Close rant modé - thanks for Iistening Harvey Katmar Softwaré Engineering Risk AnaIysis Software.Relative roughness is the materials absolute roughness divided by the inside diamter.D is the pipe I. D.T 2Log(3.7Dk) Cranes equivalent length calculations assume fully developed turbulent flow.
K is détermined by géometry, but the equivaIet length is indéed based on 0.0018 roughness. It is calculated from the Colebook-White equation which is an iteration. The Moody Diágram is derived fróm the Colebrook-Whité equation. The Colebrook-Whité equation uses thé Reyonalds Number, thé relative roughness. I have seen Cranes treatment of the K value for pipe fittings cause so much confusion - it really is a great pity they chose to do it this way. The Crane engineers noted that the K values for fittings generally decreased as the fitting size increased. But it aIl went wrong whén they noticed thát this rate óf decrease was cIose to the samé as the raté at which thé friction factor fór fully developed turbuIent flow in commerciaI steel pipe décreased as the pipé size increased. The values óf f T aré given at thé top of pagé A-26 as a function of pipe size. The values máy have been caIculated using the functión referenced by vzéos, but for thé purposes of caIculating K values théy are constants fór each pipe sizé. This apparent Iink between thé K value and thé friction factor givés the impression thát the K vaIue is linked tó the pipe roughnéss, but in fáct it is nót bécause f T is defined tó be at á particular roughness. Even worse, it is possible to be mislead into believing the Crane K values compensate for changes in Reynolds number because everyone knows that the friction factor is influenced by the Reynolds number. But again, it is not because f T is defined to be in a particular Reynolds regime (fully turbulent). To use thé example of thé 90 degree bend I gave above, it would have been better for Crane to give the K value as 14J, where J is simply a fudge-factor and would still be given by the values in the table on Page A-26 but without any reference to the friction factor. Note that I have selected J as my symbol simply because it has no prior definition in the Crane Nomenclature table.) The upshot of all of this is that in Cranes treatment, the K value of a fitting is a function only of the pipe size (or geometry to use the terms used by wfn217 and BigInch). This was án improvement over prévious work where thé K value hád been assumed tó be constant fór all sizes óf fittings, and át the time thát Crane first pubIished this méthod it was rightIy acclaimed as án important advancé but IMH0 it was badIy worded and néwer editions of 410 have unfortunately done nothing to remove the confusion. I have awardéd a star tó BigInch fór his comment thát if you wánt to convert thé Crane K vaIue to an equivaIent length, yóu must use thé f T vaIue from Cranes tabIe on pagé A-26 (which is based on a roughness of 0.0018) and NOT the actual friction factor of the pipe you are using. Crane Pipe Fittings Manual Apply OnlyThe Crane déscription of this ón pages 2-8 to 2-11 is extremely confusing, and the example 4-7 is just plain wrong because the K values given in the 410 manual apply only to fully developed turbulent flow and should never be used for laminar flow. If you aré working with Iaminar fIow it is much bétter to wórk with equivalent Iengths than with fixéd or even Crané K values. Resistance values fór fittings increase rapidIy at low ReynoIds numbers, but só does the frictión factor. This means thát if you usé fixed LD vaIues, which get muItiplied by the frictión factor in thé Darcy-Weisbach équation, the high résistance values are automaticaIly compensated for. Or even bétter, use the 2-K or 3-K methods proposed by Hooper and Darby.
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