{"id":7562,"date":"2024-04-15T02:46:54","date_gmt":"2024-04-15T02:46:54","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=7562"},"modified":"2024-04-15T02:46:54","modified_gmt":"2024-04-15T02:46:54","slug":"solution-of-laplacian-equation-in-three-dimensions-fractextd2varphi-textdtextx2-fractextd2varphi-textdtexty2-fract","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/solution-of-laplacian-equation-in-three-dimensions-fractextd2varphi-textdtextx2-fractextd2varphi-textdtexty2-fract\/","title":{"rendered":"Solution of Laplacian equation in three dimensions $$\\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{x}}^2}}} + \\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{y}}^2}}} + \\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{z}}^2}}} = 0$$ of water in a syphon, is done by A. Analytical method B. Khosla&#8217;s method C. Method of relaxation D. Unwin&#8217;s method"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9832a93d750\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    Analytical method                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    Khosla&#039;s method                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    Method of relaxation                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    Unwin&#039;s method                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is: C. Method of relaxation.<\/p>\n<p>The method of relaxation is a numerical method for solving partial differential equations. It is based on the idea of iteratively updating the solution until it converges to the desired solution. The method of relaxation is particularly well-suited for solving elliptic partial differential equations, such as the Laplacian equation.<\/p>\n<p>The Laplacian equation is a second-order partial differential equation that describes the equilibrium of a physical system. In the case of water in a syphon, the Laplacian <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> equation can be used to describe the equilibrium <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> of the water pressure. The method of relaxation can be used to solve the Laplacian equation and find the equilibrium pressure distribution in the syphon.<\/p>\n<p>The method of relaxation is a relatively simple and efficient method for solving partial differential equations. It is often used in engineering and physics applications.<\/p>\n<p>The other options are incorrect because they are not methods for solving partial differential equations.<\/p>\n<ul>\n<li>Analytical method is a method for solving problems by using mathematical equations. It is not a method for solving partial differential equations.<\/li>\n<li>Khosla&#8217;s method is a method for solving problems in structural engineering. It is not a method for solving partial differential equations.<\/li>\n<li>Unwin&#8217;s method is a method for solving problems in fluid dynamics. It is not a method for solving partial differential equations.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[649],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Solution of Laplacian equation in three dimensions $$\\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{x}}^2}}} + \\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{y}}^2}}} + \\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{z}}^2}}} = 0$$ of water in a syphon, is done by A. Analytical method B. Khosla&#039;s method C. Method of relaxation D. 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Analytical method B. Khosla's method C. Method of relaxation D. Unwin's method","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/solution-of-laplacian-equation-in-three-dimensions-fractextd2varphi-textdtextx2-fractextd2varphi-textdtexty2-fract\/","og_locale":"en_US","og_type":"article","og_title":"Solution of Laplacian equation in three dimensions $$\\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{x}}^2}}} + \\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{y}}^2}}} + \\frac{{{{\\text{d}}^2}\\varphi }}{{{\\text{d}}{{\\text{z}}^2}}} = 0$$ of water in a syphon, is done by A. Analytical method B. Khosla's method C. Method of relaxation D. 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Analytical method B. Khosla's method C. Method of relaxation D. 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Analytical method B. Khosla&#8217;s method C. Method of relaxation D. 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