Problem 45391. Calculate the sphericity of a Raschig ring

Created by Karl Ezra Pilario

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId1","target":"/media/image1.JPEG"}],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Sphericity is a measure of the roundness of any particle. It was defined by Wadell in 1935 as the ratio of the 'surface area of a sphere having the same volume as the given particle' to the 'surface area of the given particle'. By definition, the maximum value of sphericity is 1, which is that of a perfect sphere. The more elongated a particle is, the lesser its sphericity.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A Raschig ring is a common particle found in packed beds that are shaped like small pieces of a tube (see figure). As a hollow cylinder, it has a height H, inner radius R1, and outer radius R2. The sphericity of a Raschig ring is important to calculate as it can influence the performance of a packed bed for adsorption.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Make a function that takes three values: H, R1, and R2. Output the sphericity of this hollow cylinder rounded to 4 decimal places. You are ensured that:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>H, R1, and R2 are all positive integers</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>R1 &lt; R2</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>All inputs have consistent units; and</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>No input value exceeds 100.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"},{"partUri":"/media/image1.JPEG","contentType":"image/JPEG","content":"data:image/JPEG;base64,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"}]}

Sphericity is a measure of the roundness of any particle. It was defined by Wadell in 1935 as the ratio of the 'surface area of a sphere having the same volume as the given particle' to the 'surface area of the given particle'. By definition, the maximum value of sphericity is 1, which is that of a perfect sphere. The more elongated a particle is, the lesser its sphericity.A Raschig ring is a common particle found in packed beds that are shaped like small pieces of a tube (see figure). As a hollow cylinder, it has a height H, inner radius R1, and outer radius R2. The sphericity of a Raschig ring is important to calculate as it can influence the performance of a packed bed for adsorption.<img src = "https://upload.wikimedia.org/wikipedia/commons/thumb/4/4e/RaschigRings005.JPG/296px-RaschigRings005.JPG">Make a function that takes three values: H, R1, and R2. Output the sphericity of this hollow cylinder rounded to 4 decimal places. You are ensured that:<ul><li>H, R1, and R2 are all positive integers</li><li>R1 &lt; R2</li><li>All inputs have consistent units; and</li><li>No input value exceeds 100.</li></ul>

Sphericity is a measure of the roundness of any particle. It was defined by Wadell in 1935 as the ratio of the 'surface area of a sphere having the same volume as the given particle' to the 'surface area of the given particle'. By definition, the maximum value of sphericity is 1, which is that of a perfect sphere. The more elongated a particle is, the lesser its sphericity.

A Raschig ring is a common particle found in packed beds that are shaped like small pieces of a tube (see figure). As a hollow cylinder, it has a height H, inner radius R1, and outer radius R2. The sphericity of a Raschig ring is important to calculate as it can influence the performance of a packed bed for adsorption.

<<https://upload.wikimedia.org/wikipedia/commons/thumb/4/4e/RaschigRings005.JPG/296px-RaschigRings005.JPG>> 
 
Make a function that takes three values: H, R1, and R2. Output the sphericity of this hollow cylinder rounded to 4 decimal places. You are ensured that:

* H, R1, and R2 are all positive integers
* R1 < R2
* All inputs have consistent units; and 
* No input value exceeds 100.

Solve

Solution Stats

268 Solutions
61 Solvers

Last Solution submitted on Sep 09, 2021

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Nikolaos Nikolaou on 3 Apr 2020

Please clarify : Outside surface of a tube or the inner on aswell
Volume of the entire tube or minus the hollow part

Karl Ezra Pilario on 3 Apr 2020

For surface area: Both inner + outer are included. For volume: subtract the hollow part.

mahesh kumar on 29 Aug 2021

Also include small rings on either side.

Problem Recent Solvers61

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!