{"id":1359,"date":"2021-05-26T14:02:08","date_gmt":"2021-05-26T08:32:08","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=1359"},"modified":"2021-10-30T07:40:42","modified_gmt":"2021-10-30T07:40:42","slug":"what-is-bernoullis-equation","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-bernoullis-equation\/","title":{"rendered":"What Is Bernoulli&#8217;s Equation?"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Overview<\/strong><\/h2>\n\n\n\n<p>The Bernoulli&#8217;s equation was introduced by the mathematician Jacob Bernoulli in 1695.<\/p>\n\n\n\n<p>Bernoulli equation is the nonlinear differential equation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Definition<\/strong><\/h2>\n\n\n\n<p>The equation of the form-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/Ahi0IxgMtXRp8mRi-AJc-hXZQoE6v9D-zPO_byrrqEBfbbqCp9QH0a6Nt9N76xyQytPINzlzCV6TxyXW-Ni14MNw21PgOL1NgI60dQbDvTe4pKwTHGdcmlAv9dphPe9WQLhT75hq\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>is called the <strong>Bernoulli equation<\/strong>.<\/p>\n\n\n\n<p>Here P and Q are constants of x<\/p>\n\n\n\n<p>On dividing the equation (1) by y^n we get-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/sEaQv_nF6PcLvdIB8ydo-5Mv-o-fz5kALJ9DDGHgv3vuYDBjbGgZMgeI3TqQD-yU7ejf4aXBMM8s50a3ppwcMy_NlKN34wI7YPZA3umxDcJfIw6d3jKI9FermJuFszy-GFjD5IIA\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>And putting&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/WXfFkuBrLRbfAiWZJmNt-t2qjqU9QEzdVK46QQRdiN4AU1bgp-a_ZZ0jif-798kZHAvYduiJ3MuyMzvKozOMIRiyNbBfKsvyWQOLg2ZdyZRBiWsBp6y7SgFsf0oyzh8M8CPf0h8k\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>so that<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/GS2ViBOFDRqaAbJWglFE88Cc7rKu4ATo-TW6v0Yh4qf6olf_sxhlcJ2RcKN3Lno_Lo5__zC9xtM9wejQC47BNB6al8bqDp8m8fYT6Hcp5J0HXVJ-yjdpBQsqUwtmglzVfLubcn0U\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Or<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/kMRxDVm2gVgEbyLpIdZcF8nCQ3vAFT-5o4lwBickLEU36JfU9P4Z25L_Ty-P5-s_-x4lOyn1PrDHBrddQP0eGXlCGwgcgLH07z9g4jhNJqbe0tG1KUyn3WZWiuApRxDlwmkyxbFm\" alt=\"\" width=\"111\" height=\"49\"\/><\/figure>\n\n\n\n<p>Equation (2) becomes,<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/ahKAa-G4LkrboidPkZyBuyv1JpQZVERFE5rSLCPS3V5AXsrQyILXRMq_1E-3rMEFzWvqHzErWezASU6vkNpP68Figmwvq2BHvCJ9CRF3NXsQaIbwHEEFokh745ywtLOd-YG9Ugoh\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center\">Or<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/f0pc-cgFl4uC9rjFDDKMpPLNDL-ZurMVFP8RJ90G0azhcw2iKg1PAlYcI3cOHjSbGP0sPVKNNe_VjOvy5nS5CpzA1krOdGM5-pTIUPweBf6fW60P2Bb7-seuKw13tQHkpmOQdI0q\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Which is properly a linear equation and can be solved easily.<\/p>\n\n\n\n<p>Lets understand the theory by doing an example.<\/p>\n\n\n\n<p><strong>Example-1: Solve-<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/bDsFxvcOAjdejS2OyT0CL9bDtfsC_GiA6ZtX3TiT2fHFEL5njubepDNMeCBmswHjz4XT8L3MpdoIiyOn5yNKQ4QrEgLxzEG7qaABCJTQy5-cAeHP882O_Xkv4_3m5SvDG--QhZk6\" alt=\"\" width=\"166\" height=\"41\"\/><\/figure>\n\n\n\n<p>Solution.<\/p>\n\n\n\n<p>Here we have-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/tAh_PPKG2WEtdGIpfvrrJui40xSMkIJX_nO_o_rU-9gIVkfVZi21pZL_4TOM3z9USsUj9cVTYXntB9T3adYOABDOYfmXBYJ6LukrC5WOJw9vZS0GoSLtaLAYQJp91EXuaSpTO1U7\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Which is the form of <strong>Bernoulli equation<\/strong>,<\/p>\n\n\n\n<p>Now divide the given equation by xy, we get-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/8NetNLx5xeJAnIeZlODEhSsCuMe9ZAGyo-X3lf1WtmRgHUqnMPdjMvtX67MRsSXgXRT9B9eL2rQ_koBqroebOih0tWXw6WwG4_qyPIdiEVlloFW1q9FjqzJyuNLhpV4S3J-fEJJ0\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Put&nbsp;<\/p>\n\n\n\n<p>z=log\u2061y<\/p>\n\n\n\n<p>So that<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/m-nVf4h610NbemhBj8oCPF4VtQNWMKZWzARBXAFAOVHK5NxXSHwCk8PJLH_0zRmG8yGJamWc6ghLM6IkNGtcOtCUl3HIgpwi_D-htOqP2Xi7aChb5qymzuOzkDRCNDgv4RuxmPDh\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Then equation (1) reduces to-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/moPdf6P9zCFz2cz9qebXLCspXhFhR4C3OZOVOgV-NVr4JbHTKHBKXneTeW4nHlo_ypJwuoldpy-F9ig1R2w05YHLPWs0CTfHdIK_2q2JXi2zHzmVVA3iTHohXkRa7ysYMT2bbmIm\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Now<\/p>\n\n\n\n<p>Integrating factor-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/04_SvAu8tDxMpqqbu6BWwvKI4LIkv8VJmc1i5gEjtgoX55PhE8GkRufTnCkIFX0g2apGowOLFWWEUzund3roLg1e0OHkvz4qkeXlgsWv2VVwWB1eHqn47sqL0GFAoYWddzwT_lym\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>The solution will be-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/-Mv6WVskNsvHczUkHLTpOXtSenyu6dymFa0octDBHv8sEZYe10rjHd2qXR0Zshy6yz9YP5vB2hOBdj1DC-cOrD9ooTryMCqbHbMS4IN6BwBtbtHieJj2qtLxsNOa_J9D3_WrIPnp\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-fourier-series\" target=\"_blank\" rel=\"noreferrer noopener\">What is Fourier series?<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-are-the-asymptotes\" target=\"_blank\" rel=\"noreferrer noopener\">What are Asymptotes?<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-an-inverse-of-a-matrix\" target=\"_blank\" rel=\"noreferrer noopener\">What is inverse of a matrix?<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-a-symmetric-matrix\" target=\"_blank\" rel=\"noreferrer noopener\">What is symmetric matrix?<\/a><br><\/li><\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bernoulli equation is the nonlinear differential equation.<\/p>\n","protected":false},"author":3,"featured_media":1788,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-1359","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What Is Bernoulli&#039;s Equation? 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