{"id":28690,"date":"2013-05-21T17:06:28","date_gmt":"2013-05-21T11:36:28","guid":{"rendered":"http:\/\/www.kopykitab.com\/blog\/?p=28690"},"modified":"2013-05-21T17:06:28","modified_gmt":"2013-05-21T11:36:28","slug":"the-darcy-weisbach-equation-notes","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/the-darcy-weisbach-equation-notes\/","title":{"rendered":"The Darcy-Weisbach Equation Notes"},"content":{"rendered":"

The Darcy-Weisbach Equation Notes
\n<\/span><\/b><\/h1>\n

The Darcy-Weisbach equation is now considered the best empirical relation for pipe-flow resistance. In terms of head units it is,<\/span><\/p>\n

 <\/p>\n

\"\"\u00a0(pipe friction)<\/p>\n

where,\u00a0hl<\/sub><\/i>\u00a0is the head loss,\u00a0f<\/i>\u00a0is the friction factor,\u00a0L<\/i>\u00a0is the pipe length,\u00a0V<\/i>\u00a0is the average flow velocity, and\u00a0g<\/i>\u00a0is the acceleration of gravity.<\/span><\/p>\n

In terms of pressure drop,\u00a0<\/span>D<\/span>p<\/span><\/i>\u00a0it is,<\/span><\/p>\n

\"\"<\/p>\n

where<\/span>\u00a0r<\/span><\/i>\u00a0is the fluid density. The Darcy-Weisbach\u00a0f<\/i>\u00a0is a complex function of the Reynolds Number and relative roughness. The Reynolds number,\u00a0Re<\/i>\u00a0is defined as,<\/span><\/p>\n

\"\"<\/span><\/p>\n

where\u00a0<\/span>m<\/span><\/i>\u00a0is the fluid absolute viscosity, and\u00a0D<\/i>\u00a0is the pipe diameter. The relative pipe roughness is the ratio of the pipe surface roughness,\u00a0e<\/i>\u00a0to its diameter,\u00a0D<\/i>, or e\/D.<\/span><\/p>\n

For laminar flow where Re\u00a0< 2,000,\u00a0<\/i>pipe roughness is not a factor and,<\/span><\/p>\n

f = 64\/Re<\/i><\/p>\n

For\u00a0hydraulically smooth pipes (e = 0)<\/i>\u00a0such as glass, copper and plastic tubing in turbulent flow, use Blasius equation for\u00a0f<\/i><\/span><\/p>\n

\"\"\u00a0(4,000 < R<\/i>e < 100,000)<\/p>\n

For rough pipe in turbulent flow you must use the\u00a0Moody diagram\u00a0to obtain\u00a0f<\/i>. That may require an iterative solution where a flow rate is guessed,\u00a0f<\/i>\u00a0estimated and than a new flow calcuated.<\/span><\/p>\n

An easier, and almost as accurate procedure as the Moody Diagram is to use the empirical formulas of Swamee and Jain, (J. of Hydraulics Division,. Proc. ASCE, pp 657-664, May 1976).<\/span><\/p>\n

 <\/p>\n

\"\"\u00a0(10^-6 <\u00a0e\/D\u00a0<\/i>< 0.01; 5,000 <\u00a0Re<\/i>\u00a0< 3×10^8)<\/p>\n

(Note base 10 log used)<\/span><\/p>\n

\"\"\u00a0\"\"\u00a0(3000<Re<3×10^8 ; 10^-6<e\/d<.01)<\/span><\/p>\n

\"\"\u00a0(R<\/span><\/i>e > 2,000)<\/span><\/p>\n

\"\"\u00a0(10-6 <\u00a0e\/D\u00a0<\/i>< 0.01; 5,000 <\u00a0Re<\/i>\u00a0< 3×10^8)<\/span><\/p>\n

where\u00a0<\/span>n<\/span>\u00a0is the kinematic viscosity, or\u00a0<\/span>m\/r<\/span>. The equation for\u00a0f\u00a0<\/i>is a form of the Colebrook-White equation. The equation for\u00a0Q\u00a0<\/i>is as accurate as the Moody diagram, while equations for\u00a0hl<\/i>\u00a0and\u00a0D<\/i>\u00a0are within 2%.<\/span><\/p>\n

Equivalent Diameter for Noncircular Ducts:<\/span><\/b>\u00a0For noncircular ducts the hydraluic diameter,\u00a0Dh<\/i>\u00a0is used as the characteristic length in\u00a0R<\/i>e and\u00a0e\/D<\/i>.<\/span><\/p>\n

Dh<\/span><\/i>\u00a0= 4 x area of flow \/ perimeter of duct in contact with fluid.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

The Darcy-Weisbach Equation Notes The Darcy-Weisbach equation is now considered the best empirical relation for pipe-flow resistance. In terms of head units it is,   \u00a0(pipe friction) where,\u00a0hl\u00a0is the head loss,\u00a0f\u00a0is the friction factor,\u00a0L\u00a0is the pipe length,\u00a0V\u00a0is the average flow velocity, and\u00a0g\u00a0is the acceleration of gravity. In terms of pressure drop,\u00a0Dp\u00a0it is, where\u00a0r\u00a0is the fluid … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[4773],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28690"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=28690"}],"version-history":[{"count":0,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28690\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=28690"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=28690"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=28690"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}