{"id":152638,"date":"2022-03-23T10:07:06","date_gmt":"2022-03-23T04:37:06","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=152638"},"modified":"2024-08-29T18:06:33","modified_gmt":"2024-08-29T12:36:33","slug":"dimensions-of-pressure-gradient","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-pressure-gradient\/","title":{"rendered":"Dimensions of Pressure Gradient"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-pressure-gradient\/#Dimensional_Formula_of_Pressure_Gradient\" title=\"Dimensional Formula of Pressure Gradient\">Dimensional Formula of Pressure Gradient<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-pressure-gradient\/#Derivation\" title=\"Derivation:\">Derivation:<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-pressure-gradient\/#Significance_of_dimensions_of_pressure_gradient_in_IIT_JEE_exam\" title=\"Significance of dimensions of pressure gradient in IIT JEE exam\">Significance of dimensions of pressure gradient in IIT JEE exam<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-pressure-gradient\/#FAQs_for_Dimensions_of_Pressure_Gradient\" title=\"FAQs for Dimensions of Pressure Gradient\">FAQs for Dimensions of Pressure Gradient<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-pressure-gradient\/#Infinity_Learn_App\" title=\"Infinity Learn App\">Infinity Learn App<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>The pressure gradient (generally of air, but more broadly of any fluid) is a physical quantity in atmospheric science that describes the direction and rate at which pressure increases most rapidly around a specific location. The pressure gradient is really a three-dimensional quantity measured in pascals per meter (Pa\/m). Arithmetically, it is the gradient of pressure as a function of position. The force density has been defined as the negative gradient of pressure.<\/p>\n<p>A pressure gradient is just a local characterization of the air (more generally of the fluid under investigation). The pressure gradient will only be defined at the spatial scales where the pressure (or, more broadly, fluid dynamics) is defined.<\/p>\n<p>The pressure gradient within planetary atmospheres (including the Earth&#8217;s) is a vector pointing roughly downwards, because pressure changes most rapidly vertically, increasing downwards (see vertical pressure variation). The strength (or norm) of the pressure gradient in the troposphere is typically around 9 Pa\/m (or 90 hPa\/km).<\/p>\n<p>The pressure gradient frequently includes a small but critical horizontal component that is largely responsible for wind circulation in the atmosphere. The lateral pressure gradient is a two-dimensional vector that results from the pressure gradient being projected onto a local horizontal plane. One such horizontal pressure gradient force is directed from higher to lower pressure near the Earth&#8217;s surface. Its specific orientation at any given time and location is strongly influenced by the weather conditions. At semi-latitudes, the normal horizontal pressure gradient can be in the order of 102 Pa\/m (or 10 Pa\/km), though much higher values can be found along meteorological fronts.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-152642\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/pressure-gauge-4345880_960_720-300x200.jpg\" alt=\"Dimensions of Pressure Gradient\" width=\"525\" height=\"350\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/pressure-gauge-4345880_960_720-300x200.jpg?v=1647959358 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/pressure-gauge-4345880_960_720-768x512.jpg?v=1647959358 768w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/pressure-gauge-4345880_960_720.jpg?v=1647959358 960w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>The pressure-gradient force is created when there is a pressure difference across a surface. In fact, pressure has been defined as a force per unit area applied to a surface. When there is no additional force to balance it, a difference in pressure across a surface implies a difference in force, which can result in acceleration according to Newton&#8217;s second law of motion.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Dimensional_Formula_of_Pressure_Gradient\"><\/span><span style=\"color: #0000ff;\"><strong>Dimensional Formula of Pressure Gradient<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The dimensional formula of pressure gradient can be represented as:<\/p>\n<p style=\"text-align: center;\"><strong>[M<sup>1 <\/sup>L<sup>-2 <\/sup>T<sup>-2<\/sup>]<\/strong><\/p>\n<p>Here,<\/p>\n<p>M = Mass<\/p>\n<p>L = Length<\/p>\n<p>T = Time<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Derivation\"><\/span><span style=\"color: #0000ff;\"><strong>Derivation:<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>We have, Pressure Gradient = Pressure \u00d7 [Distance]<sup>-1<\/sup> . . . . (1)<\/p>\n<p>Then the dimensional formula of distance = [M<sup>0 <\/sup>L<sup>1 <\/sup>T<sup>0<\/sup>] . . . . (2)<\/p>\n<p>\u21d2 Pressure = Force \u00d7 [Area]<sup>-1<\/sup> . . . . (3)<\/p>\n<p>As because, Force = mass \u00d7 acceleration<\/p>\n<p>Therefore, the dimensions of force = [M] \u00d7 [L<sup>1 <\/sup>T<sup>-2<\/sup>] = [M<sup>1 <\/sup>L<sup>1 <\/sup>T<sup>-2<\/sup>] . . . (4)<\/p>\n<p>Similarly, the dimensional formula of area = [M<sup>0 <\/sup>L<sup>2 <\/sup>T<sup>0<\/sup>] . . . (5)<\/p>\n<p>When substituting equation (4) and (5) in equation (3) we get,<\/p>\n<p>Pressure (P) = [M<sup>1 <\/sup>L<sup>1 <\/sup>T<sup>-2<\/sup>] \u00d7 [M<sup>0 <\/sup>L<sup>2 <\/sup>T<sup>0<\/sup>]<sup>-1<\/sup><\/p>\n<p>Thus, the dimensional formula of pressure = [M<sup>1 <\/sup>L<sup>-1 <\/sup>T<sup>-2<\/sup>] . . . . (6)<\/p>\n<p>When substituting equation (2) and (6) in equation (1) we get,<\/p>\n<p>Pressure Gradient = Pressure \u00d7 [Distance]<sup>-1<\/sup><\/p>\n<p>That is, P = [M<sup>1 <\/sup>L<sup>-1 <\/sup>T<sup>-2<\/sup>] \u00d7 [M<sup>0 <\/sup>L<sup>1 <\/sup>T<sup>0<\/sup>]<sup>-1<\/sup> = [M<sup>1 <\/sup>L<sup>-2 <\/sup>T<sup>-2<\/sup>]\n<p>Thus, the pressure gradient can be dimensionally represented as <strong>[M<sup>1 <\/sup>L<sup>-2 <\/sup>T<sup>-2<\/sup>].<\/strong><\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center;\" colspan=\"2\"><strong>JEE Online Courses &amp; Study Materials<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-9\"><strong>JEE Foundation Class 9 Online Course<\/strong><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-10\"><strong>JEE Foundation Class 10 Online Course<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/jee-class-11-online-course\"><strong>JEE Class 11 Online Course<\/strong><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-jee-main-prep\"><strong>One Stop Solution for JEE Prep<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Significance_of_dimensions_of_pressure_gradient_in_IIT_JEE_exam\"><\/span><span style=\"color: #0000ff; font-size: 18pt;\"><strong>Significance of dimensions of pressure gradient in IIT JEE exam<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>It is critical to take a holistic approach to every facet of a subject\u2019s chapter. It will not only adequately prepare you for the exam, but will also clarify your understanding of each topic. It will help you in<span style=\"color: #0000ff;\"> <strong><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/jee\" target=\"_blank\" rel=\"noopener\">JEE preparation<\/a><\/strong><\/span> and answer conceptual problems in the exam. The number of questions from the chapter unit and dimensions would be one or two, with a weightage of roughly four marks.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"FAQs_for_Dimensions_of_Pressure_Gradient\"><\/span><span style=\"color: #0000ff; font-size: 18pt;\"><strong>FAQs for Dimensions of Pressure Gradient<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #0000ff;\"><strong>Q. What is called a pressure gradient?<\/strong><\/span><\/p>\n<p><span style=\"color: #ff0000;\"><strong>Ans:<\/strong> <\/span>A &#8220;pressure gradient&#8221; is indeed the change in pressure measured over a given distance. The pressure gradient produces a net force directed from high to low pressure, which is known as the &#8220;pressure gradient force.&#8221;<\/p>\n<p><span style=\"color: #0000ff;\"><strong>Q. How do you calculate pressure gradient?<\/strong><\/span><\/p>\n<p><span style=\"color: #ff0000;\"><strong>Ans:<\/strong> <\/span>The pressure gradient could be calculated mathematically by dividing the pressure difference between two locations (in Pascals) by the distance between the two locations (in meters).<\/p>\n<p><span style=\"color: #0000ff;\"><strong>Q. What is the dimensional formula of pressure gradient?<\/strong><\/span><\/p>\n<p><span style=\"color: #ff0000;\"><strong>Ans:<\/strong> <\/span>The pressure gradient can be dimensionally represented as <strong>[M<sup>1 <\/sup>L<sup>-2 <\/sup>T<sup>-2<\/sup>].<\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Infinity_Learn_App\"><\/span><span style=\"color: #0000ff;\">Infinity Learn App<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Now you can find answers to all your subject queries &amp; prepare for your Exams on our<span style=\"color: #0000ff;\"> <strong><a style=\"color: #0000ff;\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.infinitylearn.learn\" target=\"_blank\" rel=\"noopener\">test preparation app<\/a><\/strong><\/span> \u2013 Infinity Learn.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The pressure gradient (generally of air, but more broadly of any fluid) is a physical quantity in atmospheric science that [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Dimensions of Pressure Gradient","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The pressure gradient (generally of air, but more broadly of any fluid) is a physical quantity in atmospheric science that describes the direction and rate at which pressure increases most rapidly around a specific location. The pressure gradient is really a three-dimensional quantity measured in pascals per metre (Pa\/m). Arithmetically, it is the gradient of pressure as a function of position. The force density has been defined as the negative gradient of pressure.","custom_permalink":"blog\/iit-jee\/dimensions-of-pressure-gradient\/"},"categories":[53,57,4],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Dimensions of Pressure Gradient - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The pressure gradient (generally of air, but more broadly of any fluid) is a physical quantity in atmospheric science that describes the direction and rate at which pressure increases most rapidly around a specific location. The pressure gradient is really a three-dimensional quantity measured in pascals per metre (Pa\/m). 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