{"id":213604,"date":"2025-05-11T20:54:26","date_gmt":"2025-05-11T20:54:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=213604"},"modified":"2025-05-11T20:54:28","modified_gmt":"2025-05-11T20:54:28","slug":"if-the-mach-number-of-the-incoming-flow-is-2-4-compute-the-mach-number-after-the-first-oblique-shock-and-the-mach-number-after-the-reflected-oblique-shock","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/11\/if-the-mach-number-of-the-incoming-flow-is-2-4-compute-the-mach-number-after-the-first-oblique-shock-and-the-mach-number-after-the-reflected-oblique-shock\/","title":{"rendered":"If the Mach number of the incoming flow is 2.4, compute the Mach number after the first oblique shock, and the Mach number after the reflected oblique shock"},"content":{"rendered":"\n<p>Consider a ramp as shown in Figure 1. If the Mach number of the incoming flow is 2.4, compute the Mach number after the first oblique shock, and the Mach number after the reflected oblique shock. Compute the total and stagnation pressure ratios across the two shock system. Compute also the net change in entropy across the two shock system. Is the angle of incidence equal to the angle of reflection as the shock reflects off the engine cowling? Comment on what you observe.<\/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 answer this question, we need to analyze a <strong>double oblique shock system<\/strong>, which typically occurs in supersonic flow over a <strong>compression corner<\/strong> followed by <strong>shock reflection<\/strong> off a surface, such as an engine cowling. Let\u2019s go step by step. Since the figure is not provided, we\u2019ll assume a standard case often found in textbooks: a compression ramp followed by a reflected oblique shock, with a <strong>turning angle \u03b8 = 15\u00b0<\/strong> for the ramp. The freestream Mach number is <strong>M\u2081 = 2.4<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Given:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Freestream Mach number, M\u2081 = 2.4<\/li>\n\n\n\n<li>Deflection angle (\u03b8) = 15\u00b0<\/li>\n\n\n\n<li>\u03b3 (ratio of specific heats) = 1.4 (air)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: First oblique shock<\/strong><\/h3>\n\n\n\n<p>Using <strong>\u03b8-\u03b2-M<\/strong> relation (from oblique shock tables or solver), for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>M\u2081 = 2.4<\/li>\n\n\n\n<li>\u03b8 = 15\u00b0<br>We find:<\/li>\n\n\n\n<li>Shock angle \u03b2\u2081 \u2248 39.7\u00b0<\/li>\n\n\n\n<li>M\u2082 (after first shock) \u2248 <strong>1.87<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Reflected shock (off engine cowling)<\/strong><\/h3>\n\n\n\n<p>The flow is now turning back to horizontal \u2014 i.e., an <strong>expansion<\/strong> of \u221215\u00b0, so we expect:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A reflected shock to realign flow with the wall<\/li>\n\n\n\n<li>New deflection angle = \u221215\u00b0 (opposite to original)<\/li>\n<\/ul>\n\n\n\n<p>Using M\u2082 = 1.87 and \u03b8 = \u221215\u00b0, the reflected shock yields:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Shock angle \u03b2\u2082 \u2248 52.3\u00b0<\/li>\n\n\n\n<li>M\u2083 (after second shock) \u2248 <strong>1.45<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Pressure and stagnation pressure ratios<\/strong><\/h3>\n\n\n\n<p><strong>Across first shock:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>p\u2082\/p\u2081 \u2248 2.83<\/li>\n\n\n\n<li>p\u2080\u2082\/p\u2080\u2081 \u2248 0.841 (total pressure loss)<\/li>\n<\/ul>\n\n\n\n<p><strong>Across second shock:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>p\u2083\/p\u2082 \u2248 1.77<\/li>\n\n\n\n<li>p\u2080\u2083\/p\u2080\u2082 \u2248 0.857<\/li>\n<\/ul>\n\n\n\n<p>So total pressure ratio:<br><strong>p\u2080\u2083\/p\u2080\u2081 = 0.841 \u00d7 0.857 \u2248 0.72<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 4: Entropy change<\/strong><\/h3>\n\n\n\n<p>Entropy change per unit mass:<\/p>\n\n\n\n<p>$$<br>\\Delta s = c_p \\ln\\left(\\frac{T_3}{T_1}\\right) &#8211; R \\ln\\left(\\frac{p_3}{p_1}\\right)<br>$$<\/p>\n\n\n\n<p>Or using:<\/p>\n\n\n\n<p>$$<br>\\Delta s = R \\ln\\left(\\frac{p_{01}}{p_{03}}\\right)<br>$$<\/p>\n\n\n\n<p>$$<br>\\Delta s \u2248 R \\ln\\left(\\frac{1}{0.72}\\right) \u2248 R \\cdot 0.328<br>$$<\/p>\n\n\n\n<p>Thus, <strong>entropy increases<\/strong>, consistent with shock behavior.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Angle of incidence vs. reflection<\/strong><\/h3>\n\n\n\n<p><strong>No<\/strong>, the angle of reflection is <strong>not equal<\/strong> to the angle of incidence unless symmetry is enforced. Here, the geometry and flow turnings mean the reflection angle adjusts to satisfy flow turning requirements \u2014 usually resulting in a <strong>different \u03b2 angle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>M\u2082 \u2248 1.87<\/strong>, <strong>M\u2083 \u2248 1.45<\/strong><\/li>\n\n\n\n<li><strong>p\u2080\u2083\/p\u2080\u2081 \u2248 0.72<\/strong>, showing total pressure loss<\/li>\n\n\n\n<li><strong>Entropy increases<\/strong> across the shock system<\/li>\n\n\n\n<li><strong>Reflection angle \u2260 incidence angle<\/strong> due to flow geometry constraint<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Consider a ramp as shown in Figure 1. If the Mach number of the incoming flow is 2.4, compute the Mach number after the first oblique shock, and the Mach number after the reflected oblique shock. Compute the total and stagnation pressure ratios across the two shock system. Compute also the net change in entropy [&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-213604","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213604","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=213604"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213604\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213604"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213604"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}