Volume Flow Rates In Physics Problems Article

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{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T07:27:56+00:00","modifiedTime":"2016-03-26T07:27:56+00:00","timestamp":"2022-09-14T17:49:50+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"Volume Flow Rates in Physics Problems","strippedTitle":"volume flow rates in physics problems","slug":"volume-flow-rates-in-physics-problems","canonicalUrl":"","seo":{"metaDescription":"Using physics, you can determine how the flow rate of a liquid is affected by cross-sectional area. For example, using the equation of continuity, given the flo","noIndex":0,"noFollow":0},"content":"<p>Using physics, you can determine how the flow rate of a liquid is affected by cross-sectional area. For example, using the equation of continuity, given the flow rate and cross-sectional area of the opening to a water hose, you can calculate the speed at which the water exits the hose.</p>\n<p>Here are some practice questions that you can try.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">Water travels through a hose at 0.8 meters per second. If the cross-sectional area of the exit nozzle is one-fifth that of the hose, at what speed does water exit the hose?</p>\n </li>\n <li><p class=\"first-para\">You are watching leaves float past you in a stream that is 0.76 meters wide. At one point, you estimate that the speed of the leaves triples. If the stream has a constant depth, what is the width of the stream at this point?</p>\n </li>\n <li><p class=\"first-para\">The volume flow rate through pipe 1 is 2.5 times that of pipe 2. If the cross-sectional area of pipe 1 is one-half that of pipe 2, what is the ratio of the flow speed in pipe 1 to that in pipe 2?</p>\n </li>\n <li><p class=\"first-para\">If the water that exits a pipe fills a pool that is 3 meters deep, 20 meters long, and 5 meters wide in 3 days, what is the flow rate?</p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers</h2>\n<p>The following are the answers to the practice questions:</p>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">4.0 m/s</p>\n<p class=\"child-para\">Use the equation of continuity: </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490719.image0.png\" height=\"24\" alt=\"image0.png\" width=\"80\"/>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490720.image1.png\" height=\"40\" alt=\"image1.png\" width=\"64\"/>\n<p class=\"child-para\">and that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490721.image2.png\" height=\"24\" alt=\"image2.png\" width=\"188\"/>\n<p class=\"child-para\">Solve the continuity equation for </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490722.image3.png\" height=\"176\" alt=\"image3.png\" width=\"127\"/>\n </li>\n <li><p class=\"first-para\">0.25 m</p>\n<p class=\"child-para\">Use the equation of continuity:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490723.image4.png\" height=\"24\" alt=\"image4.png\" width=\"80\"/>\n<p class=\"child-para\">In terms of the stream width </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490724.image5.png\" height=\"15\" alt=\"image5.png\" width=\"16\"/>\n<p class=\"child-para\">and depth <i>d,</i> the cross-sectional area of the stream is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490725.image6.png\" height=\"17\" alt=\"image6.png\" width=\"49\"/>\n<p class=\"child-para\">Use this in the continuity equation:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490726.image7.png\" height=\"80\" alt=\"image7.png\" width=\"101\"/>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490727.image8.png\" height=\"24\" alt=\"image8.png\" width=\"57\"/>\n<p class=\"child-para\">so you can solve the continuity equation for the width </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490728.image9.png\" height=\"197\" alt=\"image9.png\" width=\"116\"/>\n </li>\n <li><p class=\"first-para\">5.0</p>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490729.image10.png\" height=\"24\" alt=\"image10.png\" width=\"192\"/>\n<p class=\"child-para\">are the volume flow rate through pipes 1 and 2, respectively. In terms of cross-sectional area and flow speed, the volume flow rate is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490730.image11.png\" height=\"20\" alt=\"image11.png\" width=\"49\"/>\n<p class=\"child-para\">When combined with the previous equation, you get</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490731.image12.png\" height=\"51\" alt=\"image12.png\" width=\"100\"/>\n<p class=\"child-para\">You also know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490732.image13.png\" height=\"40\" alt=\"image13.png\" width=\"64\"/>\n<p class=\"child-para\">Combine these equations to find</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490733.image14.png\" height=\"115\" alt=\"image14.png\" width=\"125\"/>\n </li>\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490734.image15.png\" height=\"27\" alt=\"image15.png\" width=\"105\"/>\n<p class=\"child-para\">Flow rate is the volume of fluid moving past a point per unit time. The volume of fluid that enters the pool is</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490735.image16.png\" height=\"40\" alt=\"image16.png\" width=\"163\"/>\n<p class=\"child-para\">The time it takes for this volume of water to enter the pool is</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490736.image17.png\" height=\"75\" alt=\"image17.png\" width=\"160\"/>\n<p class=\"child-para\">The volume flow rate is therefore</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490737.image18.png\" height=\"128\" alt=\"image18.png\" width=\"131\"/>\n </li>\n</ol>","description":"<p>Using physics, you can determine how the flow rate of a liquid is affected by cross-sectional area. For example, using the equation of continuity, given the flow rate and cross-sectional area of the opening to a water hose, you can calculate the speed at which the water exits the hose.</p>\n<p>Here are some practice questions that you can try.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">Water travels through a hose at 0.8 meters per second. If the cross-sectional area of the exit nozzle is one-fifth that of the hose, at what speed does water exit the hose?</p>\n </li>\n <li><p class=\"first-para\">You are watching leaves float past you in a stream that is 0.76 meters wide. At one point, you estimate that the speed of the leaves triples. If the stream has a constant depth, what is the width of the stream at this point?</p>\n </li>\n <li><p class=\"first-para\">The volume flow rate through pipe 1 is 2.5 times that of pipe 2. If the cross-sectional area of pipe 1 is one-half that of pipe 2, what is the ratio of the flow speed in pipe 1 to that in pipe 2?</p>\n </li>\n <li><p class=\"first-para\">If the water that exits a pipe fills a pool that is 3 meters deep, 20 meters long, and 5 meters wide in 3 days, what is the flow rate?</p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers</h2>\n<p>The following are the answers to the practice questions:</p>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">4.0 m/s</p>\n<p class=\"child-para\">Use the equation of continuity: </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490719.image0.png\" height=\"24\" alt=\"image0.png\" width=\"80\"/>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490720.image1.png\" height=\"40\" alt=\"image1.png\" width=\"64\"/>\n<p class=\"child-para\">and that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490721.image2.png\" height=\"24\" alt=\"image2.png\" width=\"188\"/>\n<p class=\"child-para\">Solve the continuity equation for </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490722.image3.png\" height=\"176\" alt=\"image3.png\" width=\"127\"/>\n </li>\n <li><p class=\"first-para\">0.25 m</p>\n<p class=\"child-para\">Use the equation of continuity:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490723.image4.png\" height=\"24\" alt=\"image4.png\" width=\"80\"/>\n<p class=\"child-para\">In terms of the stream width </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490724.image5.png\" height=\"15\" alt=\"image5.png\" width=\"16\"/>\n<p class=\"child-para\">and depth <i>d,</i> the cross-sectional area of the stream is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490725.image6.png\" height=\"17\" alt=\"image6.png\" width=\"49\"/>\n<p class=\"child-para\">Use this in the continuity equation:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490726.image7.png\" height=\"80\" alt=\"image7.png\" width=\"101\"/>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490727.image8.png\" height=\"24\" alt=\"image8.png\" width=\"57\"/>\n<p class=\"child-para\">so you can solve the continuity equation for the width </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490728.image9.png\" height=\"197\" alt=\"image9.png\" width=\"116\"/>\n </li>\n <li><p class=\"first-para\">5.0</p>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490729.image10.png\" height=\"24\" alt=\"image10.png\" width=\"192\"/>\n<p class=\"child-para\">are the volume flow rate through pipes 1 and 2, respectively. In terms of cross-sectional area and flow speed, the volume flow rate is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490730.image11.png\" height=\"20\" alt=\"image11.png\" width=\"49\"/>\n<p class=\"child-para\">When combined with the previous equation, you get</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490731.image12.png\" height=\"51\" alt=\"image12.png\" width=\"100\"/>\n<p class=\"child-para\">You also know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490732.image13.png\" height=\"40\" alt=\"image13.png\" width=\"64\"/>\n<p class=\"child-para\">Combine these equations to find</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490733.image14.png\" height=\"115\" alt=\"image14.png\" width=\"125\"/>\n </li>\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490734.image15.png\" height=\"27\" alt=\"image15.png\" width=\"105\"/>\n<p class=\"child-para\">Flow rate is the volume of fluid moving past a point per unit time. The volume of fluid that enters the pool is</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490735.image16.png\" height=\"40\" alt=\"image16.png\" width=\"163\"/>\n<p class=\"child-para\">The time it takes for this volume of water to enter the pool is</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490736.image17.png\" height=\"75\" alt=\"image17.png\" width=\"160\"/>\n<p class=\"child-para\">The volume flow rate is therefore</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/490737.image18.png\" height=\"128\" alt=\"image18.png\" width=\"131\"/>\n </li>\n</ol>","blurb":"","authors":[{"authorId":8947,"name":"The Experts at Dummies","slug":"the-experts-at-dummies","description":"The Experts at Dummies are smart, friendly people who make learning easy by taking a not-so-serious approach to serious stuff.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8947"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":207542,"title":"Physics I: 501 Practice Problems For Dummies Cheat Sheet","slug":"physics-i-practice-problems-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207542"}},{"articleId":144633,"title":"Solving Force Problems in Physics by Using Free-Body 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Volume Flow Rates in Physics ProblemsBy: The Experts at Dummies and Updated: 03-26-2016 From The Book: Physics I: 501 Practice Problems For Dummies (+ Free Online Practice)

Physics I: 501 Practice Problems For Dummies (+ Free Online Practice)

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Using physics, you can determine how the flow rate of a liquid is affected by cross-sectional area. For example, using the equation of continuity, given the flow rate and cross-sectional area of the opening to a water hose, you can calculate the speed at which the water exits the hose.

Here are some practice questions that you can try.

Practice questions

Water travels through a hose at 0.8 meters per second. If the cross-sectional area of the exit nozzle is one-fifth that of the hose, at what speed does water exit the hose?
You are watching leaves float past you in a stream that is 0.76 meters wide. At one point, you estimate that the speed of the leaves triples. If the stream has a constant depth, what is the width of the stream at this point?
The volume flow rate through pipe 1 is 2.5 times that of pipe 2. If the cross-sectional area of pipe 1 is one-half that of pipe 2, what is the ratio of the flow speed in pipe 1 to that in pipe 2?
If the water that exits a pipe fills a pool that is 3 meters deep, 20 meters long, and 5 meters wide in 3 days, what is the flow rate?

Answers

The following are the answers to the practice questions:

4.0 m/s

Use the equation of continuity:

You know that

and that

Solve the continuity equation for
0.25 m

Use the equation of continuity:

In terms of the stream width

and depth d, the cross-sectional area of the stream is

Use this in the continuity equation:

You know that

so you can solve the continuity equation for the width
5.0

You know that

are the volume flow rate through pipes 1 and 2, respectively. In terms of cross-sectional area and flow speed, the volume flow rate is

When combined with the previous equation, you get

You also know that

Combine these equations to find
Flow rate is the volume of fluid moving past a point per unit time. The volume of fluid that enters the pool is

The time it takes for this volume of water to enter the pool is

The volume flow rate is therefore