compressible flow

[YBM]

I have compressible flow thru a 2" x 200ft pipeline,air inlet at 25 to 30 psig, outlet 2 psig.

In using the complete isothermal equation, with this DP ratio, I believe it is appropriate to use the average specific volume in the equation. (Using Crane TP410 Eq. 1-6)

Comments appreciated.

Thanks
YBM

 

[Latexman]

No, in that equation V (with a bar ovet it) is for inlet conditions as referenced by the subscript 1.

Good luck,
Latexman

 

[YBM]

Hey my thanks to you. I simply missed the subscript completely, and am I embarassed!

Appreciate the help.

YBM

 

[sailoday28]

I suggest that you also check to see if the flow is "isothermally choked".

Regards

 

[Latexman]

One doubt I have about Equation 1-6 is the previous page introduces "the next two pages" to be used when dP/P1 > 40%, but limitation #6 for Equation 1-6 says it is applicable as long as an average velocity can be used, which in my mind puts it in the same category as a method when 10% < dP/P1 < 40%. What do you think?

Good luck,
Latexman

 

[BigInch]

Its the same.

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com

 

[vzeos]

For a development of the compressible flow equation check out A Handbook of the Petroleum Industry by David Talbot Day, page 438:

http://books.google.com/books?id=Qq...",+"pipe-line+formula"&amp;as_brr=1#PPA438,M1

Equation 10 corresponds to Crane equation 1-6. Equation 11 is pretty much the general pipe flow equation used today. Note that this book was published in 1922 and the Prandlt, von Karman and Colebrook equations for friction factor were not yet published. So for friction factor, use the more modern equations.

Also check out Engineering Thermodynamics by Charles Edward Lucke, page1111:

http://books.google.com/books?id=pp9KAAAAMAAJ&amp;pg=PR6&amp;dq="Thermodynamic",+"Lucke"#PPA1111,M1

 

[YBM]

Latexman and all,

First I find the wording in Crane, "The velocity may be represented by the average velocity at a cross section." to be confusing, at least to me.

"...average velocity at a cross section" does not mean anything to me. What cross section? Average velocity? Reading the principles on page 1-9 does not seem to support this statement.

Next if we go back to page 1-6 where the Darcy equation is introduced in Eq. 1-4, it has the statement, "(For other forms of this equation see page 3-2)" and if you go there, and it will move you thru many forms, then to p. 3-3 where the same notes appear in relation to Darcy and it further takes you to Eq. 3-20, which has a simpler equation,also seen previously as Eq. 1-11 (last eq. on page 3-4). It also says (p. 3-3)to use this for DP>10% as well as >40%. This seems to say it is pretty much used for most situations.

Of course this has choking considered in the form of "Y".

Additional equations are in the Summary so I believe that this is not exact. I think I shall compare 3-7 to 3-20 substituting K for fL/D in 3-7 as I have entrance and exit losses, but they only increase the fL/D by about 10% and who knows how accurate f is anyway.

Does this make any sense?

 

[BigInch]

Average velocity is flowrate @ Press & Temp / pipe_x-sectional_area.

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com

 

[BigInch]

Average velocity is volumetric flowrate @ Press & Temp / pipe_x-sectional_area.

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com

 

[YBM]

BigInch,I wasn't clear in my statement. I understand what you have said, but where would one take that calculation along the pipeline, because P if not T varies and not linearly along the line. My L/D is not large, but is still 1200.

 

[YBM]

All,

I did compare eq. 3-7 to 3-20 and the results are significantly different. For 3-20 I get approx 18,000 vs 40,000 for 3-7. Note that 3-7 does not consider choking but even so Y=0.79 for my case and that will not account for the 40/18x larger. I found a British calculator online, and while I don't know what equations it uses, it calculated 24,000 for this case when factored by Y would agree with eq. 3-20.

YBM

 

[Latexman]

YBM,

What are your flow units? 18,000 what?

Good luck,
Latexman

 

[BigInch]

2/3 the distance from inlet to outlet (if I remember right).

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com

 

[YBM]

Sorry about that, scfh air.

 

[Latexman]

What's your inlet temperature?

Good luck,
Latexman

 

[YBM]

About 75F. If you are calculating then I have inlet and outlet losses totaling 1.5K, which is insignificant compared to the fL/D of 29, but I totaled them together anyway. (I am not asking you to do my work for me.)

 

[Latexman]

Based on 27.5 psig and 75 F inlet, 2.0 psig outlet, MW = 29, 200 feet of 2" Sch. 40 pipe, and K = 1.5, I got 41,000 scfh.

The difference between isothermal (exit Mach = 0.45) and adiabatic (exit Mach = 0.38) was 0.6%, so it really doesn't matter in this case.

It took me longer to type this, than to get the answer out of my handy dandy spreadsheet.

Good luck,
Latexman

 

[YBM]

Well that is about the same as mine for eq.3-7. What is your ss calculating with? The same eq.?

Even so, it is not clear to me which is appropriate, but since this air has to be vented from a tank, I have little choice but to use the larger value, even though the vents may become larger, and possibly oversized.

I do appreciate your, and the others efforts on this.

YBM

 

[Latexman]

It is numerically integrating several simultaneous equations to a converged solution. Similar to this faq1203-1293 , except it has additional terms for pipe (fL/D) and fittings ([&Sigma;]K_i).

Good luck,
Latexman