{"id":2948,"date":"2011-12-02T09:20:44","date_gmt":"2011-12-02T14:20:44","guid":{"rendered":"https:\/\/blogs.mathworks.com\/pick\/?p=2948"},"modified":"2017-01-06T21:33:14","modified_gmt":"2017-01-07T02:33:14","slug":"will-my-flow-be-turbulent","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/pick\/2011\/12\/02\/will-my-flow-be-turbulent\/","title":{"rendered":"Will my flow be turbulent?"},"content":{"rendered":"<div xmlns:mwsh=\"https:\/\/www.mathworks.com\/namespace\/mcode\/v1\/syntaxhighlight.dtd\" class=\"content\">\r\n   <introduction><\/introduction>\r\n   <p><a href=\"https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/authors\/911\">Brett<\/a>'s Pick this week is <a href=\"https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/7747-moody-diagram\">Moody,<\/a> by <a href=\"https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/authors\/18628\">Tom Davis<\/a>.\r\n   <\/p>\r\n   <p>I am not a mechanical engineer, though I did study fluid mechanics in my biomedical engineering past. In fluid flows, the\r\n      <a href=\"http:\/\/en.wikipedia.org\/wiki\/Reynolds_number\">Reynolds number<\/a> is a dimensionless parameter that describes the ratio of inertial to viscous forces. This relationship is significant because,\r\n      among other things, it can be used to predict the nature of the flow--whether laminar or turbulent. In biomechanics, fully\r\n      developed fluid flows are typically of low Reynolds numbers, certainly below the critical threshold at which flow becomes\r\n      turbulent.\r\n   <\/p>\r\n   <p>However, in classical mechanics and hydraulics, flows are typically through long, often rigid, pipes. Flows become \"fully\r\n      developed,\" and can be of much higher Reynolds numbers. In these regimes, assuming one knows the characteristics of the pipe,\r\n      one can calculate the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Darcy_friction_factor\">Darcy friction factor<\/a> to determine the (pressure) head loss during flow.\r\n   <\/p>\r\n   <p>Okay, geeking out a bit. The relevance here is that the interplay of Reynolds numbers and Darcy factors can be difficult to\r\n      deal with; <a href=\"http:\/\/en.wikipedia.org\/wiki\/Moody_diagram\">Moody diagrams<\/a> allow us to relate the two graphically, and to see at a glance whether, given a Darcy Factor and a Reynolds number,  flow\r\n      will be laminar or turbulent for pipes of a specified roughness.\r\n   <\/p>\r\n   <p>Creating a Moody diagram is no trivial task, though. Or at least, it wasn't until Tom shared his MATLAB code for creating\r\n      one. Function 'Moody' allows you to specify units (SI or Imperial) and paper size (A4 or Letter), and the name of an output\r\n      file, and it will create a beautiful Moody diagram for you!\r\n   <\/p>\r\n\r\n   <p>Thanks for sharing that, Tom! As always, <a href=\"https:\/\/blogs.mathworks.com\/pick\/?p=2948#respond\">comments to this blog post<\/a> are welcome. Or leave a comment for Tom <a href=\"https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/7747-moody-diagram#comments\">here<\/a>.\r\n   <\/p><script language=\"JavaScript\">\r\n<!--\r\n\r\n    function grabCode_f03c6c08bdaf4303811bde78eb669c4c() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='f03c6c08bdaf4303811bde78eb669c4c ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' f03c6c08bdaf4303811bde78eb669c4c';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        author = 'Brett Shoelson';\r\n        copyright = 'Copyright 2011 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add author and copyright lines at the bottom if specified.\r\n        if ((author.length > 0) || (copyright.length > 0)) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (author.length > 0) {\r\n                d.writeln('% _' + author + '_');\r\n            }\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n      \r\n      d.title = title + ' (MATLAB code)';\r\n      d.close();\r\n      }   \r\n      \r\n-->\r\n<\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_f03c6c08bdaf4303811bde78eb669c4c()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n            the MATLAB code \r\n            <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; 7.13<br><\/p>\r\n<\/div>\r\n<!--\r\nf03c6c08bdaf4303811bde78eb669c4c ##### SOURCE BEGIN #####\r\n%% Will my flow be turbulent?\r\n%% \r\n% <https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/authors\/911 Brett>'s Pick this week is\r\n% <https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/7747-moody-diagram Moody,> by \r\n% <https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/authors\/18628 Tom Davis>.\r\n\r\n%%\r\n% I am not a mechanical engineer, though I did study fluid\r\n% mechanics in my biomedical engineering past. In fluid\r\n% flows, the <http:\/\/en.wikipedia.org\/wiki\/Reynolds_number Reynolds number>\r\n% is a dimensionless parameter that describes the ratio of\r\n% inertial to viscous forces. This relationship is significant because,\r\n% among other things, it can be used to predict the\r\n% nature of the flowREPLACE_WITH_DASH_DASHwhether laminar or turbulent. In\r\n% biomechanics, fully developed fluid flows are typically of\r\n% low Reynolds numbers, certainly below the critical\r\n% threshold at which flow becomes turbulent.\r\n\r\n%%\r\n% However, in classical mechanics and hydraulics, flows are typically through\r\n% long, often rigid, pipes. Flows become \"fully developed,\"\r\n% and can be of much higher Reynolds numbers. In these\r\n% regimes, assuming one knows the characteristics of the\r\n% pipe, one can calculate the <http:\/\/en.wikipedia.org\/wiki\/Darcy_friction_factor Darcy friction factor> to \r\n% determine the (pressure) head loss during flow. \r\n\r\n%% \r\n% Okay, geeking out a bit. The relevance here is that the\r\n% interplay of Reynolds numbers and Darcy factors can be\r\n% difficult to deal with;\r\n% <http:\/\/en.wikipedia.org\/wiki\/Moody_diagram Moody diagrams> allow us to relate the two graphically, and to\r\n% see at a glance whether, given a Darcy Factor and a Reynolds number,  flow will be laminar or turbulent for pipes of a specified roughness.\r\n\r\n%%\r\n% Creating a Moody diagram is no trivial task, though. Or at\r\n% least, it wasn't until Tom shared his MATLAB code for\r\n% creating one. Function 'Moody' allows you to specify units\r\n% (SI or Imperial) and paper size (A4 or Letter), and the\r\n% name of an output file, and it will create a beautiful\r\n% Moody diagram for you!\r\n\r\n%%\r\n% \r\n% <<https:\/\/www.mathworks.com\/matlabcentral\/fx_files\/7747\/1\/moody.png>>\r\n% \r\n\r\n%% \r\n% Thanks for sharing that, Tom! As always, <https:\/\/blogs.mathworks.com\/pick\/?p=2948#respond comments to this blog post> are welcome. Or leave a\r\n% comment for Tom\r\n% <https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/7747-moody-diagram#comments here>.\r\n\r\n##### SOURCE END ##### f03c6c08bdaf4303811bde78eb669c4c\r\n-->","protected":false},"excerpt":{"rendered":"<p>\r\n   \r\n   Brett's Pick this week is Moody, by Tom Davis.\r\n   \r\n   I am not a mechanical engineer, though I did study fluid mechanics in my biomedical engineering past. In fluid flows, the\r\n     ... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/pick\/2011\/12\/02\/will-my-flow-be-turbulent\/\">read more >><\/a><\/p>","protected":false},"author":34,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[16],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/posts\/2948"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/users\/34"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/comments?post=2948"}],"version-history":[{"count":35,"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/posts\/2948\/revisions"}],"predecessor-version":[{"id":8343,"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/posts\/2948\/revisions\/8343"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/media?parent=2948"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/categories?post=2948"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/pick\/wp-json\/wp\/v2\/tags?post=2948"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}