Compressible Flow - Pressure Drop Calculation

[jobarrco]

Hello,
I'm not a fluids guy... but I need to determe the pressure drop of a natural gas supply line.

The line size is fixed - 2 inches. I'm trying to flow 47,100 ft^3/hr (1,2627 lb/hr) with an inlet pressure of 94.7 psia.
After a few calcs the mach number at the inlet is .411.

I'm a little lost on the theory now. I used the Fanno flow equations and determined the flow is choked.
L* = 2.77 ft <<< Normal shock at 2.77 ft?
P* = 60.4 psia
V* = 1378 ft/sec <<< the initial velocity increased to 1378 ft/sec? but constant mass flow rate = change in density?

So now I know the conditions at L*... how do I determine the conditions at L = 150 ft?

I have the Crane TP410 - I'm not sure it is useful for this problem though.
If anyone can recommend any other books, that would be helpful too.

I searched the forum and found a reference to another thread that describes compressible flow, but had no luck finding it.

Thank you!

 

[vpl]

Crane Technical Paper 410 is what I would normally recommend. It has the formulas you need and it has example problems in Section 4.

Is this the gas supply to your house?

Patricia Lougheed

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[jobarrco]

The supply is for a bank of natural gas engines. I would cry if my house used that much natural gas.. The bill would be outrageus

Section 4 is about measuring flow with differential pressure meters..
After re-reading the "Principles of Compressible Flow in Pipe" section I think equation 1-29 is what I am after - however the Fanno flow/choked flow is perplexing to me.
I think I'll give the guys at Crane a call and discuss it with them.

 

[BigInch]

Natural gas pipeline, or plant pipe supply lines do not flow at mach numbers!
What kind of system are you trying to design.

For that flowrate (assuming reasonabe pressures) in plant piping I would say you need at least a 4" pipe diameter, for which you will lose about 2 psi/100 ft.



If it ain't broke, don't fix it. If it's not safe ... make it that way.

 

[vpl]

Sorry about the assumption, I was going by the pipe diameter size; 2" just seemed too small for most applications. Don't just go off the first example in Crane, again it is a good reference for your situation.

Patricia Lougheed

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[GHartmann]

If you have the newest Crane 410, the flow examples are now in Chapter 7. The closest one I see to your situation is example 7-18.

The Fanno flow analysis assumes adiabatic conditions (short pipe) ; whereas the equation 1-29 in Crane 410 assumes isothermal (long pipe lines)

See this article:

http://www.lmnoeng.com/Gas/choke.htm

You can make your life more simple by using the various Darcy equations using your inlet conditions and calculate dP per 100 ft of pipe (as Big Inch suggested). That is a simple way to size lines and avoid the complicating calculations.

In any case, I would agree with Big Inch that your 2" line is a bit small for the nominal 80 psig supply pressure.


One thing for sure, this new version of Crane (2011) is sure different from the one I use (1965).

 

[BigInch]

I find this online gas flow calculator easier to use.

http://www.freecalc.com/gasfric.htm

You can use the Darcy equation. For compressible flow, break up the line into segments short enough such that the pressure drop is less than 10% of the inlet pressure to each segment.

If it ain't broke, don't fix it. If it's not safe ... make it that way.

 

[Latexman]

Is your "exit" 150 ft. of pipe away from the inlet? If not, how far? Any other fittings in the flow path? What pressure is needed at the "exit" to run the engines? Then the diameter can be calculated.

Good luck,
Latexman

 

[jobarrco]

Thank you all for the responses!

A little more detail may clarify the use of a 2" line. The line is a hose. As it turns out, it is difficult to find hoses rated for natural gas (other than CNG which is only available up to 3/4" or so). The 2" hose is the largest available - without giong to stainless hose.
There are no other fittings in the hose. The outlet is 150 feet from the inlet.
A hard pipe of a larger diameter would be ideal, but not practical.

The "exit" presssure needs to be approximately 50-60 psi. It runs into a manifold with other tees. I already have all of the calculations complete for the manifold.

Basically, since it looks like I cannot flow what I need through a 2" hose 150 feet long, I will need to specify that the hose is shorter.


BigInch, that was going to be my next question - so you can use the darcy equation if you break it up into shorter sections. Simply use the density, etc. after said increment? Dacry-FEA. Haha

Thanks again for all the input. This is my first time posting and am very impressed!

 

[jobarrco]

Just FYI, the guys at Crane responded to my question and said the isothermal equation or modified Darcy equation will give me the most accurate results.

I did ask him about breaking the pipe up into sections and using the Darcy equation, as BigInch suggested. I'll let you know what the answer is.

 

[Latexman]

3 x 150 ft. hoses will do the full job.
As will 2 x 60 ft.
As will 1 x 6 ft.

Good luck,
Latexman

 

[BigInch]

Breaking up into segments to keep pressure drops < 10% is to account for the change in compressibility factors over each segment. Gas properties are first assumed constant at an estimated average pressure & temperature for a segment, the outlet conditions are calculated and based on that result, the averages are then recalculated and verified or a different compressibility factor is selected for the next calculation.

Depending on flow, diameters, pressures, temperature and gas gravity, there are other equations that account directly for compressible flow over longer lengths and higher pressure drops which are available, but the Q,D,P, T, Re, L and product property parameters must be within the validity range of the equations used. See Panhandle formula, AGA, Weymouth. They are for long distance transmission pipelines containing transmission quality natural gas, so they are not suitable for small diameter, short pipe lengths.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[davefitz]

Nowadays it should be a simple matter to program the calculation so as to be able to break the pipe into 100+ segments, but thtat could be avoided by use of the Darcy equations.

There may be other practical issues with the system design described above. At a starting velocity of M=0.4 there are going to be noise and vibration issues. And process control of the fluid during transients is going to be an issue as well. A better design might be to use a solid 4" line ( with block valve) routed close to the consumer and then a 4" header with 3-4 flex hoses to allow for pipe flexibility reactions- but you must observe all OEM restricitons listed for proper configuration of flex piping.

 

[BigInch]

Using Darcy still won't avoid splitting the segments into lengths small enough so that the compressibility factor, density, viscosity, velocity, etc. can all be assumed constant in any given section, unless you are willing to accept the errors generated by their variations. At low pressures and temperatures and a short length of pipe, maybe that won't mean much, but at high pressures and temperatures, breaking it down into short segments will avoid what could be some very large errors.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[jobarrco]

Breaking the pipe up in to many segments will be simple.. Matlab can handle that. Thanks again.

 

[GHartmann]

Don't forget that you won't get very far. As stated by Latexman, you will only need 6 feet of 2" pipe/hose to use up your available pressure drop.

 

[BigInch]

I'll bet the line size will start to change .... now.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek