\n\n\n<div style=\"margin-top: 20px\">\n\n\n<div style=\"float: left; width: 18%\">\n<\/div>\n<div style=\"float:left; width: 78%; margin-left: 2%\">\n<div>\n\n<div><h3 class=\"entry-title\" style=\"\"><a href=\"https:\/\/www.experimentoscientificos.es\/en\/experimento-demostracion-efecto-venturi\/\">Venturi Effect Demonstration Experiment<\/a><\/h3><\/div>\n\n<strong><\/strong> This experiment was recorded at the Alcobendas Science Museum. In it you can experience the overpressure produced by the Venturi effect by widening the air duct section.<\/div>\n\n<\/div>\n<div class=\"clear\"><\/div>\n<\/div>\n<div class=\"clear\"><\/div>\n\n\n    <\/div>\n<p>&nbsp;<\/p>\n<h2><span id=\"Ecuaci\u00f3n_de_Bernoulli_con_fricci\u00f3n_y_trabajo_externo\" class=\"mw-headline\">BERNOULLI EQUATION WITH FRICTION\u00a0<\/span><\/h2>\n<p>Bernoulli's equation, as we have explained it so far, applies to non-viscous, incompressible fluids in which there is no external work, such as a pump or a turbine. These factors can be added into the equation to obtain a complete equation of the <strong>conservation of the quantity of motion, <\/strong>including friction and work.<\/p>\n<blockquote><p><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0f5a730ac82c9b2eaae7ba4945e996b875574365\" alt=\"{\\displaystyle {\\frac {{V_{1}}^{2}}{2g}}+{\\frac {P_{1}}{\\gamma }}+z_{1}+W\/g=h_{f}+{\\frac {{V_{2}}^{2}}{2g}}+{\\frac {P_{2}}{\\gamma }}+z_{2}}\" aria-hidden=\"true\" \/><\/span><\/p><\/blockquote>\n<p>where:<\/p>\n<ul>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/a223c880b0ce3da8f64ee33c4f0010beee400b1a\" alt=\"\\gamma \" aria-hidden=\"true\" \/><\/span>\u00a0is the specific gravity (<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/565f72d90db4ee85db6911526a3a2e3901c34b9b\" alt=\"{\\displaystyle \\gamma =\\rho g}\" aria-hidden=\"true\" \/><\/span>). This value is assumed to be constant throughout the travel as the fluid is incompressible.<\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/54a9c4c547f4d6111f81946cad242b18298d70b7\" alt=\"W\" aria-hidden=\"true\" \/><\/span>\u00a0external work supplied to (+) or extracted from (-) the fluid per unit mass flow rate through the fluid path.<\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/1d42c1996a2927feda919e6b49d2966b9fee866b\" alt=\"{\\displaystyle h_{f}}\" aria-hidden=\"true\" \/><\/span>\u00a0frictional dissipation through the fluid path.<\/li>\n<li>g = <a href=\"https:\/\/www.experimentoscientificos.es\/en\/gravedad\/\">gravity<\/a>= 9.81 m\/s<sup>2<\/sup>.<\/li>\n<\/ul>\n<h2>YOU MAY BE INTERESTED IN<\/h2>\n<p><a href=\"https:\/\/www.experimentoscientificos.es\/en\/efecto-venturi\/\">Venturi effect<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>Bernoulli's principle (Bernoulli's equation or Bernoulli's trinomial) describes the behaviour of a liquid or gas in a closed system. Bernoulli's principle describes the law of conservation of energy: in an ideal fluid (moving without friction and without viscosity), its energy remains constant along its entire length when it flows [...].<\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Principio de Bernoulli - Enunciado y Ejemplos<\/title>\n<meta name=\"description\" content=\"El principio de Bernoulli o principio de conservaci\u00f3n de Energ\u00eda en sistemas cerrados. 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