K factor for reducer Ambiguity 1

[Iomcube]

Crane TP-410M while calculating K values for reducer / expander only uses physical geometry of said fitting. The formulas are here:

https://www.enggcyclopedia.com/2019/04/reducer-k-value/

However, in all other fittings (like valves, turns) K value is dependent on Reynolds (or Darcy frictional factor). This latter approach appeals to common sense & such formulas for reducers/expanders I have seen here:

https://neutrium.net/fluid-flow/pressure-loss-from-fittings-expansion-and-reduction-in-pipe-size/

or

https://cheguide.com/piping_fitting.html

or

https://www.katmarsoftware.com/articles/pipe-fitting-equivalent-length.htm

(last & 2nd-last tables)

Can anyone explain this independency of reducer K-factors on Reynolds number as adopted by Crane??

 

[1503-44]

K factors or equivalent pipe lengths. If equivalent pipe legths, Which diameter will you use as the equivalent pipe for a reducer, the larger, or the smaller. Rather than complicate the calculation using two diameters, I expect that Crane determined an average factor for all typical reducers for turbulent flow condition based on usually turbulent flow conditions. It's most likely a conservative approach that gives acceptable answers to 95% of applications.

I lost my Crane reference a long time ago. Not sure but I think Crane factors are multiplied by the loss of 1ft of the upstream "equivalent" pipe diameter pipe, whereas K values are an absolute head loss for the fitting, ie not mutiplied by the loss of 1ft of equivalent pipe.

The first two links do not address the diameter problem at all.
The last link shows some factors in the discussion of reducer K values that are specifically based on the larger diameter.

 

[Iomcube]

Basically I am calculating inlet line losses for a steam PSV. I am attaching x2 PDFs ...the one name Neutrium is using formulae from neutrium/cheguide weblink. These are providing a greater K value thus pressure drops resulting is more conservative

See blue rectangles in 2nd page of pdf

 

[Iomcube]

Cannot attach x2 files I suppose ..here the 2nd

 

[1503-44]

My tablet does not seem to want to open downloads today???

Please notice my edited comment above. Are we sure that the value is in terms of equivalent pipe, or are they absolute losses for the fitting?

How much difference is there between them.

 

[1503-44]

I have one reference, Piping Handbook" old edition, that references a Crane Figure of EQUIVALENT lengths. The Crane figure states that the SMALLER diameter should be used.
The Piping Handbook states that K values are a multiplier for V²/2g, or velocity head. Therefore K values are not multipliers of equivalent lengths, as are the Crane values.

Does that explain the different values you see?

The Handbook also says that there are a number of commonly used fitting loss references and their values often differ.

I'd use the most conservative value and move on. As long as you are sure which type of value is being used, I would think differences would not be too significant.

"Piping Handbook" 5th Edition, Reno C. King, McGraw Hill 1967/1973

 

[Iomcube]

I'd use the most conservative value and move on.

Done...

The Piping Handbook states that K values are a multiplier for V2/2g, or velocity head. Therefore K values are not multipliers of equivalent lengths, as are the Crane values.

As per the link:

https://neutrium.net/fluid-flow/pressure-loss-from-fittings-expansion-and-reduction-in-pipe-size/

K-values in formulae are based on Darcy friction factor ...same as Crane & not on velocity heads

 

[Iomcube]

How much difference is there between them.

Using Crane

Using Neutrium

Neutrium gives 0.05bar more drop in pressure under process conditions

 

[1503-44]

I don't know how or on what Crane based their values, but that figure's nomograph shows it in equivalent lengths.


Anyway that's even less of a difference than what I thought it would be. Not even 1 psi.
Thanks for running the numbers and confirming that it was insignificant.

Yes. Let's move on. 2022 is knocking. Have a good new year.

 

[Iomcube]

Thanks for your time

 

[pierreick]

Hi,
A good reference to have :
Pipe flow a practical and comprehensive guide by Donald C. Rennels and Hobart M. Hudson (Wiley edition).
Pierre

 

[Iomcube]

Thanks pierreick ...your mentioned book is a great compliment to Crane

 

[pierreick]

Hi,
To add to the discussion , a document from Hooper (2K method) supplied to me by Katmar.
Good luck
Pierre

 

[Iomcube]

Thanks pierreick ...old but gold literature