{"id":7559,"date":"2024-04-15T02:46:51","date_gmt":"2024-04-15T02:46:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=7559"},"modified":"2024-04-15T02:46:51","modified_gmt":"2024-04-15T02:46:51","slug":"fundamental-momentum-equation-for-a-hydraulic-jump-is-a-textd_12-textd_22-frac2textqtextgleft-textv_1-textv_2-right-b-textd","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/fundamental-momentum-equation-for-a-hydraulic-jump-is-a-textd_12-textd_22-frac2textqtextgleft-textv_1-textv_2-right-b-textd\/","title":{"rendered":"Fundamental momentum equation for a hydraulic jump, is A. $${\\text{D}}_1^2 &#8211; {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} &#8211; {{\\text{V}}_2}} \\right)$$ B. $${\\text{D}}_2^2 &#8211; {\\text{D}}_1^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} &#8211; {{\\text{V}}_2}} \\right)$$ C. $${\\text{D}}_1^2 &#8211; {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_2} &#8211; {{\\text{V}}_1}} \\right)$$ D. $${\\text{D}}_1^2 + {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_2} &#8211; {{\\text{V}}_1}} \\right)$$"},"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_6a9832a08e8d3\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    $${\text{D}}_1^2 - {\text{D}}_2^2 = \frac{{2{\text{q}}}}{{\text{g}}}left( {{{\text{V}}_1} - {{\text{V}}_2}} \right)$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $${\text{D}}_2^2 - {\text{D}}_1^2 = \frac{{2{\text{q}}}}{{\text{g}}}left( {{{\text{V}}_1} - {{\text{V}}_2}} \right)$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $${\text{D}}_1^2 - {\text{D}}_2^2 = \frac{{2{\text{q}}}}{{\text{g}}}left( {{{\text{V}}_2} - {{\text{V}}_1}} \right)$$                <\/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: $${\\text{D}}_1^2 &#8211; {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} &#8211; {{\\text{V}}_2}} \\right)$$<\/p>\n<p>The fundamental momentum equation for a hydraulic jump is a relationship between the depth of water upstream and downstream of the jump, the velocity of water upstream and downstream of the jump, and the discharge of water over the jump. The equation can be derived from the principle of conservation of momentum.<\/p>\n<p>The equation states that the change in the kinetic energy of the water is equal to the work done by the pressure forces on the water. The change in the kinetic energy of the water is given by:<\/p>\n<p>$$\\Delta K = \\frac{1}{2} \\left( {\\text{D}}_1^2{{\\text{V}}_1^2 &#8211; {\\text{D}}_2^2{{\\text{V}}_2^2} \\right)$$<\/p>\n<p>The work done by the pressure forces on the water is given by:<\/p>\n<p>$$W = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} &#8211; {{\\text{V}}_2}} \\right)$$<\/p>\n<p>where ${\\text{D}}_1$ and ${\\text{D}}_2$ are the depths of water upstream and downstream of the jump, respectively, ${\\text{V}}_1$ and ${\\text{V}}_2$ are the velocities of water upstream and downstream of the jump, respectively, and ${\\text{q}}$ is the discharge of water over the jump.<\/p>\n<p>Substituting the expression for the work done by the pressure forces on the water into the expression for 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> change in the kinetic energy of the water, we get:<\/p>\n<p>$$\\frac{1}{2} \\left( {\\text{D}}_1^2{{\\text{V}}_1^2 &#8211; {\\text{D}}_2^2{{\\text{V}}_2^2} \\right) = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} &#8211; {{\\text{V}}_2}} \\right)$$<\/p>\n<p>Simplifying the equation, we get:<\/p>\n<p>$${\\text{D}}_1^2 &#8211; {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} &#8211; {{\\text{V}}_2}} \\right)$$<\/p>\n<p>This is the fundamental momentum equation for a hydraulic jump.<\/p>\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>Fundamental momentum equation for a hydraulic jump, is A. $${\\text{D}}_1^2 - {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} - {{\\text{V}}_2}} \\right)$$ B. $${\\text{D}}_2^2 - {\\text{D}}_1^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} - {{\\text{V}}_2}} \\right)$$ C. $${\\text{D}}_1^2 - {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_2} - {{\\text{V}}_1}} \\right)$$ D. $${\\text{D}}_1^2 + {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_2} - {{\\text{V}}_1}} \\right)$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/fundamental-momentum-equation-for-a-hydraulic-jump-is-a-textd_12-textd_22-frac2textqtextgleft-textv_1-textv_2-right-b-textd\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fundamental momentum equation for a hydraulic jump, is A. $${\\text{D}}_1^2 - 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{{\\text{V}}_2}} \\right)$$ B. $${\\text{D}}_2^2 - {\\text{D}}_1^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_1} - {{\\text{V}}_2}} \\right)$$ C. $${\\text{D}}_1^2 - {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_2} - {{\\text{V}}_1}} \\right)$$ D. $${\\text{D}}_1^2 + {\\text{D}}_2^2 = \\frac{{2{\\text{q}}}}{{\\text{g}}}\\left( {{{\\text{V}}_2} - {{\\text{V}}_1}} \\right)$$","og_description":"Subscribe on YouTube","og_url":"https:\/\/exam.pscnotes.com\/mcq\/fundamental-momentum-equation-for-a-hydraulic-jump-is-a-textd_12-textd_22-frac2textqtextgleft-textv_1-textv_2-right-b-textd\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:46:51+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/fundamental-momentum-equation-for-a-hydraulic-jump-is-a-textd_12-textd_22-frac2textqtextgleft-textv_1-textv_2-right-b-textd\/","url":"https:\/\/exam.pscnotes.com\/mcq\/fundamental-momentum-equation-for-a-hydraulic-jump-is-a-textd_12-textd_22-frac2textqtextgleft-textv_1-textv_2-right-b-textd\/","name":"Fundamental momentum equation for a hydraulic jump, is A. $${\\text{D}}_1^2 - 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