Net Expansion Factor; K>100??

[Bourbon103]

Hello All,

My brain's a little fuzzy this afternoon, but I'm running into a problem with Crane T.P. No. 410, pg. A-22 "Net Expansion factor Y for Compressible Flow..."

For my example:
P1 = 40 psig + 14.7 = 54.7 psia
P2 = 0.397 psig + 14.7 = 15.097 psia
DP = 39.603 psia
DP/P1 = 0.724

K = 752

Y = ???

The charts in Crane only go up to K = 100. Am I missing something?

Thanks again for your help.

 

[vpl]

You're right the charts only go up to 100.

How did you come up with a K of 752?

Patricia Lougheed

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[Bourbon103]

E.g.

Largest diameter of pipe in system is 3.94 ID.

One section of pipe in the system is 330 ft of 2.067 ID pipe.

Beta = 2.067/3.94= 0.525

If Moody friction factor = 0.020, then:

K= 12*0.020*330/(2.067*0.525^4) = 497

Just this section alone has K greater than 100. Adding up the other sections similarly, K = 752.

Is there something I'm missing?

 

[Bourbon103]

What I am attempting to do now, in leiu of simulation software, is break up the piping in nodes with K < 100, changing the specific volume accordingly...

 

[Latexman]

It looks like you put the 2" K in terms of the 3.94" diameter. Try putting all your K's in terms of your smallest diameter pipe. You'll end up with the lowest possible overall K. If you are lucky it'll be < 100.

With compressible flow in a multiple diameter system it's always best to work in terms of the smallest diameter with these simple methods. That's where it will most likely choke anyway.

Good luck,
Latexman

 

[vpl]

I'm presuming you're using the formula K=fL/D and then dividing by [&Beta;][sup]4[/sup] to get it to the larger diameter size pipe. Based on that, your answer seems correct (though you appear to have introduced a fairly sizeable roundoff error).

I don't work much with compressible fluids, so I'm taking a swag here ... Based on the graphs on page A-22, it appears that for K>20, Y reaches a maximum value of 0.718 or 0.710. For a first round, try using that as your maximum.

Patricia Lougheed

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[Bourbon103]

Latexman,

Thank you for your suggestion. Interestingly enough I did it the way you suggested, as well as breaking it up into nodes, and both results only differ by about 4% (though I could iterate further and get it a little closer).

Thanks for your help!

 

[Latexman]

Good luck,
Latexman