{"id":6258,"date":"2020-10-13T15:13:45","date_gmt":"2020-10-13T09:43:45","guid":{"rendered":"http:\/\/astan.lk\/al_virtualclassroom\/?p=6258"},"modified":"2020-10-13T15:15:18","modified_gmt":"2020-10-13T09:45:18","slug":"fluid-dynamics","status":"publish","type":"post","link":"https:\/\/astan.lk\/al_virtualclassroom\/fluid-dynamics\/","title":{"rendered":"Fluid dynamics"},"content":{"rendered":"<p><strong>Steady flow \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/strong>All the fluid particles that pass any given point, follow the same path at same speed. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 In steady flow streamlines never cross each other.<\/p>\n<p><strong>Laminar flow \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong>In laminar flow, the velocities of all the particles on any given streamline are equal.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/lf-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8041\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/lf-1.png\" alt=\"lf\" width=\"246\" height=\"107\" \/><\/a><\/p>\n<p><strong>Turbulent flow \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong>Above a certain critical speed,fluid become turbulent .It is an \u00a0irregular flow ,we can&#8217;t predict the motion.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/tf.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8040\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/tf.jpg\" alt=\"tf\" width=\"180\" height=\"117\" \/><\/a><\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Incompressible flui<\/strong><\/span><span style=\"text-decoration: underline;\"><strong>d<\/strong><\/span><\/p>\n<p>In incompressible fluid change in pressure produces no change in density of the fluid. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Liquids can be considered incompressible and gases can be considered for small pressure differences.<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Viscous force<\/strong><\/span><\/p>\n<p>When two layers of liquid are moving with different velocities they experience tangental forces which tend to retard the faster layer and accelerate the slower layer.These forces are called viscous forces.<\/p>\n<p><strong>Ideal fluid flow means a fluid incompressible,non viscous at streamline flow.<\/strong><\/p>\n<h3><span style=\"text-decoration: underline;\">Equation of continuity<\/span><\/h3>\n<p>If a fluid is undergoing streamline flow then the mass of fluid which enters one end of a tube of flow must be equal to the mass that leaves at the other end during same time.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/slide_4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8044\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/slide_4.jpg\" alt=\"slide_4\" width=\"487\" height=\"366\" \/><\/a><\/p>\n<h3>Example &#8211; Equation of Continuity<\/h3>\n<p><i>10 m<sup>3<\/sup>\/h<\/i> of water flows through a pipe with <i>100 mm<\/i> inside diameter. The pipe is reduced to an inside dimension of <i>80 mm<\/i>.<\/p>\n<p>Using equation <em>(2)<\/em> the velocity in the <em>100 mm<\/em> pipe can be calculated<\/p>\n<blockquote><p><i>(10 m<sup>3<\/sup>\/h) (1 \/ 3600 h\/s) = v<sub>100<\/sub> (3.14 (0.1 m)<sup>2<\/sup> \/ 4)<\/i><\/p>\n<p><i>or<\/i><\/p>\n<p><i>v<sub>100<\/sub> = (10 m<sup>3<\/sup>\/h) (1 \/ 3600 h\/s) \/ (3.14 (0.1 m)<sup>2<\/sup> \/ 4)<\/i><\/p>\n<p><i>\u00a0\u00a0\u00a0 = 0.35 m\/s<\/i><\/p><\/blockquote>\n<p>Using equation <em>(2)<\/em> the velocity in the <em>80 mm<\/em> pipe can be calculated<\/p>\n<blockquote><p><i>(10 m<sup>3<\/sup>\/h) (1 \/ 3600 h\/s) = v<sub>80<\/sub> (3.14 (0.08 m)<sup>2<\/sup> \/ 4)<\/i><\/p>\n<p><i>or<\/i><\/p>\n<p><i>v<sub>80<\/sub> = (10 m<sup>3<\/sup>\/h) (1 \/ 3600 h\/s) \/ (3.14 (0.08 m)<sup>2<\/sup> \/ 4)<\/i><\/p>\n<p><i>= 0.55 m\/s<\/i><\/p><\/blockquote>\n<p>&nbsp;<\/p>\n<h3><span style=\"text-decoration: underline;\"><strong>Energy possessed by a fluid<\/strong><\/span><\/h3>\n<h3 align=\"center\"><span style=\"text-decoration: underline;\">Fluid Kinetic Energy<\/span><\/h3>\n<p>The kinetic energy of a moving fluid is more useful in applications like the Bernoulli equation when it is expressed as kinetic energy per unit volume<\/p>\n<p><center><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/fluids\/imgflu\/pke.gif\" width=\"378\" height=\"83\" \/><\/center><\/p>\n<h3 align=\"center\"><span style=\"text-decoration: underline;\">Fluid Potential Energy<\/span><\/h3>\n<p>The potential energy of a moving fluid is more useful in applications like the Bernoulli equation when is expressed as potential energy per unit volume<\/p>\n<p><center><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/fluids\/imgflu\/ppe.gif\" width=\"422\" height=\"92\" \/><\/center><\/p>\n<h3 align=\"center\"><span style=\"text-decoration: underline;\">Pressure as Energy Density<\/span><\/h3>\n<p>Pressure in a fluid may be considered to be a measure of energy per unit volume or energy density. For a force exerted on a fluid, this can be seen from the definition of pressure:<\/p>\n<p><center><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/fluids\/imgflu\/press2.gif\" width=\"478\" height=\"105\" \/><\/center><\/p>\n<h3><span style=\"text-decoration: underline;\"><strong>Bernoulli&#8217;s principle<\/strong><\/span><\/h3>\n<p>The Bernoulli Equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/imgmec\/bernoul.gif\" width=\"506\" height=\"339\" \/><\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Applications<\/strong><\/span><\/p>\n<ul>\n<li>Bernoulli&#8217;s principle can be used to calculate the lift force on an airfoil, if the behaviour of the fluid flow in the vicinity of the foil is known. For example, if the air flowing past the top surface of an aircraft wing is moving faster than the air flowing past the bottom surface, then Bernoulli&#8217;s principle implies that the pressure on the surfaces of the wing will be lower above than below. This pressure difference results in an upwards lifting force.\u00a0Whenever the distribution of speed past the top and bottom surfaces of a wing is known, the lift forces can be calculated (to a good approximation) using Bernoulli&#8217;s equations\u00a0established by Bernoulli over a century before the first man-made wings were used for the purpose of flight. Bernoulli&#8217;s principle does not explain why the air flows faster past the top of the wing and slower past the underside. See the article on aerodynamic lift for more info.<\/li>\n<\/ul>\n<ul>\n<li>The carburettor used in many reciprocating engines contains a venturi to create a region of low pressure to draw fuel into the carburettor and mix it thoroughly with the incoming air. The low pressure in the throat of a venturi can be explained by Bernoulli&#8217;s principle; in the narrow throat, the air is moving at its fastest speed and therefore it is at its lowest pressure.<\/li>\n<li>An injector on a steam locomotive (or static boiler).<\/li>\n<li>The pitot tube and static port on an aircraft are used to determine the airspeed of the aircraft.<\/li>\n<li>The flow speed of a fluid can be measured using a device such as a Venturi meter or an orifice plate, which can be placed into a pipeline to reduce the diameter of the flow. For a horizontal device, the continuity equation shows that for an incompressible fluid, the reduction in diameter will cause an increase in the fluid flow speed. Subsequently, Bernoulli&#8217;s principle then shows that there must be a decrease in the pressure in the reduced diameter region. This phenomenon is known as the Venturi effect.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3 align=\"center\"><span style=\"text-decoration: underline;\">Airfoil<\/span><\/h3>\n<p>One of the most common everyday applications of Bernoulli&#8217;s principle is in air flight.\u00a0The main way that Bernoulli&#8217;s principle works in air flight has to do with the architecture of the wings of the plane. In an airplane wing, the top of the wing is somewhat curved, while the bottom of the wing is totally flat. While in the sky, air travels across both the top and the bottom concurrently. Because both the top part and the bottom part of the plane are designed differently, this allows for the air on the bottom to move slower, which creates more pressure on the bottom, and allows for the air on the top to move faster, which creates less pressure. This is what creates lift, which allows planes to fly. An airplane is also acted upon by a pull of gravity in which opposes the lift, drag and thrust. Thrust is the force that enables the airplane to\u00a0move\u00a0forward while drag is air resistance that opposes the thrust force.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/bpn.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-8155\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/bpn.png\" alt=\"bpn\" width=\"863\" height=\"396\" \/><\/a><\/p>\n<h3 id=\"siteSub\"><span style=\"text-decoration: underline;\">Venturi meter<\/span><\/h3>\n<div id=\"jump-to-nav\" class=\"mw-jump\"><\/div>\n<div id=\"mw-content-text\" class=\"mw-content-ltr\" dir=\"ltr\" lang=\"en\">\n<div class=\"thumb tright\">\n<div class=\"thumbinner\">\n<p><a class=\"image\" href=\"https:\/\/en.wikipedia.org\/wiki\/File:Venturifixed2.PNG\"><img loading=\"lazy\" decoding=\"async\" class=\"thumbimage\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/54\/Venturifixed2.PNG\/300px-Venturifixed2.PNG\" srcset=\"\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/54\/Venturifixed2.PNG\/450px-Venturifixed2.PNG 1.5x, \/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/54\/Venturifixed2.PNG\/600px-Venturifixed2.PNG 2x\" alt=\"\" width=\"300\" height=\"147\" data-file-width=\"1268\" data-file-height=\"622\" \/><\/a><\/p>\n<div class=\"thumbcaption\">\n<div class=\"magnify\"><\/div>\n<p>The pressure in the first measuring tube (1) is higher than at the second (2), and the fluid speed at &#8220;1&#8221; is lower than at &#8220;2&#8221;, because the cross-sectional area at &#8220;1&#8221; is greater than at &#8220;2&#8221;.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"thumb tright\">\n<div class=\"thumbinner\">\n<p><a class=\"image\" href=\"https:\/\/en.wikipedia.org\/wiki\/File:VenturiFlow.png\"><img loading=\"lazy\" decoding=\"async\" class=\"thumbimage\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/7\/78\/VenturiFlow.png\" alt=\"\" width=\"220\" height=\"205\" data-file-width=\"220\" data-file-height=\"205\" \/><\/a><\/p>\n<div class=\"thumbcaption\">\n<div class=\"magnify\"><\/div>\n<p>A flow of air through a venturi meter, showing the columns connected in a manometer and partially filled with water. The meter is &#8220;read&#8221; as a differential pressure head in cm or inches of water<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The <b>Venturi effect<\/b> is the reduction in fluid pressure that results when a fluid flows through a constricted section of a pipe.<\/p>\n<p>In fluid dynamics, a fluid&#8217;s velocity must <i>increase<\/i> as it passes through a constriction in accord with the principle of mass continuity, while its static pressure must <i>decrease<\/i> in accord with the principle of conservation of mechanical energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is balanced by a drop in pressure.<\/p>\n<p>By measuring the change in pressure, the flow rate can be determined, as in various flow measurement devices such as venturi meters, venturi nozzles and orifice plates.<\/p>\n<p>Using Bernoulli&#8217;s equation in the special case of steady, incompressible, non viscous flows \u00a0along a streamline, the theoretical pressure drop at the constriction is given by:<\/p>\n<dl>\n<dd><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\/5867d9ef7ba2631627c12a000ec0096b9550c390\" alt=\"p_{1}-p_{2}={\\frac {\\rho }{2}}\\left(v_{2}^{2}-v_{1}^{2}\\right)\" \/><\/span><\/dd>\n<\/dl>\n<p>where <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\/72514fc82cf2078e1cc460f8fce1953225f3ee6a\" alt=\"\\scriptstyle \\rho \\,\" \/><\/span> is the density of the fluid, <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\/1639c3ff620c72b038ba08c9bea05673ee02e01a\" alt=\"\\scriptstyle v_{1}\" \/><\/span> is the (slower) fluid velocity where the pipe is wider, <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\/04e492ae2272fcfcfa1dae1f71c6e414cff04687\" alt=\"\\scriptstyle v_{2}\" \/><\/span> is the (faster) fluid velocity where the pipe is narrower (as seen in the figure)<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Steady flow \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [&hellip;]<\/p>\n","protected":false},"author":842,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[16,1948],"tags":[],"class_list":["post-6258","post","type-post","status-publish","format-standard","hentry","category-physics","category-unit-02-en"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Fluid dynamics - Learning &amp; 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