{"id":46241,"date":"2025-07-02T02:16:11","date_gmt":"2025-07-02T02:16:11","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=46241"},"modified":"2025-07-02T02:16:12","modified_gmt":"2025-07-02T02:16:12","slug":"in-a-filled-fluid-container-the-system-mass-is-0-41-slugs","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/in-a-filled-fluid-container-the-system-mass-is-0-41-slugs\/","title":{"rendered":"In a filled fluid container, the system&#8217;$ mass is 0.41 slugs."},"content":{"rendered":"\n<p>. In a filled fluid container, the system&#8217;$ mass is 0.41 slugs. Its density is 30 Ibm\/ft? &amp; g-31.5 fps?. Find (a) specific volume (b) the total volume<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to understand the relationship between mass, density, and volume. The formula for specific volume (vvv) is:v=1\u03c1v = \\frac{1}{\\rho}v=\u03c11\u200b<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>vvv is the specific volume,<\/li>\n\n\n\n<li>\u03c1\\rho\u03c1 is the density.<\/li>\n<\/ul>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass m=0.41\u2009slugsm = 0.41 \\, \\text{slugs}m=0.41slugs,<\/li>\n\n\n\n<li>Density \u03c1=30\u2009lbm\/ft3\\rho = 30 \\, \\text{lbm\/ft}^3\u03c1=30lbm\/ft3,<\/li>\n\n\n\n<li>Gravitational acceleration g=31.5\u2009fps2g = 31.5 \\, \\text{fps}^2g=31.5fps2.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Part (a) Specific Volume<\/h3>\n\n\n\n<p>The specific volume is the volume occupied by a unit mass of the substance. We calculate it by using the given density.<\/p>\n\n\n\n<p>Since the mass is in slugs and the density is given in lbm\/ft\u00b3, we first need to convert the units of mass into lbm. We know that:1\u2009slug=32.174\u2009lbm.1 \\, \\text{slug} = 32.174 \\, \\text{lbm}.1slug=32.174lbm.<\/p>\n\n\n\n<p>So:m=0.41\u2009slugs\u00d732.174\u2009lbm\/slug=13.2\u2009lbm.m = 0.41 \\, \\text{slugs} \\times 32.174 \\, \\text{lbm\/slug} = 13.2 \\, \\text{lbm}.m=0.41slugs\u00d732.174lbm\/slug=13.2lbm.<\/p>\n\n\n\n<p>Now, we can calculate the specific volume. We use the formula:v=VolumeMass=1\u03c1=130\u2009lbm\/ft3=0.0333\u2009ft3\/lbm.v = \\frac{\\text{Volume}}{\\text{Mass}} = \\frac{1}{\\rho} = \\frac{1}{30 \\, \\text{lbm\/ft}^3} = 0.0333 \\, \\text{ft}^3\/\\text{lbm}.v=MassVolume\u200b=\u03c11\u200b=30lbm\/ft31\u200b=0.0333ft3\/lbm.<\/p>\n\n\n\n<p>Thus, the <strong>specific volume<\/strong> of the system is 0.0333\u2009ft3\/lbm0.0333 \\, \\text{ft}^3\/\\text{lbm}0.0333ft3\/lbm.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part (b) Total Volume<\/h3>\n\n\n\n<p>To find the total volume (VVV) of the system, we can use the formula:V=v\u00d7m.V = v \\times m.V=v\u00d7m.<\/p>\n\n\n\n<p>Substitute the values for specific volume and mass:V=0.0333\u2009ft3\/lbm\u00d713.2\u2009lbm=0.44\u2009ft3.V = 0.0333 \\, \\text{ft}^3\/\\text{lbm} \\times 13.2 \\, \\text{lbm} = 0.44 \\, \\text{ft}^3.V=0.0333ft3\/lbm\u00d713.2lbm=0.44ft3.<\/p>\n\n\n\n<p>Thus, the <strong>total volume<\/strong> of the system is 0.44\u2009ft30.44 \\, \\text{ft}^30.44ft3.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>specific volume<\/strong> tells us how much space one unit mass (1 lbm) occupies. It is inversely related to density: the higher the density, the lower the specific volume.<\/li>\n\n\n\n<li>The <strong>total volume<\/strong> is simply the product of the specific volume and the total mass of the system.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-134.jpeg\" alt=\"\" class=\"wp-image-46242\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-134.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-134-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-134-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-134-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>. In a filled fluid container, the system&#8217;$ mass is 0.41 slugs. Its density is 30 Ibm\/ft? &amp; g-31.5 fps?. Find (a) specific volume (b) the total volume The Correct Answer and Explanation is: To solve this problem, we need to understand the relationship between mass, density, and volume. The formula for specific volume (vvv) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-46241","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=46241"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46241\/revisions"}],"predecessor-version":[{"id":46243,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46241\/revisions\/46243"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=46241"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=46241"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=46241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}