Crane 410 fittings 12

[wfn217]

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?

 

[dtn6770]

fT is related to roughness by way of the Moody Diagram and its use of relative roughness. Relative roughness is the materials absolute roughness divided by the inside diamter.

 

[STYMIEDPIPER]

Crane 410 lists values for fT

 

[wfn217]

I wanted to know whether the listed fT values are strictly due to geometry or also a function of roughness.

 

[BigInch]

geometry

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[vzeos]

wfn217- In Crane TP 410 f_T is the fully turbulent flow friction factor defined by the equation below. D is the pipe I. D. and k is the pipe roughness.

1/[√]f_T= 2Log{(3.7D/k)

Crane's equivalent length calculations assume fully developed turbulent flow. See Crane TP 410, Page 26. The f_T values provided by Crane imply a k value of about 0.00180".

 

[BigInch]

vzeos,

You are totally correct. Seems I reversed the question. K is determined by geometry, but the equivalet length is indeed based on 0.0018 roughness.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[DLANDISSR]

fT is the friction factor in the turbulent region of flow. It is calculated from the Colebook-White equation which is an iteration. The Moody Diagram is derived from the Colebrook-White equation.
The Colebrook-White equation uses the Reyonalds Number, the relative roughness.

 

[katmar]

BigInch nailed the answer with his first post, but this question highlights what I consider to be one of the weaker points of the Crane 410 manual so please forgive me a little rant here. I have seen Crane's 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 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 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.

[Close rant mode - thanks for listening!]

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[Montemayor]

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.

Great comments and good engineering knowledge, Harvey!

 

[wfn217]

The number that Crane multiplies by fT to obtain K is the same number listed as L/D in Cameron Hydraulic Data. For example, for a 90 degree elbow K is 30 times fT. L/D in Cameron is 30.

 

[katmar]

wfn217, the Darcy-Weisbach correlation for pressure drop is

?P = ( fL/D + K ) ?V² / 2

So if you want to express the resistance of a fitting in terms of the equivalent length (i.e. L/D) instead of K then you have to calculate

L/D = K/f

and since Crane express their K's as (Constant) x f_T you would get

L/D = (Constant) x f_T / f

If f is evaluated at the same conditions as f_T (which is what my rant above was all about!) then of course

L/D = (Constant)

which means that for commercial steel pipe in the fully turbulent regime the (Constant) used by Crane will indeed be the L/D value given by Cameron. You just have to remember that because Crane evaluated these (Constants) for commercial steel pipe in the fully turbulent regime, if you want to get back to the L/D values you must use f_T and not the friction factor in your particular case.



Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[wfn217]

katmar,

My point was that I don't see why equivalent lengths are now prefered (per Montemayor).

 

[katmar]

wfn217,

it has been found experimentally that the resistance factor (i.e. K value) for a fitting depends on both the fitting size and the Reynolds number. In the Darcy-Weisbach equation (in which I managed to get the wrong symbols before)

[Δ]P = ( fL/D + K ) [ρ]V² / 2

you can see that if you use a K value the pressure drop is not influenced by the fitting size or the Reynolds number. When you use Crane K values the value is corrected (via the table on page A-26) for fitting size before you insert the value into the D-W equation, but many of the older references gave single K values for all fitting sizes.

On the other hand, you can see that if you use equivalent lengths, then the value is multiplied by the actual friction factor for your application, and because the friction factor does depend on the fitting size and the Reynolds number it automatically corrects the calculation for both these factors. This makes the equivalent length method both easier to use, and more accurate than K values. It is easier to use because you only have to remember a single L/D value for a given type of fitting.

As Montemayor and I said before, the very best way is to use the 2-K or 3-K method but these are computationally much more involved. In my software I use 3-K because once it is programmed it makes no extra work to use it, but if I am doing a hand calc then I use the equivalent length method.

Hope this makes it clear

Harvey

 

[tickle]

Thank you Katmar for your wonderful explanation.

I have questioned Crane myself, but learnt to accept that its findings were as practical as required.

I think that younger engineers blindly use equations and computer programs - because they are there. They do not understand the applicable circumstances or the limitations. In fact whilst reading the post one of the junior engineers questioned me regarding recommended pipe diameters. They had sized the steam piping for maximum flow and minimum pressure. They were blindly going to use a calculated diameter because it was less than or equal to the recommended velocity without considering the application and whether the worst case conditions could occur at the same time, (they can't and a smaller pipe diameter was my recommendation).

I have printed the post and passed it to my younger engineers.

 

[pleckner]

I invite everyone to read my article on this subject published at

http://www.cheresources.com/eqlength.shtml

I don't agree that using equivalent lengths is the proper way to perform a system hydraulcs calculation (my arguments are in the above mentioned article). You must not mix the friction factor for a fitting with the friction factor of a pipe because they are not the same, whether we are talking about CRANE's friction factor at fully developed turbulent flow or the two-K or three-K methods. The pressure loss of a fitting obtained from these methods is not the same nor nearly the same as the pressure loss of a fitting obtained from multiplying the pipe friction factor x the equivalent length of the fitting.

The most accurate way to perform the calculation is to use one of these methods (three-k perferred) and add the losses to those of the pipe, not to combine them all into an equivalent length of straight pipe and multiply by the pipe friction factor.

The two-K or three-K methods were developed to address the fact that fittings are indded somewhat dependent on Reynolds number, but this is still not the same as a pipe friction factor.

I will also argue that for fully developed turbulent flow, there is nothing wrong with CRANE's values. I believe you will find that the K values from all three methods are basically the same at these conditions.

 

[katmar]

pleckner,

There is a lot more that we agree on than on which we differ. It was never my intention to suggest that there is anything wrong with applying Crane's K values to fully developed turbulent flow. I have recommended MANY times here that people should get their hands on a copy of Crane 410. Probably 95% or more of our flow calcs are for fully developed turbulent flow, and Crane is ideal for this.

My main objection was to the confusion caused by Crane's wording and their linking of the K value to the turbulent friction factor. I believe the posts in this thread confirm that this confusion is widespread, and I have often seen engineers struggle to come to terms with it. Despite the shortcomings of Crane 410, my copy "lives" in the very front of the top drawer of the filing cabinet right next to my desk.

We all agree that the multi-K methods are better than the L/D method. However, I disagree with Crane's statement (which is echoed in your article) that "K is a constant under all flow conditions, including laminar flow". In your example you give the K value for a long radius bend as 0.36. Applying the 3-K method at a Reynolds number of 100 in the same sized pipe gives a K value of 8.3. This means that a pressure drop calculation using the Crane value will be 90% understated, if we take 3-K as the benchmark. I accept that a similar calculation at Re=100 using the L/D method will over-estimate the pressure drop but for most calculations this would be the conservative option.

I have one objection to the example in your article. 92% of the pressure drop is due to the reducer, but nobody would ever try to calculate the pressure drop through a reducer with the L/D method. Including the reducer exagerates the negative aspects of the L/D method.

Neglecting the reducer, the calculated pressure drops using the various methods are

L/D method - 0.97 psi
Crane K - 0.75 psi
Darby 3-K - 0.87 psi

Who would put his neck on the block over which of these numbers is correct? The L/D and Crane answers are within 15% of the 3-K answer, and all three answers are probably adequate for practical purposes.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BigInch]

That's my humble opinion also. With all the other inaccuracies inherent in hydraulics and more specifically how systems are usually operated at one or the other of the extreme ranges, if you design a system close enough so that you have to worry about the difference in pressure drops from laminar or turbulent flow in a few fittings, that's just plain tooooo close. If for some reason you need to examine an existing system, the actual data's there for the taking.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[pleckner]

We are in agreement.

I put the reducers into the L/D equation only as a means for comparison. I agree with you (Katmar) on that. But then again, I don't use the equivalent length method, ever.

Katmar, I'm one up on you, I keep CRANE on my desk, I'm too lazy to go into my file cabinet.

 

[wfn217]

It should be noted that pleckner's article states that K for a fitting has little to do with friction, which answers my original question. I have seen someone try to scale the fT values in Crane from pipe to tubing based on roughness.