{"id":217336,"date":"2025-05-21T18:16:56","date_gmt":"2025-05-21T18:16:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217336"},"modified":"2025-05-21T18:16:59","modified_gmt":"2025-05-21T18:16:59","slug":"to-calculate-the-air-velocity-in-a-duct-using-a-pitot-static-tube","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/21\/to-calculate-the-air-velocity-in-a-duct-using-a-pitot-static-tube\/","title":{"rendered":"To calculate the air velocity in a duct using a Pitot-static tube"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">To calculate the <strong>air velocity<\/strong> in a duct using a <strong>Pitot-static tube<\/strong>, we apply Bernoulli\u2019s principle and account for the manometer reading, which gives the pressure difference (dynamic pressure) between the total and static pressures.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Given:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Manometer reading<\/strong> = 8 cm of water = 0.08 m of water<\/li>\n\n\n\n<li><strong>Static pressure<\/strong> = 9 kN\/m\u00b2 = 9000 N\/m\u00b2<\/li>\n\n\n\n<li><strong>Air temperature<\/strong> = 320 K<\/li>\n\n\n\n<li><strong>Barometric pressure<\/strong> = 740 mm Hg = $740 \\times 133.322 = 98657 \\, \\text{Pa}$<\/li>\n\n\n\n<li><strong>Gas constant for air<\/strong> = 287 J\/kg\u00b7K<\/li>\n\n\n\n<li><strong>Coefficient of velocity (Cv)<\/strong> = 0.98<\/li>\n\n\n\n<li><strong>Density of water<\/strong> \u2248 1000 kg\/m\u00b3<\/li>\n\n\n\n<li><strong>Acceleration due to gravity<\/strong> = 9.81 m\/s\u00b2<\/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: Calculate differential pressure from manometer<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dynamic pressure (\u0394P) = \u03c1_water \u00d7 g \u00d7 h<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\u0394P = 1000 \\times 9.81 \\times 0.08 = 784.8 \\, \\text{Pa}<br>$$<\/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 2: Find air density (\u03c1_air)<\/strong> using ideal gas law:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\u03c1 = \\frac{P}{RT} = \\frac{9000}{287 \\times 320} = \\frac{9000}{91840} \\approx 0.098 \\, \\text{kg\/m}^3<br>$$<\/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 3: Calculate theoretical velocity (V)<\/strong> from dynamic pressure:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>V = \\sqrt{\\frac{2 \\times \u0394P}{\u03c1}} = \\sqrt{\\frac{2 \\times 784.8}{0.098}} = \\sqrt{16016.3} \\approx 126.5 \\, \\text{m\/s}<br>$$<\/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: Apply velocity coefficient (Cv)<\/strong>:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>V_{\\text{actual}} = C_v \\times V = 0.98 \\times 126.5 \\approx \\boxed{124 \\, \\text{m\/s}}<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words):<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A <strong>Pitot-static tube<\/strong> measures the fluid velocity based on the difference between the <strong>stagnation (total) pressure<\/strong> and the <strong>static pressure<\/strong>. When air flows into the Pitot tube, it is brought to rest, causing the pressure to rise \u2014 this rise is captured by the manometer in terms of the height of a liquid column, which here is <strong>8 cm of water<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine the velocity, the pressure difference (\u0394P) is first calculated using the hydrostatic pressure formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\u0394P = \\rho_{\\text{water}} \\cdot g \\cdot h<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This gives the dynamic pressure caused by the velocity of air in the duct.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Next, we calculate the <strong>air density<\/strong> using the <strong>ideal gas law<\/strong>, which is essential because air density changes with pressure and temperature. The static pressure (9000 Pa) and temperature (320 K) allow us to compute this density accurately using the gas constant for air (287 J\/kg\u00b7K).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Then, we apply Bernoulli&#8217;s equation to solve for velocity based on dynamic pressure:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>V = \\sqrt{\\frac{2 \\cdot \u0394P}{\u03c1_{\\text{air}}}}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This gives the theoretical velocity. However, real-world readings are affected by non-idealities like tube friction and turbulence. Thus, we multiply the result by a <strong>velocity coefficient (Cv)<\/strong>, typically slightly less than 1, to obtain the <strong>actual velocity<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In conclusion, after incorporating all these parameters, the air velocity in the duct is approximately <strong>124 m\/s<\/strong>, providing a reliable estimate of flow speed using practical fluid mechanics principles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>To calculate the air velocity in a duct using a Pitot-static tube, we apply Bernoulli\u2019s principle and account for the manometer reading, which gives the pressure difference (dynamic pressure) between the total and static pressures. The Correct Answer and Explanation is: Given: Step 1: Calculate differential pressure from manometer Dynamic pressure (\u0394P) = \u03c1_water \u00d7 [&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-217336","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217336","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=217336"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217336\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217336"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217336"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217336"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}