Isothermal Flow for Compressible Gas in Vertical Pipes 1

[choack]

Hi,

I would like to ask for the integrated form of the equation of isothermal compressible flow in vertical or with angle pipes (with reference).
I saw an integrated form of isothermal compressible for horizontal pipes in equation 6.49 in the 7th edition of McCabe and Smith.

Pa^2-Pb^2=G^2RT{2ln(densitya/densityb)+f(Lb-La)/r)/M

Regards,
Chris

Christopher Kenneth Choa

 

[zdas04]

"With reference". You don't ask much for FREE. I was composing a substantive answer until I went back and saw that. I don't know about others, but I only provide references and external documentation to paying clients. For free you get opinions.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[choack]

Hi zdas04,

I'm sorry to sound demanding. Haha, even without reference.

Regards,

Christopher Kenneth Choa

 

[Latexman]

Chris,

Attach what you have so far, and we'll review it and give you some guidance.

Good luck,
Latexman

 

[choack]

Hi Latexman,

I attached part of McCabe and Smith.

Regards,
Chris

Christopher Kenneth Choa

 

[dcasto]

here is a solution, integrate it in excel. make small steps in the lenght, say 1 cm, then replicate the formula as it steps 1 cm at a time

that will impress your teachers

 

[choack]

Hi dcastro,

How about for vertical pipes? I think it has no term factoring in height difference. Thanks.

Regards,
Chris

Christopher Kenneth Choa

 

[katmar]

The reason the fluid mechanics texts explicitly specify horizontal pipe is so that they can ignore the static head change in the general case. But for us real-life engineers who don't make our reputations by performing beautiful elegant mathematical analyses the change in head when working with gases is negligible in most cases and we just use the horizontal pipe forms for vertical pipes as well.

The one important deviation from this situation is low pressure gas supply to high rise buildings. When the gauge pressure of the gas is low the friction losses also have to be low and then the static head can actually be significant relative to the friction loss. zdas04 has a lot more experience with LP gas than I do, and hopefully he will be tempted back into this thread to tell us whether specialists in the field do perform rigorous analyses of gas in vertical pipes, or they do like I do and make a few safe assumptions???

Katmar Software - Engineering & Risk Analysis Software

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[Latexman]

This is a very theoretical question with no very few apparent real world applications, why do you ask?



Good luck,
Latexman

 

[zdas04]

For gas flow in a real pipes, the preponderance of cases are well below 0.6 Mach where the incompressible-flow assumptions work pretty well. I have never come across a situation where I got more representative data by going to the compressible-flow arithmetic. I took a class on compressible flow in grad school and that discussion was almost entirely about high-speed body in effectively still air with the occasional reference to flows accelerated in convergent/divergent nozzles within pipes.

For low pressures, I mostly use the isothermal gas flow equation (incompressible), but I break the pipe up into small enough chunks to keep downstream density greater than 90% of upstream density and rigorously recalculate compressibility, density, Reynolds Number, and Fanning Friction Factor for each step (I love MathCAD for this). I find that with modern pipes I'm never in the fully turbulent region at low pressures so friction factor changes noticeably from step to step.

As you might expect, in Oil & Gas we deal with vertical flows quite a bit. For small vertical changes (say less than 1000 ft), I use the horizontal calcs without much deviation from observed data. For greater distances the industry has developed empirical closed-form equations that explicitly include hydrostatic head from a gas column. If you find yourself calculating flows from 20,000 ft under the sea floor in 6,000 ft of water, then you probably want to use them. At 3000 ft onshore, including the hydrostatic head in the calculations gives you an answer that is within about +/-5% of ignoring it.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[Latexman]

Chris,

Thank you, but I have the identical information in my 3rd Edition. This leads me to believe you have not tried to derive the equatiob you seek, right?

Good luck,
Latexman