Crane Resistance Coefficient (K factor) for Pipe Elbows 2

[greenche]

In Crane TP410, on page A-29, there is a table for K values of 90 degree pipe bends as a function of r/d. I deal with many r/d values in between the increments in the table. For the purposes of putting K in spreadsheet formulas, is there a generally accepted curve fit for K as a function of r/d?

I realize I could make a lookup table and interpolate, but this would make the spreadsheet much more complicated. I am also aware that there is considerable variation in the data as seen in the graph on Crane page 2-13.

Garrett

 

[katmar]

Dennis Kirk has published some information on this at

http://members.ozemail.com.au/~denniskb/work/bendel.gif

You could fit a curve to his data and convert from Le to K

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[greenche]

It appears the data in Dennis' plot is directly from Crane pg. A-29. I could come up with my own curve fit but I was first wanting to make sure there was not already an "official" curve fit or underlying formula for this data.

Garrett

 

[vzeos]

A few years ago I came up with 2 correlation equations to calculate K/ft as a function of r/d. The first equation is for r/d <= 4 and the second equation is for r/d > 4. See the attached file, it may help.

 

[vpl]

greenche

Since it's Crane's book, any "official" curve fit or underlying formula would come from them. They have a website (

http://www.crane.com).

Patricia Lougheed

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[LSThill]

vzeos (Mechanical)

Thank you

Leonard

 

[ValveEngineer123]

Greenche: Is it possible to just make a conservative assumption for the value of r/d and input that to your spreadsheet? If the answer is favourable then your problem is solved. If not, then look at spending the time to produce some sort of interpolation.

Or perhaps you need a more accurate answer from your calcs than a conservative assumption would provide (?)

ValveEngineer

 

[rconner]

I know that MANY years ago some families of curves (essentially parabolic curves were published plotting loss coefficient vs the R/D ratio for some bends of "uniform diameter" in the publication, "Pipe Friction Manual, Hydraulic Institute". e.g. for a 90 bend (and I suspect similar basic appearance for others) there are individual sort of concentric parabolic curves plotted for varying degrees of rugosity. Maybe this will help you track down what you are looking for.

 

[greenche]

vzeos,
That is the type of function I was looking for. I wanted to avoid splitting the range in two, so I came up with:

K = a( atan(r/d) ) + b (r/d)^-1 + c (r/d)^0.5
where,
a = -19.1084132244392
b = 17.0419398956139
c = 17.487997553414

I did not find anything on the Crane web site [URL unfurl="true"]http://www.cranevalve.com/[/url].
The systems I am looking at have many bends, so I do not want to build in a conservative r/d as it will get multiplied many times. So far, the above formula is working ok.

Garrett

 

[vzeos]

greenche,
Your curve is better. However, note that you are not calculating the resistance coefficient K. You are calculating K/ft (or L/D, since K/ft = L/D) where ft is the fully turbulent flow friction factor. According to Crane, you need to multiply K/ft (or L/D) by ft to get K.

Good job!

 

[greenche]

Good point for clarification, the right side should be multiplied by f_T to get K.