Reference for Y vs. deltaP / P' plots in Crane

[presso]

Does anyone know how were those plots obtained (page A-22 in Crane)? I'm trying to compare data from another source and they are quite different, i would like to be sure that I'm comparing apples with apples...
Thank you!

 

[athomas236]

Does the lack of responses to this question mean that a lot of guys recommend Crane 410 without understanding what they are recommending.

athomas236

 

[Latexman]

No, we have faith in the holy bible of fluid flow. LOL


Good luck,
Latexman

 

[hacksaw]

if you look on page 1-9 you'll find an explanation of the basis for A-22.

 

[presso]

I've already read page 1.9 and all it says is that the charts on page A22 are based on general gas laws for perfect gases... Not very detailed!

 

[vpl]

Presso

In a different paragraph on page 9 (i.e., reading the whole page and not just one paragraph) you'll find the following "...Investigation of the complete theoretical analysis of adiabatic flow (19) has led to a basis for establishing correction factors, which may be applied to the Darcy equation for this condition of flow. Since these correction factors compensate for the changes in fluid properties due to expansion of the fluid, they are identified as Y net expansion factors; see Table A-22."

Reference 19 can be found in the front of the book. If you can find a copy of this reference, it should tell you how the plots were derived.

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

 

[athomas236]

Thanks for pointing me to the relevant parts of Crane, does anyone know the actual formula that is used to calculate Y.

Regards,

athomas236

 

[presso]

Thanks vpl, maybe my last message was misleading but i had already read all paragraphs of page 1-9, i've been trying to track down Shapiro's book (reference 19, the bible for compressible fluids from what i gathered) for a couple of weeks with no luck... and no formula yet!

 

[Latexman]

presso,

I looked through chapter 6 of my copy of Shapiro. You will not find an equation for Y there, but it is easy to see where the idea came from. Shapiro solved the differential equations for compressible flow in various conditions, like adiabatic, isothermal, subsonic, and supersonic flow. In one section on low pressure drops, he rearranged the equations to be of the form of the conventional pressure drop formula times the rest of his somewhat complicated formula. In this particular rearrangement, the equation was a quadratic in terms of dP/P1 and he gives the explicit solution of the equation. I doubt this is the equation for Y because it was derived for "when the percent pressure drop is fairly small", though it might be. I suspect this method, of the conventional pressure drop formula times the rest of a complicated formula, sparked someone elses work who derived the expansion factor, Y. The words "expansion factor" are not in Shapiro's index or in chapter 6.

I think the derivation of Y for venturi meters and flow nozzles is given by reference 9 in Crane, based on Perry's discussion under Head Meters. Perry also gives an approximate equation for Y for orifices.

I think your best hope is to follow the trail of Crane's reference 9 and those in Perry's to find or learn how to derive Y for flow thru pipe to a larger flow area.



Good luck,
Latexman

 

[athomas236]

Hello,

The answers to this question can be found in Chapter 6 and Appendix 2 of "Simulation of Industrial Processes for Control Engineers" by Philip Thomas of City University, London, ISN 0 7506 4161 4.

There is no formula but 4 non-linear equations that can be solved by iteration. Sounds easy to me.

Regards

athomas236

 

[presso]

Thanks for the tip! I will try that as soon as I can. It could be useful to compare the results to a "purely" thermodynamic and interesting approach ("Spreadsheet calculates critical flow" by Sunil Kumar, Chemical engineering magazine, Octobre 2002).
presso

 

[psafety]

athomas236,

In reference to your question: "does anyone know the actual formula that is used to calculate Y." The best way I found to handle the issue is to curve-fitted equations to each K data point (1.2 - 100) to determine Y and then Y vs. sum K, as shown on pg. A-22.

If my losses are between I interpolate the intermediate values.

Don Coffman

 

[athomas236]

Thanks for the tip also presso

athomas236