Problem 45413. Characterize fluid flow in a pipe as to laminar or turbulent

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":[],"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>In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Hence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>Re</w:t></w:r><w:r><w:t>. For a fluid flowing inside a circular pipe,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>Re</w:t></w:r><w:r><w:t> is computed as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Re = D x v x rho / mu\n where:\n D = inside diameter of the pipe [m]\n v = mean flow velocity [m/s]\n rho = fluid density [kg/m^3]\n mu = fluid viscosity [Pa.s] or [kg/m/s]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Note: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>We can then adopt the following rule: If</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>Re</w:t></w:r><w:r><w:t> &lt; 2300, the flow is laminar; if</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>Re</w:t></w:r><w:r><w:t> &gt; 2900, the flow is turbulent; otherwise, the flow is in transition.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>D</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>v</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>rho</w:t></w:r><w:r><w:t>, and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>mu</w:t></w:r><w:r><w:t> in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>See sample test cases:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[>> flow_pattern([0.02 0.1 1000 8.9e-4])\nans =\n 'LAMINAR'\n>> flow_pattern([0.02 0.5 1000 8.9e-4])\nans =\n 'TURBULENT'\n>> flow_pattern([0.02 0.1 1200 8.9e-4])\nans =\n 'TRANSITION']]></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>"}]}

In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.Hence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, Re. For a fluid flowing inside a circular pipe, Re is computed as follows:<pre class="language-matlab">Re = D x v x rho / mu
 where:
 D = inside diameter of the pipe [m]
 v = mean flow velocity [m/s]
 rho = fluid density [kg/m^3]
 mu = fluid viscosity [Pa.s] or [kg/m/s]
</pre>Note: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.We can then adopt the following rule: If Re &lt; 2300, the flow is laminar; if Re &gt; 2900, the flow is turbulent; otherwise, the flow is in transition.Write a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of <tt>D</tt>, <tt>v</tt>, <tt>rho</tt>, and <tt>mu</tt> in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.See sample test cases:<pre class="language-matlab">&gt;&gt; flow_pattern([0.02 0.1 1000 8.9e-4])
ans =
 'LAMINAR'
&gt;&gt; flow_pattern([0.02 0.5 1000 8.9e-4])
ans =
 'TURBULENT'
&gt;&gt; flow_pattern([0.02 0.1 1200 8.9e-4])
ans =
 'TRANSITION'
</pre>

In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be laminar (smooth/sheet-like), turbulent (rough/chaotic), or transitioning from laminar to turbulent. Intuitively, flow velocity is a dominant factor in determining the flow pattern: A slow-moving fluid is laminar, while a fast-moving one is turbulent. However, the flow pattern can also be influenced by pipe geometry, fluid viscosity, and fluid density.

Hence, instead of just flow velocity, engineers are using a number that better indicates the flow pattern called the Reynolds Number, *Re*. For a fluid flowing inside a circular pipe, *Re* is computed as follows:

Re = D x v x rho / mu
    where:
    D = inside diameter of the pipe [m]
    v = mean flow velocity [m/s]
    rho = fluid density [kg/m^3]
    mu = fluid viscosity [Pa.s] or [kg/m/s]
 
Note: Although it is not customary to use SI units for these quantities, this problem deals with SI units for ease.

We can then adopt the following rule: If *Re* < 2300, the flow is laminar; if *Re* > 2900, the flow is turbulent; otherwise, the flow is in transition.

Write a function that accepts a MATLAB variable, x, which is always a 4-element row vector containing the values (in SI) of |D|, |v|, |rho|, and |mu| in that order. Output the appropriate string among 'LAMINAR', 'TRANSITION', or 'TURBULENT', according to the rule above.

See sample test cases:

>> flow_pattern([0.02 0.1 1000 8.9e-4])
ans =
    'LAMINAR'
>> flow_pattern([0.02 0.5 1000 8.9e-4])
ans =
    'TURBULENT'
>> flow_pattern([0.02 0.1 1200 8.9e-4])
ans =
    'TRANSITION'

Solve

Solution Stats

259 Solutions
110 Solvers

Last Solution submitted on May 05, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Christian Schröder on 20 Oct 2022

I gotta say, it's very nice to see a problem with an extensive test suite!

Solution Comments

Show comments

Problem Recent Solvers110

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 45413. Characterize fluid flow in a pipe as to laminar or turbulent

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers110

Suggested Problems

More from this Author19

Problem Tags

Community Treasure Hunt

Problem 45413. Characterize fluid flow in a pipe as to laminar or turbulent

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers110

Suggested Problems

More from this Author19

Problem Tags

Community Treasure Hunt

Players