{"id":7247,"date":"2024-04-15T02:41:56","date_gmt":"2024-04-15T02:41:56","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=7247"},"modified":"2024-04-15T02:41:56","modified_gmt":"2024-04-15T02:41:56","slug":"which-of-the-following-velocity-potentials-satisfies-continuity-equation-a-x2y-b-x2-y2-c-cosx-d-x2-y2","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-of-the-following-velocity-potentials-satisfies-continuity-equation-a-x2y-b-x2-y2-c-cosx-d-x2-y2\/","title":{"rendered":"Which of the following velocity potentials satisfies continuity equation? A. x2y B. x2 &#8211; y2 C. cosx D. x2 + y2"},"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_6a9b067515a41\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    x2y                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    x2 - y2                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    cosx                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"true\">\r\n                    x2 + y2                <\/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 D.<\/p>\n<p>The continuity equation states that the divergence of the velocity field is zero. In other words, the amount of fluid entering a given volume must equal the amount of fluid leaving that volume.<\/p>\n<p>The velocity potential is a scalar field that can be used to represent the velocity field. The velocity field can be obtained by taking the gradient of the velocity potential.<\/p>\n<p>The gradient of a scalar field is a vector field that points in the direction of the greatest increase in the scalar field. The magnitude of the gradient is equal to the rate of change of the scalar field in the direction of the gradient.<\/p>\n<p>The divergence of a vector field is a scalar <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> field that represents the amount of fluid leaving a given volume. The divergence is equal to the sum of the components of the vector field that point in the outward direction.<\/p>\n<p>The velocity potential satisfies the continuity equation if the divergence of the velocity field is zero. In other words, the amount of fluid entering a given volume must equal the amount of fluid leaving that volume.<\/p>\n<p>The velocity potential $x^2 + y^2$ satisfies the continuity equation because the divergence of the velocity field is zero. The velocity field is given by $\\mathbf{v} = \\nabla \\phi$, where $\\phi = x^2 + y^2$. The divergence of the velocity field is $\\nabla \\cdot \\mathbf{v} = 2x + 2y = 0$. Therefore, the velocity potential $x^2 + y^2$ satisfies the continuity equation.<\/p>\n<p>The other options do not satisfy the continuity equation. The velocity potential $x^2y$ has a divergence of $2x + y$. The <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> velocity potential $x^2 &#8211; y^2$ has a divergence of $2x &#8211; 2y$. The velocity potential $\\cos x$ has a divergence of $-\\sin x$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel 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":[648],"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>Which of the following velocity potentials satisfies continuity equation? 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