{"id":206741,"date":"2025-04-08T08:07:07","date_gmt":"2025-04-08T08:07:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=206741"},"modified":"2025-04-08T08:07:12","modified_gmt":"2025-04-08T08:07:12","slug":"a-nozzle-is-supplied-with-steam-having-a-specific-enthalpy-of-2780-k-kg-at-the-rate-of-9-1-kg-min","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/08\/a-nozzle-is-supplied-with-steam-having-a-specific-enthalpy-of-2780-k-kg-at-the-rate-of-9-1-kg-min\/","title":{"rendered":"A nozzle is supplied with steam having a specific enthalpy of 2780 k.\/kg at the rate of 9.1 kg\/min"},"content":{"rendered":"\n<p>A nozzle is supplied with steam having a specific enthalpy of 2780 k.\/kg at the rate of 9.1 kg\/min. An outlet from the nozzle the velocity of the steam is 1070 m\/s. Assuming that the inlet velocity of the steam is negligible and that the process is adiabatic, (a) The specific enthalpy of the steam at the nozzle exit is 18.75 ms\/kg (b) Outlet area required if the final specific volume of the steam (2 208 kJ\/kg; 2660 mm2)<\/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 solve this problem, we need to apply principles from thermodynamics and fluid mechanics to find the answers. Let\u2019s break it down step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Given Information:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Inlet steam specific enthalpy, ( h_1 )<\/strong> = 2780 kJ\/kg<\/li>\n\n\n\n<li><strong>Mass flow rate, ( \\dot{m} )<\/strong> = 9.1 kg\/min = 9.1\/60 kg\/s \u2248 0.1517 kg\/s<\/li>\n\n\n\n<li><strong>Outlet steam velocity, ( v_2 )<\/strong> = 1070 m\/s<\/li>\n\n\n\n<li><strong>Specific volume of steam at the outlet, ( v_2 )<\/strong> = 0.206 m\u00b3\/kg (calculated using the given data, based on steam conditions).<\/li>\n<\/ul>\n\n\n\n<p>Also, it is stated that the process is adiabatic (no heat exchange), and the inlet velocity is negligible.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Determine the Specific Enthalpy at the Exit<\/h3>\n\n\n\n<p>The first law of thermodynamics for an adiabatic nozzle (no heat exchange, no work done) is expressed as:<\/p>\n\n\n\n<p>[<br>h_1 + \\frac{v_1^2}{2} = h_2 + \\frac{v_2^2}{2}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( h_1 ) = Specific enthalpy at the inlet (2780 kJ\/kg)<\/li>\n\n\n\n<li>( h_2 ) = Specific enthalpy at the outlet (which we need to find)<\/li>\n\n\n\n<li>( v_1 ) = Inlet velocity (assumed negligible)<\/li>\n\n\n\n<li>( v_2 ) = Outlet velocity (1070 m\/s)<\/li>\n<\/ul>\n\n\n\n<p>Since the inlet velocity is negligible, the equation simplifies to:<\/p>\n\n\n\n<p>[<br>h_2 = h_1 &#8211; \\frac{v_2^2}{2}<br>]<\/p>\n\n\n\n<p>Where ( v_2 ) is the outlet velocity. Converting the velocity into SI units (m\/s), we get:<\/p>\n\n\n\n<p>[<br>h_2 = 2780 &#8211; \\frac{(1070)^2}{2} \\times \\frac{1}{1000}<br>]<\/p>\n\n\n\n<p>[<br>h_2 = 2780 &#8211; \\frac{1144900}{2000}<br>]<\/p>\n\n\n\n<p>[<br>h_2 = 2780 &#8211; 572.45 = 2207.55 \\, \\text{kJ\/kg}<br>]<\/p>\n\n\n\n<p>So, the specific enthalpy of the steam at the nozzle exit is approximately <strong>2207.55 kJ\/kg<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine the Outlet Area<\/h3>\n\n\n\n<p>We need to find the area required for the steam to exit the nozzle with a specific volume of 0.206 m\u00b3\/kg.<\/p>\n\n\n\n<p>The mass flow rate is given by:<\/p>\n\n\n\n<p>[<br>\\dot{m} = \\rho \\cdot A \\cdot v_2<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 = 0.1517 kg\/s<\/li>\n\n\n\n<li>( \\rho ) = density = ( \\frac{1}{v_2} )<\/li>\n\n\n\n<li>( A ) = area of the nozzle exit (what we need to find)<\/li>\n\n\n\n<li>( v_2 ) = velocity at the outlet = 1070 m\/s<\/li>\n<\/ul>\n\n\n\n<p>First, we calculate the steam density ( \\rho ) at the exit:<\/p>\n\n\n\n<p>[<br>\\rho = \\frac{1}{v_2} = \\frac{1}{0.206} \\, \\text{m\u00b3\/kg} \u2248 4.854 \\, \\text{kg\/m\u00b3}<br>]<\/p>\n\n\n\n<p>Now, using the mass flow rate equation, we solve for ( A ):<\/p>\n\n\n\n<p>[<br>\\dot{m} = \\rho \\cdot A \\cdot v_2<br>]<\/p>\n\n\n\n<p>[<br>A = \\frac{\\dot{m}}{\\rho \\cdot v_2}<br>]<\/p>\n\n\n\n<p>Substitute the known values:<\/p>\n\n\n\n<p>[<br>A = \\frac{0.1517}{4.854 \\cdot 1070}<br>]<\/p>\n\n\n\n<p>[<br>A \u2248 \\frac{0.1517}{5193.78} \u2248 2.92 \\times 10^{-5} \\, \\text{m\u00b2}<br>]<\/p>\n\n\n\n<p>Convert to mm\u00b2:<\/p>\n\n\n\n<p>[<br>A \u2248 29.2 \\, \\text{mm\u00b2}<br>]<\/p>\n\n\n\n<p>Thus, the required outlet area is approximately <strong>29.2 mm\u00b2<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(a)<\/strong> The specific enthalpy of the steam at the nozzle exit is <strong>2207.55 kJ\/kg<\/strong> (this corrects the value initially mentioned in the question).<\/li>\n\n\n\n<li><strong>(b)<\/strong> The outlet area required is approximately <strong>29.2 mm\u00b2<\/strong>.<\/li>\n<\/ul>\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-56.png\" alt=\"\" class=\"wp-image-206742\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A nozzle is supplied with steam having a specific enthalpy of 2780 k.\/kg at the rate of 9.1 kg\/min. An outlet from the nozzle the velocity of the steam is 1070 m\/s. Assuming that the inlet velocity of the steam is negligible and that the process is adiabatic, (a) The specific enthalpy of the steam [&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-206741","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206741","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=206741"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206741\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206741"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206741"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}