{"id":206731,"date":"2025-04-08T07:54:22","date_gmt":"2025-04-08T07:54:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=206731"},"modified":"2025-04-08T07:54:24","modified_gmt":"2025-04-08T07:54:24","slug":"steam-flows-through-a-turbine-stage-at-the-rate-of-4-500-kg-h","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/08\/steam-flows-through-a-turbine-stage-at-the-rate-of-4-500-kg-h\/","title":{"rendered":"Steam flows through a turbine stage at the rate of 4 500 kg\/h"},"content":{"rendered":"\n<p>Steam flows through a turbine stage at the rate of 4 500 kg\/h. The steam velocities at inlet and outlet are 15 m\/s and 180 m\/s respectively. The rate of heat energy flow from the turbine casing to the surroundings is 23 kJ\/kg of steam flowing. If specific enthalpy of the steam decreases by 420 kJ\/kg in passing through the turbine stage. Calculate the power developed. (476 kW)<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To calculate the power developed by the steam turbine, we need to apply the First Law of Thermodynamics and incorporate the given data: mass flow rate, velocity, heat loss, and change in enthalpy. We will use the energy equation for a control volume:<\/p>\n\n\n\n<p>[<br>\\text{Power} = \\frac{\\dot{m}}{1000} \\times (\\Delta h + \\Delta KE + \\text{Heat loss})<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\dot{m} ) = mass flow rate (kg\/s)<\/li>\n\n\n\n<li>( \\Delta h ) = change in specific enthalpy (kJ\/kg)<\/li>\n\n\n\n<li>( \\Delta KE ) = change in kinetic energy (kJ\/kg)<\/li>\n\n\n\n<li>Heat loss = heat energy lost to surroundings (kJ\/kg)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Convert Mass Flow Rate<\/h3>\n\n\n\n<p>The mass flow rate is given as 4,500 kg\/h. First, convert this to kg\/s:<\/p>\n\n\n\n<p>[<br>\\dot{m} = \\frac{4500}{3600} = 1.25 \\, \\text{kg\/s}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Change in Enthalpy (( \\Delta h ))<\/h3>\n\n\n\n<p>The problem states that the specific enthalpy of the steam decreases by 420 kJ\/kg. Thus, ( \\Delta h = -420 \\, \\text{kJ\/kg} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Change in Kinetic Energy (( \\Delta KE ))<\/h3>\n\n\n\n<p>The change in kinetic energy per unit mass of the steam can be calculated using the equation for kinetic energy:<\/p>\n\n\n\n<p>[<br>\\Delta KE = \\frac{v_2^2 &#8211; v_1^2}{2}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( v_2 = 180 \\, \\text{m\/s} ) (outlet velocity)<\/li>\n\n\n\n<li>( v_1 = 15 \\, \\text{m\/s} ) (inlet velocity)<\/li>\n<\/ul>\n\n\n\n<p>Substitute the velocities into the equation:<\/p>\n\n\n\n<p>[<br>\\Delta KE = \\frac{180^2 &#8211; 15^2}{2} = \\frac{32400 &#8211; 225}{2} = \\frac{32175}{2} = 16,587.5 \\, \\text{J\/kg} = 16.59 \\, \\text{kJ\/kg}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Heat Loss to Surroundings<\/h3>\n\n\n\n<p>The heat loss is given as 23 kJ\/kg.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Total Energy per Unit Mass<\/h3>\n\n\n\n<p>The total energy per unit mass of steam is the sum of the enthalpy change, kinetic energy change, and heat loss:<\/p>\n\n\n\n<p>[<br>\\Delta E = \\Delta h + \\Delta KE + \\text{Heat loss} = -420 + 16.59 + 23 = -380.41 \\, \\text{kJ\/kg}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 6: Power Developed<\/h3>\n\n\n\n<p>Now, calculate the power developed by multiplying the total energy change per unit mass by the mass flow rate and converting from kJ\/s to kW:<\/p>\n\n\n\n<p>[<br>\\text{Power} = \\dot{m} \\times \\Delta E = 1.25 \\times (-380.41) = -475.51 \\, \\text{kW}<br>]<\/p>\n\n\n\n<p>Since the negative sign indicates energy output, the magnitude of power developed by the turbine is:<\/p>\n\n\n\n<p>[<br>\\text{Power} = 476 \\, \\text{kW}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The power developed by the turbine is 476 kW. This value represents the mechanical power extracted from the steam, considering the heat loss and changes in velocity and enthalpy.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/04\/image-53.png\" alt=\"\" class=\"wp-image-206732\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Steam flows through a turbine stage at the rate of 4 500 kg\/h. The steam velocities at inlet and outlet are 15 m\/s and 180 m\/s respectively. The rate of heat energy flow from the turbine casing to the surroundings is 23 kJ\/kg of steam flowing. If specific enthalpy of the steam decreases by 420 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-206731","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206731","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=206731"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206731\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}