{"id":16364,"date":"2018-01-03T17:57:06","date_gmt":"2018-01-03T17:57:06","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=16364"},"modified":"2022-11-05T07:29:10","modified_gmt":"2022-11-05T07:29:10","slug":"what-is-pressure-physics","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/","title":{"rendered":"What is Pressure &#8211; Physics"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">\n<p><strong>Pressure<\/strong> is a measure of the <strong>force exerted<\/strong> per unit area on the boundaries of a substance. The standard unit for <strong>pressure<\/strong> in the SI system is the <strong>Newton per square meter or pascal (Pa)<\/strong>. Mathematically:<\/p>\n<p><strong>p = F\/A<\/strong><\/p>\n<p>where<\/p>\n<ul>\n<li><strong>p is the pressure<\/strong><\/li>\n<li><strong>F is the normal force<\/strong><\/li>\n<li><strong>A is the area of the boundary<\/strong><\/li>\n<\/ul>\n<\/div><\/div>\n<p>Pascal is defined as a force of 1N that is exerted on a unit area.<\/p>\n<ul>\n<li><strong>1 Pascal = 1 N\/m<sup>2<\/sup><\/strong><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>However, it is a fairly small unit for most engineering problems, so it is convenient to work with multiples of the pascal: the <strong>kPa<\/strong>, the <strong>bar<\/strong>, and the <strong>MPa<\/strong>.<\/p>\n<ul>\n<li><strong>1 MPa \u00a010<sup>6<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 bar \u00a0\u00a0\u00a010<sup>5<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 kPa \u00a0\u00a010<sup>3<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<\/ul>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16368 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement-235x300.png\" alt=\"manometer-pressure-measurement\" width=\"235\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement-235x300.png 235w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Manometer-Pressure-Measurement.png 290w\" sizes=\"(max-width: 235px) 100vw, 235px\" \/><\/a>In general, pressure or the force exerted per unit area on the boundaries of a substance is caused by the <strong>collisions<\/strong> of the <strong>molecules<\/strong> of the substance with the boundaries of the system. As molecules hit the walls, they exert forces that try to push the walls outward. The forces resulting from all of these collisions cause the <strong>pressure<\/strong> exerted by a system on its surroundings. Pressure as an <a title=\"Extensive and Intensive Properties\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/extensive-and-intensive-properties\/\"><strong>intensive variable<\/strong> <\/a>is constant in a closed system. It is only relevant in liquid or ga搜索引擎优化us systems.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Static Pressure<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, <strong>pressure<\/strong>\u00a0is a measure of the\u00a0<strong>force exerted<\/strong>\u00a0per unit area on the boundaries of a substance. In fluid dynamics, many authors use the term static pressure in preference to just pressure to avoid ambiguity. The term <strong>static pressure<\/strong> is identical to the term pressure and can be identified for every point in a fluid flow field.<\/p>\n<p><strong>Static pressure<\/strong> is one of the terms of\u00a0<strong><a title=\"Bernoulli\u2019s Equation \u2013 Bernoulli\u2019s Principle\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/\">Bernoulli\u2019s equation<\/a>: <\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14235\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png\" alt=\"Bernoulli Theorem - Equation\" width=\"346\" height=\"66\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png 346w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation-300x57.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/a><\/p>\n<p>Bernoulli\u2019s <strong>effect<\/strong> causes the\u00a0<strong>lowering of fluid pressure (static pressure &#8211; p)<\/strong> in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive but seems less so when you consider the pressure to be energy density. In the high-velocity flow through the constriction, kinetic energy (dynamic pressure \u2013 \u00bd.\u03c1.v<sup>2<\/sup>) must increase at the expense of pressure energy (<strong>static pressure &#8211; p<\/strong>).<\/p>\n<p>The simplified form of Bernoulli\u2019s equation can be summarized in the following memorable word equation:<\/p>\n<p style=\"text-align: center;\"><em><a title=\"Static Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/static-pressure\/\">static pressure<\/a>\u00a0+\u00a0<a title=\"Dynamic Pressure \u2013 Velocity Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/dynamic-pressure-velocity-pressure\/\">dynamic pressure<\/a>\u00a0=\u00a0<a title=\"Stagnation Pressure \u2013 Pitot Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/stagnation-pressure-pitot-pressure\/\">total pressure (stagnation pressure)<\/a><\/em><\/p>\n<p>Total and dynamic pressure are not pressures in the usual sense &#8211; they cannot be measured using an aneroid, Bourdon tube, or mercury column.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Dynamic Pressure<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, <strong>pressure<\/strong>\u00a0is a measure of the\u00a0<strong>force exerted<\/strong>\u00a0per unit area on the boundaries of a substance. The term <strong>dynamic pressure<\/strong> (sometimes called <strong>velocity pressure<\/strong>) \u00a0is associated with fluid flow and with <strong>Bernoulli\u2019s effect, <\/strong>which is described by <strong><a title=\"Bernoulli\u2019s Equation \u2013 Bernoulli\u2019s Principle\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/\">Bernoulli\u2019s equation<\/a>:<\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14235\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png\" alt=\"Bernoulli Theorem - Equation\" width=\"346\" height=\"66\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png 346w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation-300x57.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/a><\/p>\n<p>This effect causes the\u00a0<strong>lowering of fluid pressure (static pressure)<\/strong> in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive but seems less so when you consider the pressure to be energy density. In the high-velocity flow through the constriction, kinetic energy (dynamic pressure \u2013 \u00bd.\u03c1.v<sup>2<\/sup>) must increase at the expense of pressure energy (static pressure &#8211; p).<\/p>\n<p>As can be seen, dynamic pressure is one of the terms of <strong>Bernoulli\u2019s equation. <\/strong>In incompressible fluid dynamics, dynamic pressure is the quantity defined by:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/dynamic-pressure-formula.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20621\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/dynamic-pressure-formula.png\" alt=\"dynamic pressure - formula\" width=\"114\" height=\"57\" \/><\/a><\/p>\n<p>The simplified form of Bernoulli\u2019s equation can be summarized in the following memorable word equation:<\/p>\n<p style=\"text-align: center;\"><em><a title=\"Static Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/static-pressure\/\">static pressure<\/a>\u00a0+\u00a0<a title=\"Dynamic Pressure \u2013 Velocity Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/dynamic-pressure-velocity-pressure\/\">dynamic pressure<\/a>\u00a0=\u00a0<a title=\"Stagnation Pressure \u2013 Pitot Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/stagnation-pressure-pitot-pressure\/\">total pressure (stagnation pressure)<\/a><\/em><\/p>\n<p>Total and dynamic pressure are not pressures in the usual sense &#8211; they cannot be measured using an aneroid, Bourdon tube, or mercury column.<\/p>\n<p>Many authors use the term static pressure to distinguish it from total pressure and dynamic pressure to avoid potential ambiguity when referring to pressure in fluid dynamics. The term static pressure is identical to the term pressure and can be identified for every point in a fluid flow field. Dynamic pressure is the difference between stagnation pressure and static pressure.<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Stagnation Pressure<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, <strong>pressure<\/strong>\u00a0is a measure of the\u00a0<strong>force exerted<\/strong>\u00a0per unit area on the boundaries of a substance. In fluid dynamics and aerodynamics, <strong>stagnation pressure<\/strong> (or <strong>pitot pressure<\/strong> or <strong>total pressure<\/strong>) is the static pressure at a <strong>stagnation point<\/strong> in a fluid flow. At a <strong>stagnation point,<\/strong> the fluid velocity is zero, and all <a title=\"What is Kinetic Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-kinetic-energy\/\">kinetic energy<\/a> has been converted into pressure energy (isentropically). This effect is widely used in aerodynamics (velocity measurement or ram-air intake).<\/p>\n<p><strong>Stagnation pressure<\/strong> is equal to the sum of the free-stream dynamic pressure and free-stream static pressure.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/stagnation-pressure-total-pressure.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20622\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/stagnation-pressure-total-pressure.png\" alt=\"stagnation pressure - total pressure\" width=\"240\" height=\"54\" \/><\/a><\/p>\n<p>Static pressure and dynamic pressure are terms of\u00a0<strong>Bernoulli\u2019s equation: <\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-14235\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation-300x57.png\" alt=\"Bernoulli Theorem - Equation\" width=\"300\" height=\"57\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation-300x57.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Bernoulli-Theorem-Equation.png 346w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><strong>Bernoulli\u2019s effect<\/strong> causes the\u00a0<strong>lowering of fluid pressure (static pressure &#8211; p)<\/strong> in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive but seems less so when you consider the pressure to be energy density. In the high-velocity flow through the constriction, kinetic energy (dynamic pressure \u2013 \u00bd.\u03c1.v<sup>2<\/sup>) must increase at the expense of pressure energy (static pressure &#8211; p).<\/p>\n<p>The simplified form of Bernoulli\u2019s equation can be summarized in the following memorable word equation:<\/p>\n<p style=\"text-align: center;\"><em><a title=\"Static Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/static-pressure\/\">static pressure<\/a> + <a title=\"Dynamic Pressure \u2013 Velocity Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/dynamic-pressure-velocity-pressure\/\">dynamic pressure<\/a> = <a title=\"Stagnation Pressure \u2013 Pitot Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/stagnation-pressure-pitot-pressure\/\">total pressure (stagnation pressure)<\/a><\/em><\/p>\n<p>Total and dynamic pressure are not pressures in the usual sense &#8211; they cannot be measured using an aneroid, Bourdon tube, or mercury column.<\/p>\n<p><strong>Stagnation pressure<\/strong> is sometimes referred to as pitot pressure because it is measured using a pitot tube. A Pitot tube is a pressure measurement instrument used to measure fluid flow velocity. Velocity can be determined using the following formula:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/pitot-tube-formula-velocity.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20623\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/pitot-tube-formula-velocity.png\" alt=\"pitot tube - formula - velocity\" width=\"158\" height=\"73\" \/><\/a><\/p>\n<p>where:<\/p>\n<ul>\n<li>u is flow velocity\u00a0to be measured in m\/s,<\/li>\n<li>p<sub>s\u00a0<\/sub>is stagnation or total pressure in Pa,<\/li>\n<li>p<sub>t<\/sub> is static pressure in Pa,<\/li>\n<li>\u03c1 is fluid density in\u00a0kg\/m<sup>3<\/sup>.<\/li>\n<\/ul>\n<\/div><\/div><\/div><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-16371\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure-300x129.png\" alt=\"What is Pressure\" width=\"300\" height=\"129\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure-300x129.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/What-is-Pressure.png 538w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<canvas id=\"the_canvas\" width=\"250\" height=\"250\"><\/canvas>\r\n<script>\r\n\r\nvar __VERSION__ = \"0.3.5\"\r\nvar inspector = {};\r\n\r\nvar Physics = {\r\n    \r\n    collide_balls: function(ball1, ball2) {\r\n        \/\/ calculate restitution\r\n        \/\/ TODO: add elasticity attr to circles\r\n        var ball1_elasticity = 1.0;\r\n        var ball2_elasticity = 1.0;\r\n        var restitution = ball1_elasticity * ball2_elasticity;\r\n        \r\n        \/\/ invert masses\r\n        var im1 = 1.0 \/ ball1.m;\r\n        var im2 = 1.0 \/ ball2.m;\r\n        \r\n        \/\/ get minimum translation distance\r\n        var delta = ball1.point().subtract(ball2.point());\r\n        var d = delta.get_length();\r\n        var mtd = delta.multiply(ball1.r + ball2.r - d).multiply(1.0 \/ d);\r\n        \r\n        \/\/ push-pull apart based on mass\r\n        var ball1_pt = ball1.point().add(mtd.multiply(im1 \/ (im1 + im2)));\r\n        var ball2_pt = ball2.point().subtract(mtd.multiply(im2 \/ (im1 + im2)));\r\n        ball1.set_point(ball1_pt.x, ball1_pt.y);\r\n        ball2.set_point(ball2_pt.x, ball2_pt.y);\r\n        \r\n        \/\/ calculate impact speed\r\n        var v = ball1.velocity().subtract(ball2.velocity());\r\n        var vn = v.dot(mtd.normalized());\r\n        \r\n        \/\/ positive vn means balls are already moving away for one another\r\n        if ( vn > 0 ) {\r\n            return;\r\n        }\r\n        \r\n        \/\/ collision impulse\r\n        var i = (-1.0 * (1.0 + restitution) * vn) \/ (im1 + im2);\r\n        var impulse = mtd.normalized().multiply(i);\r\n        \r\n        \/\/ transfer momentum\r\n        var v1 = ball1.velocity().add(impulse.multiply(im1));\r\n        var v2 = ball2.velocity().subtract(impulse.multiply(im2));\r\n        \r\n        \/\/ set new velocities\r\n        ball1.set_velocity(v1.x, v1.y);\r\n        ball2.set_velocity(v2.x, v2.y);\r\n    },\r\n    \r\n    bounce_ball_off_world: function(ball, world) {\r\n        \/\/ translate ball back inside world\r\n        var contact_pt = this.find_contact_point(world, ball);\r\n        ball.set_point(contact_pt.x, contact_pt.y);\r\n    \r\n        \/\/ reflect velocity of ball\r\n        var new_ball_vel = this.reflect_ball(world, ball);\r\n        ball.set_velocity(new_ball_vel.x, new_ball_vel.y);\r\n    },\r\n    \r\n    find_contact_point: function(world, ball) {\r\n        \/\/ see http:\/\/gamedev.stackexchange.com\/a\/29658\r\n        var A = world.point();\r\n        var B = ball.last_point();\r\n        var C = ball.point();\r\n        var R = world.r;\r\n        var r = ball.r;\r\n        \r\n        var AB = B.subtract(A);\r\n        var BC = C.subtract(B);\r\n        var AB_len = AB.get_length();\r\n        var BC_len = BC.get_length();\r\n        \r\n        \/\/ Avoid divide-by-zero erros (this should never really happen)\r\n        if ( ! BC_len ) {\r\n            return C;\r\n        }\r\n\r\n        var b = AB.dot(BC) \/ Math.pow(BC_len, 2) * -1;\r\n        var c = (Math.pow(AB_len, 2) - Math.pow(R - r, 2)) \/ Math.pow(BC_len, 2);\r\n        var d = b * b - c;\r\n        var k = b - Math.sqrt(d);\r\n        \r\n        if ( k < 0 ) {\r\n            k = b + Math.sqrt(d);\r\n        }\r\n        \r\n        var BD = C.subtract(B);\r\n        var BD_len = BC_len * k;\r\n        BD.set_length(BD_len);\r\n        \r\n        var D = B.add(BD);\r\n        return D;\r\n    },\r\n    \r\n    reflect_ball: function(world, ball) {\r\n        \/\/ see http:\/\/stackoverflow.com\/a\/573206\/1093087\r\n        var world_pt = world.point();\r\n        var ball_pt = ball.point();\r\n        var v = ball.velocity();\r\n        var n = ball_pt.subtract(world_pt).normalized();\r\n        \r\n        \/\/ assume perfect elasticity for now\r\n        \/\/ TODO: add elasticity attr to balls\r\n        var ball_elasticity = 1.0;\r\n        var world_elasticity = 1.0;\r\n        var restitution = ball_elasticity * world_elasticity;\r\n        \r\n        \/\/ solve reflection\r\n        var u = n.multiply(v.dot(n));\r\n        var w = v.subtract(u);\r\n        var v_after = w.subtract(u);\r\n        var reflection = v_after.subtract(v).multiply(restitution);\r\n        \r\n        \/\/ return new velocity\r\n        var new_ball_vel = v.add(reflection);\r\n        return new_ball_vel\r\n    },\r\n    \r\n    polar_to_vector: function(distance, angle) {\r\n        var radians = angle * (Math.PI \/ 180);\r\n        return new Vec2d(distance * Math.cos(radians),\r\n            distance * Math.sin(radians));\r\n    },\r\n};\r\n\r\n\r\nvar Graphics = {\r\n\r\n    init: function(canvas) {\r\n        this.ctx = canvas.getContext('2d');\r\n        this.center_x = canvas.width \/ 2;\r\n        this.center_y = canvas.height \/ 2;\r\n    },\r\n\r\n    draw_circle: function(x, y, r, color, line_width, stroke_color) {\r\n        var screen_x = this.world_to_screen_x(x);\r\n        var screen_y = this.world_to_screen_y(y);\r\n\r\n        this.ctx.beginPath();\r\n        this.ctx.arc(screen_x, screen_y, r, 0, Math.PI * 2, false);\r\n        this.ctx.fillStyle = color;\r\n        this.ctx.fill();\r\n\r\n        if (line_width) {\r\n            this.ctx.lineWidth = line_width;\r\n            this.ctx.strokeStyle = stroke_color;\r\n            this.ctx.stroke();\r\n        }\r\n\r\n        this.ctx.closePath();\r\n    },\r\n\r\n    world_to_screen_x: function(x) {\r\n        return this.center_x + x;\r\n    },\r\n\r\n    world_to_screen_y: function(y) {\r\n        return this.center_y - y;\r\n    },\r\n};\r\n\r\n\r\nvar Random = {\r\n    integer: function(min, max) {\r\n        return min + Math.floor(Math.random() * (max - min + 1));\r\n    }\r\n};\r\n\r\n\r\nfunction Vec2d(x, y) {\r\n    this.x = x;\r\n    this.y = y;\r\n    \r\n    this.add = function(v2) {\r\n        return new Vec2d(this.x + v2.x, this.y + v2.y);\r\n    };\r\n    \r\n    this.subtract = function(v2) {\r\n        return new Vec2d(this.x - v2.x, this.y - v2.y);\r\n    };\r\n    \r\n    this.multiply = function(v2) {\r\n        if ( ! v2.length ) {\r\n            \/\/ v2 is a scalar\r\n            return new Vec2d(this.x * v2, this.y * v2);\r\n        }\r\n        else {\r\n            return new Vec2d(this.x * v2.x, this.y * v2.y);\r\n        }\r\n    };\r\n    \r\n    this.get_length = function() {\r\n        return Math.sqrt((this.x * this.x) + (this.y * this.y));\r\n    };\r\n    \r\n    this.set_length = function(new_length) {\r\n        var old_length = this.get_length();\r\n        this.x *= new_length\/old_length;\r\n        this.y *= new_length\/old_length;\r\n        return this;\r\n    };\r\n    \r\n    this.distance = function(v2) {\r\n        return Math.sqrt(Math.pow(this.x - v2.x, 2) + Math.pow(\r\n            this.y - v2.y, 2));\r\n    };\r\n    \r\n    this.dot = function(v2) {\r\n        return (this.x * v2.x) + (this.y * v2.y);\r\n    };\r\n    \r\n    this.normalized = function() {\r\n        var length = this.get_length();\r\n        \r\n        if ( length != 0 ) {\r\n            return new Vec2d(this.x \/ length, this.y \/ length);\r\n        }\r\n        else {\r\n            return new Vec2d(this.x, this.y);\r\n        }\r\n    };\r\n}\r\n\r\n\r\nfunction Circle(x, y, r) {    \r\n    this.init = function(x, y, r) {\r\n        this.set_point(x, y);\r\n        this.r = r;\r\n    };\r\n    \r\n    this.point = function() {\r\n        return new Vec2d(this.x, this.y);\r\n    };\r\n    \r\n    this.set_point = function(x, y) {\r\n        this.x = x;\r\n        this.y = y;\r\n        return this;\r\n    };\r\n    \r\n    this.contains_circle = function(c2) {\r\n        var d = this.point().distance(c2.point());\r\n        return d + c2.r - this.r < 0;\r\n    };\r\n    \r\n    this.overlaps_circle = function(c2) {\r\n        \/\/ overlap if combined length is less than distance (use squares for\r\n        \/\/ quicker calculations)\r\n        var dsq = Math.pow(c2.y - this.y, 2) + Math.pow(c2.x - this.x, 2);\r\n        var lsq = Math.pow(this.r + c2.r, 2);\r\n        return dsq < lsq;\r\n    };\r\n    \r\n    this.init(x, y, r);\r\n}\r\n\r\n\r\nfunction World() {\r\n    \/\/ parasitic inheritance\r\n    \/\/ see http:\/\/www.crockford.com\/javascript\/inheritance.html\r\n    var self = new Circle(0, 0, 100);\r\n    \r\n    self.balls = [];\r\n    \r\n    self.color = 'white';\r\n    self.line = 4;\r\n    self.stroke = 'lightgray';\r\n    \r\n    self.update = function() {\r\n        self.balls.map(function(ball) {\r\n            ball.update();\r\n        });\r\n        self.resolve_collisions();\r\n        self.enforce_boundaries();\r\n        return self;\r\n    };\r\n\r\n    self.draw = function () {\r\n        Graphics.draw_circle(self.x, self.y, self.r, self.color, self.line,\r\n            self.stroke);\r\n        self.balls.map(function(ball) {\r\n            ball.draw();\r\n        });\r\n        return self;\r\n    };\r\n    \r\n    self.enforce_boundaries = function() {\r\n        self.balls.map(function(ball) {\r\n            if (! self.contains_circle(ball)) {\r\n                Physics.bounce_ball_off_world(ball, self);\r\n            }\r\n        });\r\n        return self;\r\n    };\r\n    \r\n    self.resolve_collisions = function() {\r\n        for (var i=0; i<self.balls.length; i++) {\r\n            for (var j=i+1; j<self.balls.length; j++) {\r\n                if ( self.balls[i].collides_with(self.balls[j]) ) {\r\n                    self.balls[i].bounce_off(self.balls[j]);\r\n                }\r\n            }\r\n        }\r\n        return self;\r\n    };\r\n    \r\n    self.add_ball = function(ball) {\r\n        self.balls.push(ball);\r\n        return self;\r\n    };\r\n\r\n    return self;\r\n}\r\n\r\n\r\nfunction Ball(x, y, r, color) {\r\n    var self = new Circle(x, y, r);\r\n    self.color = color;\r\n    \r\n    self.m = 10;\r\n    self.vx = 0;\r\n    self.vy = 0;\r\n    \r\n    \/\/ last point: this is needed to resolve collisions with world's wall\r\n    self.lx = undefined;\r\n    self.ly = undefined;\r\n    \r\n    self.max_speed = r \/ 2.0;\r\n    \r\n    self.update = function() {\r\n        self.move();\r\n    };\r\n\r\n    self.move = function() {\r\n        self.lx = self.x;\r\n        self.ly = self.y;\r\n        self.x += self.vx;\r\n        self.y += self.vy;\r\n        return self;\r\n    };\r\n    \r\n    self.last_point = function() {\r\n        return new Vec2d(self.lx, self.ly);\r\n    };\r\n    \r\n    self.set_velocity = function(vx, vy) {\r\n        self.vx = vx;\r\n        self.vy = vy;\r\n        return self;\r\n    };\r\n    \r\n    self.velocity = function() {\r\n        return new Vec2d(self.vx, self.vy);\r\n    };\r\n    \r\n    self.clamp_speed = function () {\r\n        var v = self.velocity();\r\n        var speed = v.get_length();\r\n        if (speed > self.max_speed) {\r\n            v.set_length(self.max_speed);\r\n            self.set_velocity(v.x, v.y);\r\n        }\r\n        return self;\r\n    };\r\n\r\n    self.draw = function () {\r\n        Graphics.draw_circle(self.x, self.y, self.r, self.color, 0);\r\n        return self;\r\n    };\r\n    \r\n    self.collides_with = function(ball) {\r\n        return self.overlaps_circle(ball);\r\n    };\r\n    \r\n    self.bounce_off = function(ball) {\r\n        Physics.collide_balls(self, ball);\r\n        return self;\r\n    };\r\n    \r\n    self.set_direction = function(degrees) {\r\n        var d = self.velocity().get_length();\r\n        var v = Physics.polar_to_vector(d, degrees);\r\n        self.set_velocity(v.x, v.y);\r\n        return self;        \r\n    };\r\n    \r\n    self.set_random_direction = function() {\r\n        return self.set_direction(Random.integer(0,360));\r\n    };\r\n    \r\n    return self;\r\n}\r\n\r\n\r\nfunction main() {\r\n    console.log('launching version: ' + __VERSION__);\r\n    \r\n    \/\/ load canvas and Graphics handler\r\n    var canvas = document.getElementById(\"the_canvas\");\r\n    Graphics.init(canvas);\r\n    \r\n    \/\/ set animation handler\r\n    var fps = 30;\r\n    var mspf = 1000 \/ fps;    \r\n    window.animate = (function () {\r\n        return window.requestAnimationFrame ||\r\n            window.webkitRequestAnimationFrame ||\r\n            window.mozRequestAnimationFrame ||\r\n            window.oRequestAnimationFrame ||\r\n            window.msRequestAnimationFrame ||\r\n            function (callback, element) {\r\n                window.setTimeout(callback, mspf);\r\n            };\r\n    })();\r\n    \r\n    \/\/ init balls\r\n    var red_ball = new Ball(0, 25, 5, 'blue');\r\n    red_ball.set_velocity(5, 0).set_random_direction();\r\n    var green_ball = new Ball(-17, -17, 5, 'blue');\r\n    green_ball.set_velocity(5, 0).set_random_direction();\r\n    var blue_ball = new Ball(17, -17, 5, 'blue');\r\n    blue_ball.set_velocity(5, 0).set_random_direction();\r\n    var ad_ball = new Ball(17, -17, 5, 'blue');\r\n    ad_ball.set_velocity(5, 0).set_random_direction();\r\n    var add_ball = new Ball(17, -17, 5, 'blue');\r\n    add_ball.set_velocity(5, 0).set_random_direction();\r\n    var addd_ball = new Ball(17, -17, 5, 'blue');\r\n    addd_ball.set_velocity(5, 0).set_random_direction();\r\n    var adddd_ball = new Ball(17, -17, 5, 'blue');\r\n    adddd_ball.set_velocity(5, 0).set_random_direction();\r\n    var addddd_ball = new Ball(17, -17, 5, 'blue');\r\n    addddd_ball.set_velocity(5, 0).set_random_direction();\r\n    var adddddd_ball = new Ball(17, -17, 5, 'blue');\r\n    adddddd_ball.set_velocity(5, 0).set_random_direction();\r\n    var addddddd_ball = new Ball(17, -17, 5, 'blue');\r\n    addddddd_ball.set_velocity(5, 0).set_random_direction();\r\n   \r\n   \r\n    \r\n    \/\/ init world\r\n    var world = new World();\r\n    world.add_ball(red_ball);\r\n    world.add_ball(green_ball);\r\n    world.add_ball(blue_ball);\r\n    world.add_ball(ad_ball);\r\n    world.add_ball(add_ball);\r\n    world.add_ball(addd_ball);\r\n    world.add_ball(adddd_ball);\r\n    world.add_ball(addddd_ball);\r\n    world.add_ball(adddddd_ball);\r\n    world.add_ball(addddddd_ball);\r\n    \r\n    \r\n   \r\n    \r\n    \/\/ attach world to window so that we can inspect\r\n    inspector.world = world;\r\n    \r\n    \/\/ animate\r\n    function anim_loop() {\r\n        world.update();\r\n        world.draw();\r\n        window.animate(anim_loop);\r\n    };\r\n    anim_loop();\r\n}\r\n\r\nmain();\r\n<\/script>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Pressure Scales &#8211; Pressure Units<\/h2>\n<h3>Pascal &#8211; Unit of Pressure<\/h3>\n<p>As was discussed, the <strong>SI unit<\/strong> of <strong>pressure<\/strong> and stress is the<strong> pascal<\/strong>.<\/p>\n<ul>\n<li><strong>1 pascal \u00a01 N\/m<sup>2<\/sup> = 1 kg \/ (m.s<sup>2<\/sup>)<\/strong><\/li>\n<\/ul>\n<p><a title=\"Pascal \u2013 Unit of Pressure\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/pascal-unit-of-pressure\/\">Pascal<\/a> is defined as one Newton per square meter. However, it is a fairly small unit for most engineering problems, so it is convenient to work with multiples of the pascal: the <strong>kPa<\/strong>, the <strong>bar<\/strong>, and the <strong>MPa<\/strong>.<\/p>\n<ul>\n<li><strong>1 MPa \u00a010<sup>6<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 bar \u00a0\u00a0\u00a010<sup>5<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<li><strong>1 kPa \u00a0\u00a010<sup>3<\/sup> N\/m<sup>2<\/sup><\/strong><\/li>\n<\/ul>\n<p>The unit of measurement called <strong>standard atmosphere<\/strong> (<strong>atm<\/strong>) is defined as:<\/p>\n<ul>\n<li><strong>1 atm = 101.33 kPa<\/strong><\/li>\n<\/ul>\n<p>The standard atmosphere approximates the average pressure at sea level at the latitude of 45\u00b0 N. Note that there is a difference between the <strong>standard atmosphere<\/strong> (atm) and the<strong> technical atmosphere<\/strong> (at).<\/p>\n<p>A technical atmosphere is a non-SI unit of pressure equal to one kilogram-force per square centimeter.<\/p>\n<ul>\n<li><strong>1 at = 98.67 kPa<\/strong><\/li>\n<\/ul>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16280\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere.png\" alt=\"Table - Conversion between pressure units - pascal, bar, psi, atmosphere\" width=\"659\" height=\"289\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere.png 659w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Pressure-Units-pascal-bar-psi-atmosphere-300x132.png 300w\" sizes=\"(max-width: 659px) 100vw, 659px\" \/><\/a><\/p>\n<h3><strong><b>Pounds per square inch &#8211; psi<\/b><\/strong><\/h3>\n<p>The standard unit in the English system is the <strong>pound-force per square inch (psi)<\/strong>. It is the pressure resulting from a force of one pound-force applied to an area of one square inch.<\/p>\n<ul>\n<li><strong>1 psi \u00a01 lbf\/in<sup>2<\/sup> = 4.45 N \/ (0.0254 m)<sup>2<\/sup> \u2248 6895 kg\/m<sup>2<\/sup><\/strong><\/li>\n<\/ul>\n<p>Therefore, one pound per square inch is approximately 6895 Pa.<\/p>\n<p>The unit of measurement called standard atmosphere (atm) is defined as:<\/p>\n<ul>\n<li><strong>1 atm = 14.7 psi<\/strong><\/li>\n<\/ul>\n<p>The standard atmosphere approximates the average pressure at sea level at the latitude of 45\u00b0 N. Note that there is a difference between the <strong>standard atmosphere<\/strong> (atm) and the<strong> technical atmosphere<\/strong> (at).<\/p>\n<p>A technical atmosphere is a non-SI unit of pressure equal to one kilogram-force per square centimeter.<\/p>\n<ul>\n<li><strong>1 at = 14.2 psi<\/strong><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3><b>Bar &#8211; Unit of Pressure<\/b><\/h3>\n<p>A<strong> bar<\/strong> is a metric unit of <strong>pressure<\/strong>. It is not part of the International System of Units (SI). The <strong>bar<\/strong> is commonly used in the<strong> industry<\/strong> and <strong>meteorology<\/strong>, and an instrument used in meteorology to measure atmospheric pressure is called a barometer.<\/p>\n<p>One bar is exactly equal to <strong><em>100 000 Pa<\/em><\/strong> and is slightly less than the average atmospheric pressure on Earth at sea level (<em>1 bar = 0.9869 atm). <\/em>Atmospheric pressure is often given in millibars, where standard sea level pressure is defined as 1013 mbar, 1.013 bar, or 101.3 (kPa).<\/p>\n<p>Sometimes, \u201cBar(a)\u201d and \u201cbara\u201d are used to indicate absolute pressures, and \u201cbar(g)\u201d and \u201cbarg\u201d for gauge pressures.<\/p>\n<h2>Absolute vs. Gauge Pressure<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-16281\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure.png\" alt=\"absolute-vs-gauge-pressure\" width=\"388\" height=\"247\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure.png 388w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/absolute-vs.-gauge-pressure-300x191.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/a>Pressure, as discussed above, is called <strong>absolute pressure<\/strong>. Often it will be important to distinguish between <strong>absolute pressure<\/strong> and <strong>gauge pressure<\/strong>. In this article, the term pressure refers to absolute pressure unless explicitly stated otherwise. But in engineering, we often deal with pressures that are <strong>measured<\/strong> by some devices. Although absolute pressures must be used in thermodynamic relations, <strong>pressure-measuring<\/strong> devices often indicate the <strong>difference<\/strong> between the absolute pressure in a system and the absolute pressure of the atmosphere existing outside the measuring device. They measure the <strong>gauge pressure<\/strong>.<\/p>\n<ul>\n<li><strong>Absolute Pressure.<\/strong> When pressure is measured relative to a perfect vacuum, it is called absolute pressure (psia). Pounds per square inch absolute (psia) is used to clarify that the pressure is relative to a vacuum rather than the ambient atmospheric pressure. Since atmospheric pressure at sea level is around 101.3 kPa (14.7 psi), this will be added to any pressure reading made in air at sea level.<\/li>\n<li><strong>Gauge Pressure. <\/strong>When pressure is measured relative to atmospheric pressure (14.7 psi), it is called gauge pressure (psig). The term gauge pressure is applied when the pressure in the system is greater than the local atmospheric pressure, p<sub>atm<\/sub>. The latter pressure scale was developed because almost all pressure gauges register zero when open to the atmosphere. Gauge pressures are positive if they are above atmospheric pressure and negative if they are below atmospheric pressure.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><em>p<\/em><em><sub>gauge<\/sub><\/em><em> = p<\/em><em><sub>absolute<\/sub><\/em><em> &#8211; p<\/em><em><sub>absolute; atm<\/sub><\/em><\/p>\n<ul>\n<li><strong>Atmospheric Pressure. <\/strong>Atmospheric pressure is the pressure in the surrounding air at &#8211; or \u201cclose\u201d to &#8211; the surface of the Earth. The atmospheric pressure varies with temperature and altitude above sea level. The <strong>Standard Atmospheric Pressure <\/strong>approximates to the average pressure at sea-level at the latitude 45\u00b0 N. \u00a0The <strong>Standard Atmospheric Pressure<\/strong> is defined at sea-level at <em>273<\/em><em><sup>o<\/sup><\/em><em>K (0<\/em><em><sup>o<\/sup><\/em><em>C)<\/em> and is:\n<ul>\n<li><strong><em>101325 Pa <\/em><\/strong><\/li>\n<li><strong><em>1.01325 bar<\/em><\/strong><\/li>\n<li><strong><em>14.696 psi<\/em><\/strong><\/li>\n<li><strong><em>760 mmHg<\/em><\/strong><\/li>\n<li><strong><em>760 torr<\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n<li><strong>Negative Gauge Pressure &#8211; Vacuum Pressure. <\/strong>When the local atmospheric pressure is greater than the pressure in the system, the term <strong>vacuum pressure<\/strong> is used. A perfect vacuum would correspond to absolute zero pressure. It is certainly possible to have a negative gauge pressure but not possible to have negative absolute pressure. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of \u221221 kPa (i.e., 21 kPa below atmospheric pressure of 101 kPa).<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><em>p<\/em><em><sub>vacuum<\/sub><\/em><em> = p<\/em><em><sub>absolute; atm<\/sub><\/em><em> &#8211; p<\/em><em><sub>absolute<\/sub><\/em><\/p>\n<p>For example, a car tire pumped up to 2.5 atm (36.75 psig) above local atmospheric pressure (let say 1 atm or 14.7 psia locally), will have an absolute pressure of 2.5 + 1 = 3.5 atm (36.75 + 14.7 = 51.45 psia or 36.75 psig).<\/p>\n<p>On the other hand condensing steam\u00a0<span style=\"font-weight: 400;\">turbines (at <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\">nuclear power plants<\/a>) exhaust <a title=\"Properties of Steam \u2013 What is Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam<\/a> at a pressure well below atmospheric <\/span><span style=\"font-weight: 400;\">(e.g.,, at 0.08 bar or 8 kPa or 1.16 psia)<\/span><span style=\"font-weight: 400;\"> and in a partially condensed state. In relative units, it is a negative gauge pressure of about &#8211; 0.92 bar, &#8211; 92 kPa, or &#8211; 13.54 psig.<\/span><\/p>\n<h2>Ideal Gas Law<\/h2>\n<p>Any equation that relates the pressure, temperature and specific volume of a substance is called an <strong>equation of state<\/strong>. The simplest and <strong>best-known<\/strong> equation of state for substances in the gas phase is the <strong>Ideal Gas equation<\/strong> of state. \u00c9mile Clapeyron first stated it in 1834 as a combination of the empirical Boyle\u2019s law, Charles\u2019 law, and Avogadro\u2019s Law. This equation predicts the <strong>p-v-T behavior<\/strong> of gas quite accurately for dilute or low-pressure gases. In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with<strong> temperature<\/strong> and <strong>quantity<\/strong>\u00a0and inversely with <strong>volume<\/strong>.<\/p>\n<p style=\"text-align: center;\"><strong><i><span style=\"font-size: 25px;\">pV = nRT<\/span><\/i><\/strong><\/p>\n<p>where:<\/p>\n<ul>\n<li><strong><em>p<\/em><\/strong> is the <strong>absolute pressure<\/strong> of the gas<\/li>\n<li><strong><em>n<\/em><\/strong> is the <strong>amount<\/strong> of substance<\/li>\n<li><strong><em>T<\/em><\/strong> is the <strong>absolute temperature<\/strong><\/li>\n<li><strong><em>V<\/em><\/strong> is the <strong>volume<\/strong><\/li>\n<li><strong><em>R<\/em> <\/strong>\u00a0is the ideal, or universal,<strong> gas constant<\/strong>, equal to the product of the Boltzmann constant and the Avogadro constant,<\/li>\n<\/ul>\n<p>In this equation, the symbol R is the <strong>universal gas constant<\/strong> that has the same value for all gases\u2014namely, <strong>R = \u00a08.31 J\/mol K.<\/strong><\/p>\n<p>The power of the ideal gas law is in its <strong>simplicity<\/strong>. When any<strong> two<\/strong> thermodynamic variables, p, v, and T,<strong> are<\/strong> <strong>given<\/strong>, the <strong>third<\/strong> can <strong>easily be found<\/strong>. An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no attractive intermolecular forces. An ideal gas can be visualized as a collection of perfectly hard spheres that collide but otherwise do not interact. In reality, no real gases are like an ideal gas, and therefore no real gases follow the ideal gas law or equation completely. At temperatures near a gases boiling point, pressure increases will cause condensation and drastic decreases in volume. At very high pressures, the intermolecular forces of gas are significant. However, most gases are in approximate agreement at pressures and temperatures above their boiling point. The ideal gas law is utilized by engineers working with gases because it is simple and approximates real gas behavior.<\/p>\n<h2>Typical Pressures in Engineering &#8211; Examples<\/h2>\n<p>The <strong>pascal (Pa)<\/strong> as a unit of pressure measurement is widely used worldwide. It has largely replaced the <strong>pounds per square inch (psi)<\/strong> unit, except in some countries that still use the Imperial measurement system, including the United States. For most engineering problems, pascal (Pa) is a fairly small unit, so it is convenient to work with multiples of the pascal: the kPa, the MPa, or the bar. The following list summarizes a few examples:<\/p>\n<ul>\n<li>Typically most <strong>nuclear power plants<\/strong> operate <strong>multi-stage condensing steam turbines<\/strong>. These turbines exhaust <a title=\"Properties of Steam \u2013 What is Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam <\/a>at a pressure well below atmospheric (e.g.,, at 0.08 bar or 8 kPa or 1.16 psia) and in a partially condensed state. In relative units, it is a negative gauge pressure of about &#8211; 0.92 bar, &#8211; 92 kPa, or &#8211; 13.54 psig.<\/li>\n<li>The <strong>Standard Atmospheric Pressure<\/strong> approximates to the average pressure at sea-level at the latitude 45\u00b0 N. \u00a0The <strong>Standard Atmospheric Pressure<\/strong> is defined at sea-level at <em>273<\/em><em><sup>o<\/sup><\/em><em>K (0<\/em><em><sup>o<\/sup><\/em><em>C)<\/em> and is:\n<ul>\n<li><strong><em>101325 Pa <\/em><\/strong><\/li>\n<li><strong><em>1.01325 bar<\/em><\/strong><\/li>\n<li><strong><em>14.696 psi<\/em><\/strong><\/li>\n<li><strong><em>760 mmHg<\/em><\/strong><\/li>\n<li><strong><em>760 torr<\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n<li>Car tire overpressure is about 2.5 bar, 0.25 MPa, or 36 psig.<\/li>\n<li>Steam locomotive fire tube boiler: 150\u2013250 psig<\/li>\n<li>A high-pressure stage of condensing steam turbine at nuclear power plant operates at steady state with inlet conditions of \u00a06 MPa (60 bar, or 870 psig) t = 275.6\u00b0C, x = 1<\/li>\n<li style=\"text-align: left;\">A <a title=\"BWR \u2013 Boiling water reactor\" href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\"><strong>boiling water reactor<\/strong><\/a> is cooled and moderated by <a title=\"Properties of Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/\">water<\/a> like a PWR, but at a<strong> lower pressure<\/strong> (e.g.,, 7MPa, 70 bar, or 1015 psig), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines.<\/li>\n<li><a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\"><strong>Pressurized water reactors<\/strong><\/a> are cooled and moderated by <a title=\"Saturated and Subcooled Liquid\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturated-and-subcooled-liquid\/\">high-pressure liquid water<\/a> (e.g.,, 16MPa, 160 bar, or 2320 psig). At this pressure, water boils at approximately 350\u00b0C (662\u00b0F), which provides a subcooling margin of about 25\u00b0C.<\/li>\n<li>The <a title=\"Supercritical Water Reactor \u2013 SCWR\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/supercritical-water-reactor-scwr\/\"><strong>supercritical water reactor (SCWR)<\/strong><\/a> is operated at <strong>supercritical pressure<\/strong>. The term supercritical in this context refers to the thermodynamic <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/critical-point-of-water\/\"><strong>critical point of water<\/strong><\/a> (T<sub>CR<\/sub> = 374 \u00b0C; \u00a0p<sub>CR<\/sub> = 22.1 MPa)<\/li>\n<li><strong>Common rail direct fuel injection: <\/strong>It features a high-pressure (over 1 000 bar or 100 MPa or 14500 psi) fuel rail on diesel engines.<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Pressure in Pressurized Water Reactor<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_430\" aria-describedby=\"caption-attachment-430\" style=\"width: 324px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/pressurizer_nuclear.png\"><img loading=\"lazy\" class=\"size-full wp-image-430\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/pressurizer_nuclear.png\" alt=\"pressurizer\" width=\"334\" height=\"421\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/pressurizer_nuclear.png 334w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/pressurizer_nuclear-238x300.png 238w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/a><figcaption id=\"caption-attachment-430\" class=\"wp-caption-text\">A pressurizer is a key component of PWRs.<\/figcaption><\/figure>\n<p><strong>Pressurized water reactors<\/strong>\u00a0use a <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\">reactor pressure vessel<\/a> (RPV) to contain the nuclear fuel, <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a>, <a title=\"Control rods\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/control-rods\/\">control rods<\/a>, and coolant. They are cooled and moderated by high-pressure liquid water (e.g.,, 16MPa). At this pressure, water boils at approximately 350\u00b0C (662\u00b0F). \u00a0This high pressure is maintained by a <a title=\"Pressurizer\" href=\"http:\/\/sitepourvtc.com\/pressurizer\/\" target=\"_blank\" rel=\"noopener\">pressurizer<\/a>. The inlet temperature of the water is about 290\u00b0C (554\u00b0F). The water (coolant) is heated in the reactor core to approximately 325\u00b0C (617\u00b0F) as the water flows through the core. As it can be seen, the reactor has approximately 25\u00b0C subcooled coolant (distance from the <a title=\"Saturation \u2013 Boiling Point\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturation-boiling-point\/\">saturation<\/a>).<\/p>\n<p>A <strong>pressurizer<\/strong> is a component of a <a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\" target=\"_blank\" rel=\"noopener\">pressurized water reactor<\/a>. <strong>Pressure in the primary circuit<\/strong> of PWRs is maintained by a <strong>pressurizer<\/strong>, a separate vessel connected to the primary circuit (hot leg), and partially filled with water heated to the <strong>saturation temperature<\/strong> (boiling point) for the desired pressure by submerged <strong>electrical heaters<\/strong>.<\/p>\n<p>On the other hand, there are<strong> spray lines<\/strong> to <strong>decrease pressure<\/strong> inside the <strong>pressurizer<\/strong>, which causes a decrease in pressure in the reactor coolant system. These spray lines spray reactor coolant from the cold leg of a loop into the steam space and condense a portion of the steam. The quenching action reduces pressure and limits the pressure increases.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Pressures in Condensing Steam Turbines<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_16026\" aria-describedby=\"caption-attachment-16026\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16026\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min-300x277.png\" alt=\"engineering thermodynamics\" width=\"300\" height=\"277\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min-300x277.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min.png 650w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-16026\" class=\"wp-caption-text\">Rankine Cycle &#8211; Thermodynamics as Energy Conversion Science<\/figcaption><\/figure>\n<p>Typically most <strong>nuclear power plants<\/strong> operate <strong>multi-stage condensing steam turbines<\/strong>. In these turbines, the high-pressure stage receives <a title=\"Properties of Steam \u2013 What is Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam<\/a> (this steam is nearly saturated steam \u2013 x = 0.995 \u2013 point C at the figure; <strong>6 MPa<\/strong>; 275.6\u00b0C) from a steam generator and exhausts it to moisture separator-reheater (point D). The steam must be reheated to avoid damages caused to the steam turbine blades by low-quality steam. The reheater heats the steam (point D), and then the steam is directed to the low-pressure stage of the steam turbine, where it expands (point E to F). The exhausted steam is at a pressure well below atmospheric (absolute pressure of <strong>0.008 MPa<\/strong>) and is in a partially condensed state (point F), typically of a quality near 90%.<\/p>\n<p>See also: <a title=\"Wet Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/wet-steam\/\">Wet Steam<\/a><\/p>\n<p>See also: <a title=\"Steam Tables \u2013 Specific Properties of Water and Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\">Steam Tables<\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Pressure coefficient - How pressure influences reactivity<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a title=\"Pressure Coefficient\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/pressure-coefficient\/\"><strong>The pressure\u00a0coefficient<\/strong><\/a>\u00a0(or the moderator density coefficient) is defined as the change in <a title=\"Reactivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity\/\">reactivity<\/a> per unit change in pressure.<\/p>\n<p><span style=\"font-size: 40px;\">\u03b1<sub>P<\/sub> = <sup>d\u03c1<\/sup>\u2044<sub>dP<\/sub><\/span><\/p>\n<p>It is expressed in units of pcm\/MPa. The <strong>pressure coefficient\u2019s<\/strong>\u00a0magnitude and sign (+ or -) is primarily a function of the <strong>moderator-to-fuel ratio<\/strong>. That means it primarily depends on a certain reactor design.<\/p>\n<p>Although water is considered incompressible, in reality, it is <strong>slightly compressible\u00a0<\/strong>(especially at 325\u00b0C (617\u00b0F)). The effect of pressure in the primary circuit has <strong>similar<\/strong> consequences as the <a title=\"Moderator Temperature Coefficient \u2013 MTC\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/moderator-temperature-coefficient-mtc\/\"><strong>moderator temperature<\/strong><\/a>. Compared with the effects of moderator temperature changes, changes in pressure have a <strong>lower-order impact<\/strong> on reactivity. The causes are only <strong>in the density<\/strong> of the moderator, not in the change of microscopic cross-sections.<\/div><\/div><\/div>\n<h2>Pressure Loss &#8211; Fluids<\/h2>\n<p>Summary of: <a title=\"Head Loss \u2013 Pressure Loss\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/head-loss\/\">Head Loss &#8211; Pressure Loss<\/a><\/p>\n<ul>\n<li><strong>Head loss<\/strong> or<strong> pressure loss<\/strong> is the reduction in the<a title=\"Hydraulic Head\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/hydraulic-head\/\"><strong> total head<\/strong><\/a> (sum of<a title=\"Elevation Head\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/elevation-head-2\/\"> the potential head<\/a>, <a title=\"Velocity Head\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/velocity-head\/\">velocity head<\/a>,\u00a0and <a title=\"Pressure Head\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/pressure-head-2\/\">pressure head<\/a>) of a fluid caused by the<strong> friction<\/strong> present in the fluid\u2019s motion.<\/li>\n<li><strong>Head loss and pressure loss<\/strong> represent the same phenomenon \u2013 <strong>frictional losses<\/strong> in pipe and losses in hydraulic components, but they are expressed in <strong>different units<\/strong>.<\/li>\n<li>Head loss of the hydraulic system is divided into <strong>two main categories<\/strong>:\n<ul>\n<li><a title=\"Major Head Loss \u2013 Friction Loss\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/\"><strong>Major Head Loss<\/strong><\/a> \u2013 due to friction in straight pipes<\/li>\n<li><a title=\"Minor Head Loss \u2013 Local Losses\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/minor-head-loss-local-losses\/\"><strong>Minor Head Loss<\/strong><\/a> \u2013 due to components as valves, bends\u2026<\/li>\n<\/ul>\n<\/li>\n<li>\n<figure id=\"attachment_14429\" aria-describedby=\"caption-attachment-14429\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min.jpg\"><img loading=\"lazy\" class=\"size-medium wp-image-14429\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min-300x188.jpg\" alt=\"Moody Diagram\" width=\"300\" height=\"188\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min-300x188.jpg 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min-1024x642.jpg 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min-320x202.jpg 320w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min-700x441.jpg 700w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min.jpg 1409w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14429\" class=\"wp-caption-text\">Source: Donebythesecondlaw at the English language Wikipedia, CC BY-SA 3.0,<br \/>https:\/\/commons.wikimedia.org\/w\/index.php?curid=4681366<\/figcaption><\/figure>\n<p><a title=\"Darcy-Weisbach Equation\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/darcy-weisbach-equation\/\"><strong>Darcy\u2019s equation<\/strong><\/a> can be used to calculate <strong>major\u00a0losses<\/strong>.<\/li>\n<li>A <strong>special form of Darcy\u2019s equation<\/strong> can be used to calculate <strong>minor losses<\/strong>.<\/li>\n<li>The <a title=\"Darcy Friction Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/darcy-friction-factor-2\/\"><strong>friction factor<\/strong><\/a> for fluid flow can be determined using a <a title=\"Moody Diagram\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/moody-diagram\/\"><strong>Moody chart<\/strong><\/a>.<\/li>\n<li><strong>The <a title=\"Friction Factor for Laminar Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/friction-factor-for-laminar-flow\/\">friction factor<\/a><\/strong><a title=\"Friction Factor for Laminar Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/friction-factor-for-laminar-flow\/\">\u00a0for\u00a0laminar flow<\/a> is <strong>independent of the roughness<\/strong> of the pipe\u2019s inner surface. <strong>f = 64\/Re<\/strong><\/li>\n<li><strong>The<a title=\"Friction Factor for Turbulent Flow \u2013 Colebrook Equation\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/friction-factor-turbulent-flow-colebrook\/\"> friction factor<\/a><\/strong><a title=\"Friction Factor for Turbulent Flow \u2013 Colebrook Equation\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/friction-factor-turbulent-flow-colebrook\/\">\u00a0for turbulent flow<\/a>\u00a0depends strongly on the <strong>relative roughness. The Colebrook equation determines it<\/strong>. It must be noted and <strong>at\u00a0very large Reynolds numbers<\/strong>, the friction factor is independent of the\u00a0Reynolds number.<\/li>\n<\/ul>\n<ul>\n<li>The <strong>minor losses<\/strong> are roughly proportional to the <strong>square of the flow rate,<\/strong> and therefore they can be easily integrated into the Darcy-Weisbach equation through <a title=\"Resistance Coefficient Method \u2013 K Method \u2013 Excess head\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/minor-head-loss-local-losses\/resistance-coefficient-method-k-method-excess-head\/\"><strong>resistance\u00a0coefficient K<\/strong><\/a>.<\/li>\n<li>As a local pressure loss, <a title=\"Fluid Acceleration \u2013 Pressure Loss\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/minor-head-loss-local-losses\/fluid-acceleration-pressure-loss\/\"><strong>fluid acceleration in a heated channel<\/strong><\/a> can also be considered.<\/li>\n<\/ul>\n<h2>Critical Pressure of Water<\/h2>\n<figure id=\"attachment_14172\" aria-describedby=\"caption-attachment-14172\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Boiling-point-of-water.png\"><img loading=\"lazy\" class=\"size-medium wp-image-14172\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Boiling-point-of-water-300x255.png\" alt=\"Phase diagram of water\" width=\"300\" height=\"255\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Boiling-point-of-water-300x255.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Boiling-point-of-water.png 696w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14172\" class=\"wp-caption-text\">Phase diagram of water.<br \/>Source: wikipedia.org CC BY-SA<\/figcaption><\/figure>\n<p>At pressure that is <strong>higher than the critical pressure,\u00a0<\/strong>\u00a0<a title=\"Properties of Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/\">water<\/a> is in a special state, which is known as the <a title=\"Supercritical Fluid \u2013 Supercritical Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/supercritical-fluid-supercritical-water\/\"><strong>supercritical fluid state<\/strong><\/a>. A supercritical fluid is a fluid that is at pressures higher than its thermodynamic critical values. At the critical and supercritical pressures, a fluid is considered a <strong>single-phase substance,<\/strong> although all thermophysical properties undergo <strong>significant changes<\/strong> within the critical and pseudocritical regions.<\/p>\n<p>For water, the critical \u00a0parameters are the following:<\/p>\n<ul>\n<li><strong>P<sub>cr<\/sub> = 22.09 MPa<\/strong><\/li>\n<li><strong>T<sub>cr<\/sub> = 374.14 \u00b0C (or 647.3 K)<\/strong><\/li>\n<li><strong>v<sub>cr<\/sub> = 0.003155 m3\/kg<\/strong><\/li>\n<li><strong>u<sub>f<\/sub> = u<sub>g<\/sub> = 2014 kJ\/kg<\/strong><\/li>\n<li><strong>h<sub>f<\/sub> = h<sub>g <\/sub>= 2084 kJ\/kg<\/strong><\/li>\n<li><strong>s<sub>f<\/sub> = s<sub>g<\/sub> =4.406 kJ\/kg K<\/strong><\/li>\n<\/ul>\n<p>See also: <a title=\"Critical Point of Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/critical-point-of-water\/\">Critical Point of Water<\/a><\/p>\n<p>See also: <a title=\"Supercritical Fluid \u2013 Supercritical Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/supercritical-fluid-supercritical-water\/\">Supercritical Fluid<\/a><\/p>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Reactor Physics and Thermal Hydraulics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC\u00a0Press; 2\u00a0edition, 2012, ISBN:\u00a0978-0415802871<\/li>\n<li>Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN:\u00a0978-3-319-13419-2<\/li>\n<li>Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition,\u00a0John Wiley &amp; Sons, 2006, ISBN:\u00a0978-0-470-03037-0<\/li>\n<li>Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010,\u00a0ISBN 978-1-4020-8670-0.<\/li>\n<li>U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2, and 3. June 1992.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Thermodynamic Properties<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Pascal is defined as a force of 1N that is exerted on a unit area. 1 Pascal = 1 N\/m2 &nbsp; However, it is a fairly small unit for most engineering problems, so it is convenient to work with multiples of the pascal: the kPa, the bar, and the MPa. 1 MPa \u00a0106 N\/m2 1 &#8230; <a title=\"What is Pressure &#8211; Physics\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\" aria-label=\"More on What is Pressure &#8211; Physics\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":16185,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16364"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=16364"}],"version-history":[{"count":5,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16364\/revisions"}],"predecessor-version":[{"id":34509,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16364\/revisions\/34509"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16185"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=16364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}