{"id":253826,"date":"2025-07-12T07:35:32","date_gmt":"2025-07-12T07:35:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253826"},"modified":"2025-07-12T07:35:34","modified_gmt":"2025-07-12T07:35:34","slug":"consider-the-isentropic-flow-over-an-airfoil","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/12\/consider-the-isentropic-flow-over-an-airfoil\/","title":{"rendered":"Consider the isentropic flow over an airfoil."},"content":{"rendered":"\n<p>1 atm = 2116 lb\/ft2 = 1.01 \u00c3\u2014 10^5 N\/m^2. Consider the isentropic flow over an airfoil. The freestream conditions are T\u00e2\u02c6\u017e = 245 K and p\u00e2\u02c6\u017e = 4.35 \u00c3\u2014 10^4 N\/m^2. At a point on the airfoil, the pressure is 3.6 \u00c3\u2014 10^4 N\/m^2. Calculate the density at this point.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the density at the point on the airfoil, we need to use the <strong>Ideal Gas Law<\/strong> for air, which is:p=\u03c1RTp = \\rho R Tp=\u03c1RT<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>ppp is the pressure,<\/li>\n\n\n\n<li>\u03c1\\rho\u03c1 is the density,<\/li>\n\n\n\n<li>RRR is the specific gas constant for air (R=287\u2009J\/kg\\cdotpKR = 287 \\, \\text{J\/kg\u00b7K}R=287J\/kg\\cdotpK),<\/li>\n\n\n\n<li>TTT is the temperature.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Use the isentropic flow assumption<\/h3>\n\n\n\n<p>In isentropic flow, the temperature and pressure are related. However, since the temperature at the point on the airfoil isn&#8217;t given directly, we will use the isentropic relation to approximate it. First, we can calculate the density in terms of pressure and temperature.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Rearranging the Ideal Gas Law<\/h3>\n\n\n\n<p>We can rearrange the Ideal Gas Law to solve for density:\u03c1=pRT\\rho = \\frac{p}{RT}\u03c1=RTp\u200b<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>p=3.6\u00d7104\u2009N\/m2p = 3.6 \\times 10^4 \\, \\text{N\/m}^2p=3.6\u00d7104N\/m2,<\/li>\n\n\n\n<li>R=287\u2009J\/kg\\cdotpKR = 287 \\, \\text{J\/kg\u00b7K}R=287J\/kg\\cdotpK,<\/li>\n\n\n\n<li>T\u221e=245\u2009KT_{\\infty} = 245 \\, \\text{K}T\u221e\u200b=245K (freestream temperature).<\/li>\n<\/ul>\n\n\n\n<p>Since the flow is isentropic, we assume that the temperature at the point on the airfoil is nearly the same as the freestream temperature, so T\u2248T\u221e=245\u2009KT \\approx T_{\\infty} = 245 \\, \\text{K}T\u2248T\u221e\u200b=245K.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the density<\/h3>\n\n\n\n<p>Now, substitute the values into the Ideal Gas Law equation:\u03c1=3.6\u00d7104287\u00d7245\\rho = \\frac{3.6 \\times 10^4}{287 \\times 245}\u03c1=287\u00d72453.6\u00d7104\u200b\u03c1=3.6\u00d710470315\\rho = \\frac{3.6 \\times 10^4}{70315}\u03c1=703153.6\u00d7104\u200b\u03c1\u22480.512\u2009kg\/m3\\rho \\approx 0.512 \\, \\text{kg\/m}^3\u03c1\u22480.512kg\/m3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The density at the point on the airfoil is approximately <strong>0.512 kg\/m\u00b3<\/strong>. This calculation assumes that the temperature at the point on the airfoil is close to the freestream temperature due to the isentropic assumption.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-165.jpeg\" alt=\"\" class=\"wp-image-253832\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>1 atm = 2116 lb\/ft2 = 1.01 \u00c3\u2014 10^5 N\/m^2. Consider the isentropic flow over an airfoil. The freestream conditions are T\u00e2\u02c6\u017e = 245 K and p\u00e2\u02c6\u017e = 4.35 \u00c3\u2014 10^4 N\/m^2. At a point on the airfoil, the pressure is 3.6 \u00c3\u2014 10^4 N\/m^2. Calculate the density at this point. The Correct Answer and [&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-253826","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253826","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=253826"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253826\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253826"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253826"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}