In Crane TP 410, K for a fitting is found by multiplying a number times fT.  fT is called the friction factor.  Is fT related to the roughness?

The Crane engineers noted that the K values for fittings generally decreased as the fitting size increased. But it all went wrong when they noticed that this rate of decrease was close to the same as the rate at which the friction factor for fully developed turbulent flow in commercial steel pipe decreased as the pipe size increased.  The fatal mistake was to link the two. See Crane Fig 2-14 and associated commentary.

For example, on page A-29 the K value for a 90 degree butt-weld pipe bend with an r/d of 1.5 is given as 14f_T. The values of f_T are given at the top of page A-26 as a function of pipe size. The values may have been calculated using the function referenced by vzeos, but for the purposes of calculating K values they are constants for each pipe size.

This apparent link between the K value and the friction factor gives the impression that the K value is linked to the pipe roughness, but in fact it is not because f_T is defined to be at a 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 the example of the 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 Crane's treatment, the K value of a fitting is a function only/needlevalve of the pipe size (or geometry to use the terms used by wfn217 and BigInch).  This was an improvement over previous work where the K value had been assumed to be constant for all sizes of fittings, and at the time that Crane first published this method it was rightly acclaimed as an important advance but IMHO it was badly worded and newer editions of 410 have unfortunately done nothing to remove the confusion.

I have awarded a star to BigInch for his comment that if you want to convert the Crane K value to an equivalent length, you must use the f_T value from Crane's table on page A-26 (which is based on a roughness of 0.0018") and NOT the actual friction factor of the pipe you are using.  The Crane description of this on 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 are working with laminar flow it is much better to work with equivalent lengths than with fixed or even Crane K values. Resistance values for fittings increase rapidly at low Reynolds numbers, but so does the friction factor. This means that if you use fixed L/D values, which get multiplied by the friction factor in the Darcy-Weisbach equation, the high resistance values are automatically compensated for. Or even better, use the 2-K or 3-K methods proposed by Hooper and Darby.

And I select Harvey as the preferred Ranter of the day and worthy - as well - of recognition for bringing to everyone's attention the importance of really understanding and reading through what is put in front of our eyes.  We, as professional engineers, are not being asked to believe or accept 100% of what we are offered or given - regardless of how "sacred" the Cow may seem.  Everything in engineering is subject to scrutiny and improvements.

I have a lot of respect and gratitude for what has gone into putting together Crane's Tech Paper #410.  However, everything Harvey has stated regarding the concept of their K values is not only valid, but 100% positive criticism that should be heard and applied.  Major world-class engineering firms agree with what Harvey states - and so do some of the biggest chemical process companies.  To quote one: "Until recently, the use of K coefficients for valves and fittings has been considered more accurate than the use of equivalent lengths of pipe, but recent research has disclosed that K coefficients are not constant for all sizes of any one type of valve or fitting; so the use of equivalent lengths, with some exceptions, is now preferred."  And this is in addition to the problems of understanding/interpreting what TP 410 is saying.  We have a better option, as Harvey states, in the 2-K or 3-K methods.

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