[b]Relations for the Net Expansion Factor Y[/b]

[presso]

I'm looking for relationships (empirical or theoretical) for the net gas expansion factor Y as a function of downstream and upstream pressures and the pipe resistance coefficient K among others for the compressible fluid flow through pipes. All I could find was related to flowmeters with a diameter change...
Also does the Robert Kern formula ring a bell to anyone in relation to calculations of Y for critical flow conditions?
Thank you!

 

[TangoCleveland]

Look in Crane "Flow of Fluids", Tech Paper # 410. It has a couple charts for flowmeters with area changes, and for flow through pipe to a larger area. Kern formula doesn't ring a bell with me.....

You can get the book ($36) or the software from

http://www.cranevalves.com/store.htm

Larry

 

[presso]

Yes I already got Crane but I'm looking for the equations used to obtain plots of Y vs. deltaP / P' for example. How were they obtained?

 

[TangoCleveland]

Cranes says that the expansion factor Y "has been experimentally determined . . ..", and that the correction factor compensates for the changes in fluid properties due to expansion of the fluid. Looking at the charts, they look like linear relationships vs. deltaP / P'.

We use AFT ARROW for compressible flow modeling. It actually calculates the change in properties with fluid expansion, and agrees well with examples in Crane.

Larry

 

[EGT01]

I've seen expansion factor equations for flow meters but not familiar with any for pipe flow. Might be convenient to have something like that.

After a quick look on the internet, looks like this software has something like that built in

http://www.edstech.com/under.html

Also happened to find this which sounds like they took Crane's graphs and built a subroutine from that.

http://melcor.sandia.gov/ref/cnd/cndreference.htm

Based on what OldSohioEngr points out, guess you would have to create your own equations unless you find someone that is willing to share.

I saw you had a similar post on another forum. You mentioned about comparing data to another source. I'm curious to know the other source to which you refer.

 

[presso]

I think the plots for Y Vs. deltaP/P are "so linear" that it can't be only experimental...
Anyway I found an equation in the form of Y = m deltaP/P + 1
with m in the form a/(K+1) + b, with a and b for gamma of 1.3 and 1.4. However I'm doing calculations for propylene where you have Cp/Cv = 1.15, quite far from the 1.3 given by Crane. My idea was to find equations relating Cp/Cv with all the other factors.
My other "source" (although the term is not quite accurate) is the equations used by the spreadsheet from October 2002 Chemical Engineering magazine as suggested by TD2K on another thread (Thread798-51260). However the results I obtained are quite different when compared to Crane and I don't really understand the basis of the spreadsheet equations. Since I found other one in a textbook, I was wondering which were used in Crane...
I'm not sure all this is clear...

 

[hacksaw]

If I understand your question correctly, Y (the adiabatic expansion factor)is not used in pipe flow as such (there you have friction losses), except at points where there is a diameter change, e.g. a discharge. It can be derived for an adiabatic expansion, but for real world expansions experimental correlations involved.

 

[presso]

I agree hacksaw for the 1st part of your answer. The title of the charts on page A-22 of Crane is "net expansion factor Y for compressible flow through pipe to a larger area". However, according to page 1.9 of Crane, the charts on page A-22 are based on gas laws for perfect gas... It does not sound very experimental to me?!?