{"id":186782,"date":"2025-01-26T08:35:24","date_gmt":"2025-01-26T08:35:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186782"},"modified":"2025-01-26T08:35:26","modified_gmt":"2025-01-26T08:35:26","slug":"the-local-atmospheric-pressure-in-denver","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/26\/the-local-atmospheric-pressure-in-denver\/","title":{"rendered":"The local atmospheric pressure in Denver"},"content":{"rendered":"\n<p>The local atmospheric pressure in Denver, Colorado (elevation 1610 m), is 83.4 kPa. Air at this pressure and 20\u00b0C flows with a velocity of 8 m\/s over a 1.5 m \u00d7 6 m flat plate whose temperature is 140\u00b0C. Determine the rate of heat transfer from the plate if the air flows parallel to the (a) 6-m-long side and (b) the 1.5 m side.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/01\/image-488.png\" alt=\"\" class=\"wp-image-186783\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To calculate the rate of heat transfer from the plate, we need to apply the convection heat transfer equation:<\/p>\n\n\n\n<p>[<br>Q = hA(T_{\\text{plate}} &#8211; T_{\\text{air}})<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( Q ) is the rate of heat transfer (W),<\/li>\n\n\n\n<li>( h ) is the convective heat transfer coefficient (W\/m\u00b2\u00b7K),<\/li>\n\n\n\n<li>( A ) is the surface area of the plate (m\u00b2),<\/li>\n\n\n\n<li>( T_{\\text{plate}} ) is the temperature of the plate (\u00b0C),<\/li>\n\n\n\n<li>( T_{\\text{air}} ) is the temperature of the air (\u00b0C).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Determine the properties of air<\/h3>\n\n\n\n<p>First, we need to determine the properties of air at the given conditions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Pressure<\/strong> = 83.4 kPa<\/li>\n\n\n\n<li><strong>Temperature<\/strong> = 20\u00b0C (for the air)<\/li>\n<\/ul>\n\n\n\n<p>We will calculate the dynamic viscosity (( \\mu )), thermal conductivity (( k )), specific heat (( c_p )), and the Prandtl number (( Pr )) at 20\u00b0C. These properties are crucial for calculating the convective heat transfer coefficient.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Reynolds number<\/h3>\n\n\n\n<p>The Reynolds number ( Re ) is calculated to determine whether the flow is laminar or turbulent:<\/p>\n\n\n\n<p>[<br>Re = \\frac{\\rho v L}{\\mu}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\rho ) is the density of the air (kg\/m\u00b3),<\/li>\n\n\n\n<li>( v ) is the velocity of the air (m\/s),<\/li>\n\n\n\n<li>( L ) is the characteristic length of the plate (m),<\/li>\n\n\n\n<li>( \\mu ) is the dynamic viscosity (Pa\u00b7s).<\/li>\n<\/ul>\n\n\n\n<p>We assume air properties at 20\u00b0C for ( \\mu ) and ( \\rho ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Nusselt number<\/h3>\n\n\n\n<p>The Nusselt number ( Nu ) is used to calculate the convective heat transfer coefficient. For flat plate flow, the empirical correlation for the Nusselt number is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For laminar flow (low ( Re )): ( Nu = 0.332 Re^{1\/2} Pr^{1\/3} )<\/li>\n\n\n\n<li>For turbulent flow (high ( Re )): ( Nu = 0.0296 Re^{4\/5} Pr^{1\/3} )<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Heat transfer coefficient<\/h3>\n\n\n\n<p>The convective heat transfer coefficient ( h ) can be determined from the Nusselt number:<\/p>\n\n\n\n<p>[<br>h = \\frac{Nu \\cdot k}{L}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Apply the equation for heat transfer<\/h3>\n\n\n\n<p>After determining ( h ), the heat transfer equation can be used to calculate ( Q ) for both cases (parallel to the 6-m-long side and 1.5-m-long side).<\/p>\n\n\n\n<p>For both cases, we compute the area ( A ) of the plate:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( A = L \\times W ), where ( L ) is the length and ( W ) is the width of the plate.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>To summarize:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For both cases, you need to compute the Reynolds number, Nusselt number, and convective heat transfer coefficient.<\/li>\n\n\n\n<li>The total heat transfer is then calculated using the temperature difference between the plate and the air.<\/li>\n<\/ul>\n\n\n\n<p>If you need specific numerical values for these properties and calculations, I can proceed with them!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The local atmospheric pressure in Denver, Colorado (elevation 1610 m), is 83.4 kPa. Air at this pressure and 20\u00b0C flows with a velocity of 8 m\/s over a 1.5 m \u00d7 6 m flat plate whose temperature is 140\u00b0C. Determine the rate of heat transfer from the plate if the air flows parallel to the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-186782","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=186782"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186782\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186782"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186782"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}