{"id":14618,"date":"2017-06-16T11:29:39","date_gmt":"2017-06-16T11:29:39","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=14618"},"modified":"2022-10-25T08:11:46","modified_gmt":"2022-10-25T08:11:46","slug":"darcy-weisbach-equation","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/darcy-weisbach-equation\/","title":{"rendered":"Darcy-Weisbach Equation"},"content":{"rendered":"<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-60 lgc-tablet-grid-60 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div>\n<p>In fluid dynamics, <strong>the Darcy\u2013Weisbach equation<\/strong> is a phenomenological equation, which relates the <strong>major head loss<\/strong>, or pressure loss, due to <strong>fluid friction<\/strong> along a given length of pipe to the average velocity. This equation is valid for <strong>fully developed, steady, incompressible single-phase flow<\/strong>.<\/p>\n<p>The Darcy\u2013Weisbach equation can be written in two forms (<strong>pressure loss form<\/strong> or <strong>head loss form<\/strong>). The head loss form can be written as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Major-Head-Loss-head-form.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14583\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Major-Head-Loss-head-form.png\" alt=\"Major Head Loss - head form\" width=\"199\" height=\"88\" \/><\/a><\/p>\n<p>where:<\/p>\n<ul>\n<li>\u0394h = the head loss due to friction (m)<\/li>\n<li><em>f<\/em><em><sub>D<\/sub><\/em> = <a title=\"Darcy Friction Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/darcy-friction-factor-2\/\">the Darcy friction factor<\/a> (unitless)<\/li>\n<li>L = the pipe length (m)<\/li>\n<li>D = <a title=\"Hydraulic Diameter\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/internal-flow\/hydraulic-diameter-2\/\">the hydraulic diameter <\/a>of the pipe D (m)<\/li>\n<li>g = the gravitational constant (m\/s<sup>2<\/sup>)<\/li>\n<li>V = the mean flow velocity V (m\/s)<\/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 loss form<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">The Darcy\u2013Weisbach equation in the <strong>pressure loss form<\/strong> can be written as:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Major-Head-Loss-pressure-loss-form.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14582\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Major-Head-Loss-pressure-loss-form.png\" alt=\"Major Head Loss - pressure loss form\" width=\"171\" height=\"66\" \/><\/a>\n<p>where:<\/p>\n<ul>\n<li>\u0394p = the pressure loss due to friction (Pa)<\/li>\n<li><em>f<\/em><em><sub>D<\/sub><\/em> = the Darcy friction factor (unitless)<\/li>\n<li>L = the pipe length (m)<\/li>\n<li>D = the hydraulic diameter of the pipe D (m)<\/li>\n<li>g = the gravitational constant (m\/s<sup>2<\/sup>)<\/li>\n<li>V = the mean flow velocity V (m\/s)<\/li>\n<\/ul>\n<p>___________<\/p><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div>Evaluating the <strong>Darcy-Weisbach equation<\/strong> provides insight into factors affecting the head loss in a pipeline.\n<ul>\n<li>Consider that the <strong>length of the pipe<\/strong> or channel is <strong>doubled<\/strong>, the resulting <strong>frictional head loss will double<\/strong>.<\/li>\n<li>At constant flow rate and pipe length, the<strong> head loss is inversely proportional to the 4th power of diameter<\/strong> (for laminar flow), and thus reducing the pipe diameter by half increases the head loss by a factor of 16. This is a very significant increase in head loss, and shows why larger diameter pipes lead to much smaller pumping power requirements.<\/li>\n<li>Since the head loss is roughly proportional to the square of the flow rate, then if the <strong>flow rate is doubled<\/strong>, the <strong>head loss increases by a factor of four<\/strong>.<\/li>\n<li>The <strong>head loss is reduced by half<\/strong> (for laminar flow) when the <strong>fluid\u2019s viscosity is reduced by half<\/strong>.<\/li>\n<\/ul>\n<figure id=\"attachment_14429\" aria-describedby=\"caption-attachment-14429\" style=\"width: 659px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min.jpg\"><img loading=\"lazy\" class=\"size-large wp-image-14429\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min-1024x642.jpg\" alt=\"Source: Donebythesecondlaw at the English language Wikipedia, CC BY-SA 3.0, https:\/\/commons.wikimedia.org\/w\/index.php?curid=4681366\" width=\"669\" height=\"419\" srcset=\"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-300x188.jpg 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min.jpg 1409w\" sizes=\"(max-width: 669px) 100vw, 669px\" \/><\/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>With the exception of the <strong>Darcy friction factor<\/strong>, each of these terms (the flow velocity, <a title=\"Hydraulic Diameter\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/internal-flow\/hydraulic-diameter-2\/\">the hydraulic diameter<\/a>, the length of a pipe) can be easily measured. The Darcy friction factor takes the fluid properties of density and viscosity into account, along with the <strong>pipe roughness<\/strong>. This factor may be evaluated by the use of various empirical relations, or it may be read from published charts (e.g., <strong>Moody chart<\/strong>).<\/p>\n<\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-40 lgc-tablet-grid-40 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>Summary:<\/h2>\n<ul>\n<li>Head loss of hydraulic\u00a0system is divided into <strong>two main categories<\/strong>:\n<ul>\n<li><strong>Major Head Loss<\/strong> &#8211; due to friction in straight pipes<\/li>\n<li><strong>Minor Head Loss<\/strong> &#8211; due to components as valves, bends&#8230;<\/li>\n<\/ul>\n<\/li>\n<li><strong>Darcy\u2019s equation<\/strong> can be used to calculate <strong>major\u00a0losses<\/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>.<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min.jpg\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-14429\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Moody-chart-min-300x188.jpg\" alt=\"Moody chart-min\" 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><\/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 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><a title=\"Relative Roughness of Pipe\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/relative-roughness-of-pipe\/\">relative roughness<\/a>. <\/strong>It is determined by the Colebrook equation.\u00a0It must be noted, <strong>at very large Reynolds numbers<\/strong>, the friction factor is independent of the\u00a0Reynolds number.<\/li>\n<\/ul>\n<h2>Why is head loss very important?<\/h2>\n<p>As can be seen from the picture, the head loss is forms <strong>key characteristic<\/strong> of any hydraulic system. In systems where some certain flowrate must be maintained (e.g.,, to provide sufficient cooling or heat transfer from a <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor core<\/a>), <strong>the equilibrium<\/strong> of the<strong> head loss<\/strong> and the\u00a0<strong>head added<\/strong> by a pump determine the flow rate through the system.<\/p>\n<figure id=\"attachment_14299\" aria-describedby=\"caption-attachment-14299\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Q-H.png\"><img loading=\"lazy\" class=\"size-medium wp-image-14299\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Q-H-300x207.png\" alt=\"Q-H characteristic diagram of centrifugal pump and of pipeline\" width=\"300\" height=\"207\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Q-H-300x207.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Q-H.png 900w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14299\" class=\"wp-caption-text\">Q-H characteristic diagram of centrifugal pump and pipeline<\/figcaption><\/figure>\n<figure id=\"attachment_14305\" aria-describedby=\"caption-attachment-14305\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Hydraulic-Grade-Line-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-14305\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Hydraulic-Grade-Line-min-300x230.png\" alt=\"Hydraulic Head - Hydraulic Grade Line\" width=\"300\" height=\"230\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Hydraulic-Grade-Line-min-300x230.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Hydraulic-Grade-Line-min-180x138.png 180w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Hydraulic-Head-Hydraulic-Grade-Line-min.png 734w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14305\" class=\"wp-caption-text\">Hydraulic grade line and Total headlines for a constant diameter pipe with friction. In a real pipeline, there are energy losses due to friction &#8211; these must be taken into account as they can be very significant.<\/figcaption><\/figure>\n<\/div><\/div><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\"><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=\"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>Example: Frictional Head Loss<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Water at 20\u00b0C is pumped through a smooth 12-cm-diameter pipe <strong>10 km<\/strong> long, at a flow rate of <strong>75 m<sup>3<\/sup>\/h<\/strong>. The inlet is fed by a pump at an absolute pressure of <strong>2.4 MPa<\/strong>.<br \/>\nThe exit is at standard <strong>atmospheric pressure<\/strong>\u00a0(101 kPa) and is <strong>200 m higher<\/strong>.\n<p>Calculate\u00a0the <strong>frictional head loss H<sub>f<\/sub><\/strong>, and compare it to\u00a0the flow v<sup>2<\/sup>\/(2g) <strong>velocity head<\/strong>.<\/p>\n<p>Solution:<\/p>\n<p>Since the pipe diameter is constant, the average velocity and velocity head is the same\u00a0everywhere:<\/p>\n<p><strong>v<sub>out<\/sub> <\/strong>= <strong>Q\/A<\/strong> = 75 [m<sup>3<\/sup>\/h] * 3600\u00a0[s\/h] \/ 0.0113\u00a0[m<sup>2<\/sup>] = <strong>1.84 m\/s<\/strong><\/p>\n<p>Velocity head:<\/p>\n<p><strong>Velocity head<\/strong> = v<sub>out<\/sub><sup>2<\/sup>\/(2g) =\u00a01.84<sup>2<\/sup> \/ 2*9.81 = <strong>0.173 m<\/strong><\/p>\n<p>In order to find the frictional head loss, we have to use extended\u00a0Bernoulli\u2019s equation:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Extended-Bernoulli-Equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14315\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Extended-Bernoulli-Equation.png\" alt=\"Extended Bernoulli Equation\" width=\"441\" height=\"64\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Extended-Bernoulli-Equation.png 441w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Extended-Bernoulli-Equation-300x44.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/a><\/p>\n<p>Head loss:<\/p>\n<p>2 400 000\u00a0[Pa] \/ 1000 [kg\/m<sup>3<\/sup>] *\u00a09.81 [m\/s<sup>2<\/sup>] \u00a0+ 0.173 [m] + 0\u00a0[m] =\u00a0101\u00a0000\u00a0[Pa] \/ 1000 [kg\/m<sup>3<\/sup>] *\u00a09.81 [m\/s<sup>2<\/sup>]\u00a0+ 0.173 [m]+ 200\u00a0[m] +\u00a0H<sub>f<\/sub><\/p>\n<p><strong>H<sub>f\u00a0<\/sub><\/strong> = 244.6 &#8211; 10.3 &#8211; 200 = <strong>34.3 m<\/strong><\/p><\/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=\"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>Example: The head loss for one loop of primary piping<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">The primary circuit of typical <a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a> is divided into 4 independent loops (piping diameter of about 700mm), each loop comprises a <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\"><strong>steam generator<\/strong><\/a> and one <a title=\"Reactor Coolant Pump\" href=\"http:\/\/sitepourvtc.com\/reactor-coolant-pump\/\"><strong>main coolant pump<\/strong><\/a>.\n<p>Assume that (this data do not represent\u00a0any certain reactor design):<\/p>\n<ul>\n<li>Inside the primary piping flows water at constant temperature of <strong>290\u00b0C<\/strong> (<strong>\u2374 ~ 720 kg\/m<sup>3<\/sup><\/strong>).<\/li>\n<li>The <strong>kinematic viscosity<\/strong> of the water at 290\u00b0C is equal to <strong>0.12 x 10<sup>-6<\/sup> m<sup>2<\/sup>\/s<\/strong>.<\/li>\n<li>The primary piping flow velocity may be about <strong>17 m\/s<\/strong>.<\/li>\n<li>The primary piping of one loop is about\u00a0<strong>20m long<\/strong>.<\/li>\n<li>The <strong>Reynolds number<\/strong> inside the primary piping is equal to: Re<sub>D<\/sub> = 17 [m\/s] x 0.7 [m] \/ 0.12&#215;10<sup>-6<\/sup> [m<sup>2<\/sup>\/s] = <strong>99 000 000<\/strong><\/li>\n<li>The<strong> Darcy friction factor<\/strong> is equal to <strong>f<sub>D<\/sub> = 0.01<\/strong><\/li>\n<\/ul>\n<p><strong>Calculate the head loss<\/strong> for one loop of primary piping (without fitting, elbows, pumps etc.).<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Since we know all inputs of the <strong>Darcy-Weisbach equation<\/strong>, we can calculate the head loss directly:<\/p>\n<p><strong>Head loss form:<\/strong><\/p>\n<p><strong>\u0394h<\/strong> = 0.01 x \u00bd x 1\/9.81 x 20 x 17<sup>2<\/sup> \/ 0.7 = <strong>4.2 m<\/strong><\/p>\n<p><strong>Pressure loss form:<\/strong><\/p>\n<p><strong>\u0394p<\/strong> = 0.01 x \u00bd x 720 x 20 x 17<sup>2<\/sup> \/ 0.7 = 29 725 Pa \u2248 <strong>0.03 MPa<\/strong><\/p><\/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>Example: Change in head loss due to a decrease in viscosity.<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In fully developed <strong>laminar flow<\/strong> in a circular pipe, the head loss is given by:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Major-Head-Loss-head-form.png\"><img loading=\"lazy\" class=\" size-full wp-image-14583 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Major-Head-Loss-head-form.png\" alt=\"Major Head Loss - head form\" width=\"199\" height=\"88\" \/><\/a>where:\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/darcy-friction-factor-laminar-flow.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14580\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/darcy-friction-factor-laminar-flow.png\" alt=\"darcy friction factor - laminar flow\" width=\"202\" height=\"139\" \/><\/a><\/p>\n<p>Since the <strong>Reynolds number<\/strong> is inverse proportional to viscosity, then the <strong>resulting head loss becomes proportional to viscosity<\/strong>. Therefore, the head loss is reduced by half when the viscosity of the fluid is reduced by half, when the flow rate and thus the average velocity are held constant.<\/p><\/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=\"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,\u00a0AND FLUID FLOW.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1, 2 and 3. June\u00a01992.<\/li>\n<li>White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN:\u00a0978-0077422417<\/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>Major Loss<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/\" 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":"","protected":false},"author":1,"featured_media":0,"parent":14601,"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\/14618"}],"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=14618"}],"version-history":[{"count":2,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/14618\/revisions"}],"predecessor-version":[{"id":33050,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/14618\/revisions\/33050"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/14601"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=14618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}