{"id":31035,"date":"2025-06-21T21:51:10","date_gmt":"2025-06-21T21:51:10","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=31035"},"modified":"2025-06-21T21:51:11","modified_gmt":"2025-06-21T21:51:11","slug":"write-the-formula-for-pressure-difference-%ce%b4p%cf%81gh","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-the-formula-for-pressure-difference-%ce%b4p%cf%81gh\/","title":{"rendered":"Write the formula for pressure difference\u00a0\u0394P=\u03c1gh"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"844\" height=\"249\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-168.png\" alt=\"\" class=\"wp-image-31040\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-168.png 844w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-168-300x89.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-168-768x227.png 768w\" sizes=\"auto, (max-width: 844px) 100vw, 844px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is: <strong>151.074 Pa<\/strong><\/p>\n\n\n\n<p>To determine the pressure difference between the stagnation pressure and the static pressure, we apply the hydrostatic pressure formula:<\/p>\n\n\n\n<p>\u0394P=\u03c1gh\\Delta P = \\rho g h<\/p>\n\n\n\n<p>In this case, the change in height is not a vertical column but an inclined difference. Therefore, the vertical component of the height must be calculated using trigonometry. The full expression becomes:<\/p>\n\n\n\n<p>Pstag\u2212P0=\u03c1g(h2\u2212h1)sin\u2061(\u03b8)P_{\\text{stag}} &#8211; P_0 = \\rho g (h_2 &#8211; h_1) \\sin(\\theta)<\/p>\n\n\n\n<p>Substituting the given values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Density \u03c1=0.7\u00d71000=700\u2009kg\/m3\\rho = 0.7 \\times 1000 = 700 \\, \\text{kg\/m}^3<\/li>\n\n\n\n<li>Acceleration due to gravity g=9.81\u2009m\/s2g = 9.81 \\, \\text{m\/s}^2<\/li>\n\n\n\n<li>Difference in height h=0.0067\u22120.0023=0.0044\u2009mh = 0.0067 &#8211; 0.0023 = 0.0044 \\, \\text{m}<\/li>\n\n\n\n<li>Incline angle \u03b8=30\u2218\\theta = 30^\\circ<\/li>\n<\/ul>\n\n\n\n<p>We plug in the values:<\/p>\n\n\n\n<p>Pstag\u2212P0=700\u00d79.81\u00d70.0044\u00d7sin\u2061(30\u2218)P_{\\text{stag}} &#8211; P_0 = 700 \\times 9.81 \\times 0.0044 \\times \\sin(30^\\circ)<\/p>\n\n\n\n<p>=700\u00d79.81\u00d70.0044\u00d70.5= 700 \\times 9.81 \\times 0.0044 \\times 0.5<\/p>\n\n\n\n<p>=151.074\u2009Pa= 151.074 \\, \\text{Pa}<\/p>\n\n\n\n<p>This pressure difference arises due to the hydrostatic principle, which states that pressure increases with depth in a fluid due to the weight of the fluid above. In this scenario, the pressure difference is oriented along an inclined manometer, so the vertical component of the height difference is used. Multiplying this height by the density and gravitational acceleration gives the pressure exerted due to the fluid column. The sine function adjusts the effective height since the fluid columns are not perfectly vertical. This principle is commonly used in fluid mechanics and aerodynamics to measure velocity-related pressures and is a foundation of Pitot-static tube analysis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-331.jpeg\" alt=\"\" class=\"wp-image-31048\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-331.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-331-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-331-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is: 151.074 Pa To determine the pressure difference between the stagnation pressure and the static pressure, we apply the hydrostatic pressure formula: \u0394P=\u03c1gh\\Delta P = \\rho g h In this case, the change in height is not a vertical column but an inclined difference. Therefore, the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-31035","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31035","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=31035"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31035\/revisions"}],"predecessor-version":[{"id":31053,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31035\/revisions\/31053"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=31035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=31035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=31035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}