Darcy Weisbach equation for pipe pressure loss 1

[Speedy]

I want to make up a spreadsheet that will calculate the friction pressure loss in piping for different gases.

I found the 'Darcy Weisbach' equation but I have a few questions as follows -

Can this equation be used for compressible gases. One source says valid only for incompressible(

http://www.engineeringtoolbox.com),

the other (Piping Calculations Manual - E. sashi Menon) says it is fine for gases?

Secondly - The fluid density and viscosity, can these be specified at atmospheric or at the pipe pressure, if so where is a good source for these values.

 

[zdas04]

The first assumption in Euler's simplification of Navier-Stokes was incompressible flow. Since Bernoulli started with Euler's Equation and virtually every empirical equation after him started with the Bernoulli Equation, you can be confident that every equation that you try to use will specify "incompressible flow" which means "constant density".

"Constant" is the slippery term here. If density is within some fairly large percentage of initial density (many people use 10%, but I think that is a number grabbed from the air) then it is "constant" within the accuracy of the calculation. This means that if you are modeling a very long pipeline you may need to break the analysis up into chunks with reasonably constant density (e.g., a 300 mile pipeline that starts at 1,000 psig and ends at 800 psig should probably be modeled as three 100 mile segments), but there is no problem using Darcy Weisbach, AGA, Panhandle A, or any of the empirical equations on the flow of a fluid you would run through a compressor.

One thing that is often missed in this sort of analysis is that when velocities exceed about 0.6 Mach, the density changes rapidly with changes in velocity and the gas can no longer be considered incompressible.

Viscosity is largely pressure independent. Density depends on the equation (these equations are empirical and it is not a good idea to guess), I don't remember what D'Arcy wants.


David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

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

The harder I work, the luckier I seem

 

[zdas04]

To clarify how to bust up a line I do it iteratively. First I use the dP across the entire line to estimate a flow rate. Then I use that flow rate and the upstream pressure to estimate the pressure at the end of the segment. Continue that to the end of the line and compare the results to your original downstream pressure and adjust your flow rate and repeat.

For example (using the AGA equation), with a 20 inch pipe flowing natural gas 300 miles with an upstream pressure of 1,000 psig and a downstream pressure of 800 psig (atmospheric pressure 13 psia).

Initial guess: 95747 MCF/d

Pressure at 100 miles: 929.4 psig
Pressure at 200 miles: 853.1 psig
Pressure at 300 miles: 769.4 psig

Reduce flow rate by 5%: 90960 MCF/d

Pressure at 100 miles: 936.6
Pressure at 200 miles: 868.6
Pressure at 300 miles: 794.9

Which is probably close enough for most things, but lets drop flow rate 1% more: 90050 MCF/d

Pressure at 100 miles: 937.9
Pressure at 200 miles: 873.6
Pressure at 300 miles: 801.8

And so forth. My program to break a line into more segments is acting weird, but you get the idea.

David

 

[zdas04]

After most of a day of trying to determine what was going on with my program, I found that I was using a different specific gravity in the whole-pipe version and the segmented pipe version.

Once I fixed my mistake, I found that 1, 3, 30, or 300 segments all gave the same flow rate to 3 decimal places. I don't know if other flow equations would result in the same conclusion (I've always heard that they won't, but I also heard that the AGA equation wouldn't). It is really worthwhile to occasionally test your assumptions.

Interesting exercise, but a major waste of effort.

David

 

[vzeos]

Speedy:
The answer to your question is yes the Darcy equation can be used for gases, however, for large pressure drops you need to compensate for the decrease in density and the increase in velocity as the gas flows.

A good source for fluid properties and other technical information is

http://www.flowoffluids.com/

.

E. sashi Menon is correct although you must take what he says with a grain of salt since he apparently does not understand the difference between the Fanning transmission factor and the Darcy transmission factor (see thread378-178423). This could be a problem for the young engineer since most early work in the gas equations was done using the Fanning equation.

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

http://books.google.com/books?id=Qq...formula"&source=gbs_summary_r&cad=0#PPA438,M1

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, f, use the more modern equations (see faq378-1236 and faq378-1237.)

 

[Speedy]

vzeos,

That's great, very much appreciated.

Cheers,
Speedy