{"id":215841,"date":"2025-05-18T02:46:13","date_gmt":"2025-05-18T02:46:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=215841"},"modified":"2025-05-18T02:46:15","modified_gmt":"2025-05-18T02:46:15","slug":"convert-a-volume-flow-rate-of-3-0-gal-min-to-m3-s-6-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/18\/convert-a-volume-flow-rate-of-3-0-gal-min-to-m3-s-6-2\/","title":{"rendered":"\u00a0Convert a volume flow rate of 3.0 gal\/min to m3\/s. 6.2"},"content":{"rendered":"\n

\u00a0Convert a volume flow rate of 3.0 gal\/min to m3<\/sup>\/s. 6.2 Convert 459 gal\/min to m3<\/sup>\/s. 6.27 A small metering pump delivers 11.4 gal of a water treatment chemical per 24 h. Express this flow rate in ft3<\/sup>\/s. 6.28 A small metering pump delivers 19.5 mL\/min of water to dilute a waste stream. Express this flow rate in m3<\/sup>\/s. 6.30 Oil for a hydraulic system (sg = 0.90) is flowing at 2.35 x 10-3<\/sup>\u00a0m3<\/sup>\/s. Calculate the weight flow rate and mass flow rate. 6.36 If a pump removes 1.65 gal\/min of water from a tank, how long will it take to empty the tank if it contains 7425 lb of water? The specific weight and density of water needed in problem #30 are 9.81 kN\/m3<\/sup>\u00a0and 1000 kg\/m3<\/sup>, respectively.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s go through each problem step-by-step with correct unit conversions and explanations<\/strong>. Then I\u2019ll provide a 300-word explanation at the end<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

6.2 Convert 3.0 gal\/min to m\u00b3\/s<\/strong><\/h3>\n\n\n\n

Conversion factors<\/strong>:<\/p>\n\n\n\n

3.0\u2009gal\/min=3.0\u00d73.78541\u00d710\u2212360=1.89\u00d710\u22124\u2009m3\/s3.0 \\, \\text{gal\/min} = 3.0 \\times \\frac{3.78541 \\times 10^{-3}}{60} = 1.89 \\times 10^{-4} \\, \\text{m}^3\/\\text{s}<\/p>\n\n\n\n

\n\n\n\n

6.2 (again?) Convert 459 gal\/min to m\u00b3\/s<\/strong><\/h3>\n\n\n\n

459\u2009gal\/min=459\u00d73.78541\u00d710\u2212360=2.89\u00d710\u22122\u2009m3\/s459 \\, \\text{gal\/min} = 459 \\times \\frac{3.78541 \\times 10^{-3}}{60} = 2.89 \\times 10^{-2} \\, \\text{m}^3\/\\text{s}<\/p>\n\n\n\n

\n\n\n\n

6.27 Convert 11.4 gal\/24h to ft\u00b3\/s<\/strong><\/h3>\n\n\n\n

Conversions<\/strong>:<\/p>\n\n\n\n

    \n
  • 1 gallon = 0.133681 ft\u00b3<\/li>\n<\/ul>\n\n\n\n

    11.4\u00d70.13368186400=1.76\u00d710\u22125\u2009ft3\/s\\frac{11.4 \\times 0.133681}{86400} = 1.76 \\times 10^{-5} \\, \\text{ft}^3\/\\text{s}<\/p>\n\n\n\n

    \n\n\n\n

    6.28 Convert 19.5 mL\/min to m\u00b3\/s<\/strong><\/h3>\n\n\n\n

    Conversions<\/strong>:<\/p>\n\n\n\n

    19.5\u00d71\u00d710\u2212660=3.25\u00d710\u22127\u2009m3\/s19.5 \\times \\frac{1 \\times 10^{-6}}{60} = 3.25 \\times 10^{-7} \\, \\text{m}^3\/\\text{s}<\/p>\n\n\n\n

    \n\n\n\n

    6.30 Oil flow rate: 2.35 \u00d7 10\u207b\u00b3 m\u00b3\/s, sg = 0.90<\/strong><\/h3>\n\n\n\n
      \n
    • Density of water<\/strong> = 1000 kg\/m\u00b3 \u2192 Oil density = 0.90 \u00d7 1000 = 900 kg\/m\u00b3<\/li>\n<\/ul>\n\n\n\n

      Mass flow rate<\/strong>: m\u02d9=900\u2009kg\/m3\u00d72.35\u00d710\u22123=2.115\u2009kg\/s\\dot{m} = 900 \\, \\text{kg\/m}^3 \\times 2.35 \\times 10^{-3} = 2.115 \\, \\text{kg\/s}<\/p>\n\n\n\n

      Weight flow rate<\/strong>: W\u02d9=8.829\u2009kN\/m3\u00d72.35\u00d710\u22123=0.02075\u2009kN\/s\\dot{W} = 8.829 \\, \\text{kN\/m}^3 \\times 2.35 \\times 10^{-3} = 0.02075 \\, \\text{kN\/s}<\/p>\n\n\n\n

      \n\n\n\n

      6.36 Pump removes 1.65 gal\/min of water from a tank with 7425 lb<\/strong><\/h3>\n\n\n\n

      Convert gal\/min to lb\/min<\/strong>:<\/p>\n\n\n\n

        \n
      • 1 gallon of water \u2248 8.34 lb<\/li>\n<\/ul>\n\n\n\n

        1.65\u2009gal\/min\u00d78.34\u2009lb\/gal=13.761\u2009lb\/min1.65 \\, \\text{gal\/min} \\times 8.34 \\, \\text{lb\/gal} = 13.761 \\, \\text{lb\/min}<\/p>\n\n\n\n

        Now divide total mass by flow rate: 742513.761=539.4\u2009minutes\u22488.99\u2009hours\\frac{7425}{13.761} = 539.4 \\, \\text{minutes} \\approx 8.99 \\, \\text{hours}<\/p>\n\n\n\n

        \n\n\n\n

        300-Word Explanation<\/strong><\/h2>\n\n\n\n

        In engineering, converting between various units of flow\u2014whether it’s volume<\/strong>, mass<\/strong>, or weight flow rate<\/strong>\u2014is crucial for understanding system behavior and ensuring compatibility between equipment.<\/p>\n\n\n\n

        For volumetric flow rates, gallons per minute (gal\/min) must often be converted into cubic meters per second (m\u00b3\/s) for SI unit consistency. Since 1 gallon equals 3.78541 \u00d7 10\u207b\u00b3 m\u00b3 and 1 minute equals 60 seconds, we divide accordingly to get flow rates like 1.89 \u00d7 10\u207b\u2074 m\u00b3\/s<\/strong> for a 3.0 gal\/min flow.<\/p>\n\n\n\n

        In problem 6.27, converting daily gallon use into cubic feet per second requires attention to both volume (gallons to ft\u00b3) and time (24 hours = 86,400 seconds). Accurate conversions like 1.76 \u00d7 10\u207b\u2075 ft\u00b3\/s<\/strong> help estimate chemical dosing properly.<\/p>\n\n\n\n

        For mass and weight flow rates (problem 6.30), we apply the specific gravity<\/strong> (sg) to find density, and multiply it by volumetric flow to get the mass flow rate<\/strong> (kg\/s). Weight flow rate (kN\/s) uses specific weight (N\/m\u00b3), which is the product of specific gravity and gravitational acceleration (9.81 m\/s\u00b2).<\/p>\n\n\n\n

        Finally, problem 6.36 combines mass and volumetric flow rates. Since the pump removes a volume flow (1.65 gal\/min), we convert that to mass using the density of water (~8.34 lb\/gal). The total mass of water (7425 lb) divided by flow rate (13.761 lb\/min) gives the time to empty the tank\u2014about 539 minutes or 9 hours<\/strong>.<\/p>\n\n\n\n

        Understanding and converting these units accurately ensures engineers make correct system designs and avoid operational errors.<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u00a0Convert a volume flow rate of 3.0 gal\/min to m3\/s. 6.2 Convert 459 gal\/min to m3\/s. 6.27 A small metering pump delivers 11.4 gal of a water treatment chemical per 24 h. Express this flow rate in ft3\/s. 6.28 A small metering pump delivers 19.5 mL\/min of water to dilute a waste stream. Express this […]<\/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-215841","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215841","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=215841"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215841\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=215841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=215841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=215841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}