{"id":237484,"date":"2025-06-17T09:24:47","date_gmt":"2025-06-17T09:24:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237484"},"modified":"2025-06-17T09:24:49","modified_gmt":"2025-06-17T09:24:49","slug":"consider-a-wedge-with-a-half-angle-of-10-flying-at-mach-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/consider-a-wedge-with-a-half-angle-of-10-flying-at-mach-2\/","title":{"rendered":"Consider a wedge with a half-angle of 10\u00b0 flying at Mach 2"},"content":{"rendered":"\n<p><br>Consider a wedge with a half-angle of 10\u00b0 flying at Mach 2. The oblique shock wave angle \\beta is 38.4 10 41.5 39.3<\/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><strong>Correct Answer: 39.3\u00b0<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>In compressible flow, when a supersonic flow encounters a wedge, an <strong>oblique shock wave<\/strong> forms ahead of the wedge. The angle this shock makes with the incoming flow is called the <strong>shock wave angle<\/strong> (\u03b2). The wedge deflects the flow through a certain angle, called the <strong>deflection angle<\/strong> (\u03b8). For this problem:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mach number (M) = 2.0<\/li>\n\n\n\n<li>Wedge half-angle (\u03b8) = 10\u00b0<\/li>\n\n\n\n<li>We are to find the corresponding shock wave angle (\u03b2)<\/li>\n<\/ul>\n\n\n\n<p>To solve this, we use the <strong>\u03b8\u2013\u03b2\u2013M relation<\/strong> from oblique shock theory. This relation is complex and usually solved numerically or with charts or computational tools, but general trends and approximations help us identify the correct answer from multiple choices.<\/p>\n\n\n\n<p>The \u03b8\u2013\u03b2\u2013M relation shows that for a given Mach number and deflection angle, there is a unique shock angle for the <strong>weak shock solution<\/strong>, which is the physically realistic case (strong shocks are rare in external flows). For Mach 2 and a deflection angle of 10\u00b0, the oblique shock angle typically falls in the high 30s.<\/p>\n\n\n\n<p>Let\u2019s test the options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>38.4\u00b0<\/strong>: Slightly low for a 10\u00b0 wedge at Mach 2<\/li>\n\n\n\n<li><strong>10\u00b0<\/strong>: This is the wedge angle, not the shock angle<\/li>\n\n\n\n<li><strong>41.5\u00b0<\/strong>: Slightly high<\/li>\n\n\n\n<li><strong>39.3\u00b0<\/strong>: Most accurate<\/li>\n<\/ul>\n\n\n\n<p>Using standard oblique shock tables or computational methods, the shock angle \u03b2 for M = 2 and \u03b8 = 10\u00b0 is approximately <strong>39.3\u00b0<\/strong>, which matches the weak oblique shock solution.<\/p>\n\n\n\n<p>Therefore, the <strong>correct shock wave angle is 39.3\u00b0<\/strong>. This ensures the flow turns appropriately to follow the wedge surface after the shock, maintaining physical realism and flow continuity in supersonic conditions.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-850.jpeg\" alt=\"\" class=\"wp-image-237485\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Consider a wedge with a half-angle of 10\u00b0 flying at Mach 2. The oblique shock wave angle \\beta is 38.4 10 41.5 39.3 The Correct Answer and Explanation is: Correct Answer: 39.3\u00b0 Explanation: In compressible flow, when a supersonic flow encounters a wedge, an oblique shock wave forms ahead of the wedge. The angle this [&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-237484","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237484","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=237484"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237484\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237484"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237484"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}