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# Flow rate of N2 with know pressure

## Flow rate of N2 with know pressure

(OP)
I am trying to figure out the flow rate of nitrogen through a 1" line.  I have a high pressure (40 lb) nitrogen flowing in a 1" line.  Can anyone direct me in finding charts that would correlate pressure of a certain line size with expected N2 flow rate.  Or perhaps guidance into pressure and flow rate realtionships.
Here is what I basically did already...but i'm not sure if I am correct, the flow seems a bit too low ??!

Line Diameter : 1 " (.0254 m)
Line Length : 934 "  (28 m)
Volume = L*A = 934*.25*pi*(.0254^2)=.012 m^3

using the Ideal Gas Law :
Mass(kg)
Press (Pa)=40 psi *6894.757 Pa/PSI = 275790.3 Pa
Volume (m^3)=.012
R (Pa.m^3/Kg.mol.K) = 8314.3
T (ambient)(K)= 298
M (Molec. Weight) (Kg/Kg.mol)=28.0134

Mass=[(press*Volume)/(R*T)]*M)=.037 kg

Once I have my Mass, since I don't have two pressures because this 40 lb pressure is constant than can I assume that my mass flowrate to be the mass that I calculated per second ?
if so then it would be .037 Kg/s

and then I would divide this by my density= 1.185 kg/m^3 (at at 1 bar 15 deg C)and this will give me my Volumetric Flow Rate of 0.032 m^3/s

Can anyone tell me if I am doing this accurately or if I am making some mistakes...I am actually a mechanical engineer and havn't had too much experience with the ideal gas law.

sam

### RE: Flow rate of N2 with know pressure

If I understand you correctly, you have a reservoir of Nitrogen at about 2.8 bara with a length of 1" pipe connected that is 28 m long?  If the end of the pipe is open to atmosphere then the pressure at its end will be 1 bara, unless the flowrate is high enough to cause the flow to choke at the end of the open pipe.  The flow will choke if the velocity at the end of the pipe reaches sonic velocity.  The problem is a bit more involved than a simple pressure drop calculation due to the fact that you are dealing with a compressible fluid.  In such situations the velocity and density of the fluid vary along the length of the line as the pressure drops.

Rather than go into a long winded description here I would advise you to refer to the following technical publication:-

Crane Technical Paper No. 410 (TP-410)

This publication has many practical examples that are quite similar to your case.  This publication is available from most technical book shops.  It can also be purchased on line from www.cranevalve.com.  Hope this helps?

### RE: Flow rate of N2 with know pressure

Assuming your pressure is absolute pressure, you seem to have calculated the mass of N2 in the line successfully. This has no relationship to the flow however. As you say you have no pressure drop, you actually imply that there is no flow.

It might help to say what your line goes to and/or where it comes from. Is it flowing freely to the air? Does it feed a piece of equipment running at 40psia? Does it feed a regulator? Is this the branch line off a header?

I think it is cool that mechanical engineers can get some simple help like this in the forum, but you must provide a little more detail. Best of luck, sshep

p.s. most engineers in this forum wouldn't consider 40 psia very high pressure.

### RE: Flow rate of N2 with know pressure

(OP)
Yes...sorry the unclarification earlier.  high pressure 40 PSI is fed into a 1 " line 28 meters (78 ft) long that runs into a neutralizing column which is at atmoshperic.  Well, I think its safe to assume its at atmospheric...the vessel is designed for 15-2 psig but there is a drain line which opens up to the atmosphere...there is mixing in this neutralizer so I assume from the reaction some pressure build up but not significant at all...so I am going to assume atmospheric pressure.

I actually have a copy of 410 and so I will try to look through it.  But SSHEP is correct if there is no pressure drop than that would imply no flow.  So in this case since we are feeding 40 psi nitrogen into a 1" line that runs into a tank at atmospheric...how will this change my calculations.

sam

### RE: Flow rate of N2 with know pressure

There is a small typing error in your formula for the internal volume of the pipe, and the result also shows a small error, 0.012 vs 0.0142.

The estimation of the pipe gas content at the given conditions can be done with the help of tables in a much shorter way.

Tables give:

→  for a 1" pipe sch 40, a flow cross-section of 0.006 ft2 = 5.5742 x 10-4 m2

→  the density of nitrogen at 298 K and 40 psia: 3.1198 kg/m3

Thus the mass contained in 28 m of pipe would be:

28 x 5.5742 x 10-4 x 3.1198 = 0.0487 kg

Kindly recheck my estimates for errors .

For flow under possible critical conditions I suggest you read:

### RE: Flow rate of N2 with know pressure

Sam,

Compressible flow problems can be complex and very frustrating.  Is it isothermal flow, or is it adiabatic flow?  Which one of these two “models” is my “real world” problem closest to?  Is the flow subsonic, choked (sonic), or supersonic?

From my interpretation of what you wrote and did (calculation wise), I can see you need lots of help on this particular problem.  My first advice to you is get someone there that knows chemical process engineering to help you.  If that is not possible, then I have a lot of questions to ask in order to help you:

What schedule is the 1” pipe?  We are after the inside diameter.

On the upstream end of the 1” line, what is the 1” line connected to?  Does it tee into a larger nitrogen supply header at 40 psia?  Is it connected to a pressure vessel with nitrogen at 40 psia?  For the purposes of this problem, can it be considered an unlimited supply of nitrogen, or is it a standard cylinder of nitrogen going through a regulator connected to the 1” line?  In short, what’s the source of the nitrogen?

How long is the 1” line?  You said 934 inches, which is 23.7 meters, not 28 meters.

What type of fittings are in the 1” line and how many are they?  How many valves are in the 1” line?  What types and what size?  How many 90 degree elbows are in the 1” line? How many 45 degree elbows are in the 1” line?  Are there any Y-type strainers in the 1” line?  Is there a control valve in the 1” line?  What size?  What type?  What’s the Cv?  Are there any branch-run tees in the 1” line? Are there any line-run tees in the 1” line?  Is there a check valve in the 1” line?  Is there any other fittings in the 1” line?  Describe the connection of the 1” line to the  neutralizer column.  Does it go into the column below the liquid surface, or into the vapor space?

Is the 1” line insulated?

Are there any controls in place that regulate the flow of nitrogen in the 1” line or downstream of the 1” line?  I don’t know your process, but nitrogen is not inexpensive, and I find it hard to believe that a neutralization column would need a large flow of nitrogen all the time, unless it was also being used as a stripper.

Sorry for all the questions, but these are what came to my mind.

Good luck,
Latexman

### RE: Flow rate of N2 with know pressure

(OP)
I went back through Crane T410 as sugested and found a neat sample problem to the one I am after.  My pipe is schd. 40, insulated and steam traced pipe with a nitrogen source off our main header (unlimited supply)...40 PSI Nitrogen flows through the 24 meter long line to keep the line open and ensure no plugage.

I used the simplified Compressible Flow Formula :

q'h=.01361*sqrt(((p^2-p^2)/(f*L*T*SG))*d^5) and I got a flow rate of about .0726 m^3/s

I also rechecked my work using the Weymouth Formula :
q'h=.00261*d^2.667 * sqrt(((p^2-p^2)/(L*SG))*(288/T)) and I got a flow rate of about 0.0724 m^3/s

I'm pretty sure the problem would get a bit involved if you take into consideration the losses due to pipe and fittings such as bends, valves,branch's but for this particular application I am only after a rough estimate of what the flow rate might be.  I don't anticapate a huge pressure loss since we only have 2 90 deg bends and a 45 deg. bend.  There are no branch T's as this line goes right into the neutralizer...however there is an elevation (about 40 ft) that the line goes through.  But in anycase if my calculations are correct with these minor losses the flow rate I have calculated will be reduced and so I can assume that my flow rate will be less than 0.1 m^3/s

I appreciate everone's input on this particular problem, and any comment to my new calculations and the use of the above (2) equations would also be appreciated.

sam

### RE: Flow rate of N2 with know pressure

I ran your problem on two different, in-house programs.  Of course, they gave different answers, so the range they gave was 770 to 950 lb/hr.  At exit conditions, that comes to 0.082 to 0.099 m^3/sec after conversions.  You got it!

Good luck,
Latexman

### RE: Flow rate of N2 with know pressure

It is stated that the pipe is insulated.  If my memory serves me right, I believe the formula
q'h=.01361*sqrt(((p^2-p^2)/(f*L*T*SG))*d^5)

is for isothermal flow.   Can someone support or critiqe my response?

### RE: Flow rate of N2 with know pressure

Sailoday is right.  Sam said the 1" line was "insulated and steam traced".  In adiabatic flow, the temperature decreases as the pressure drops towards the exit, so if the line was "insulated and steam traced" it may approach isothermal closer than adiabatic.  It depends on how much heat is transferred.  Since heat transfer to a gas is lousey at best, IMHO, it's probably between isothermal and adiabatic.

Good luck,
Latexman

### RE: Flow rate of N2 with know pressure

(OP)
The average temperature in the line is probably around 160 deg C.  It rises to about 190 deg C.  Because of the tracing and insulation, there seems to be minimum heat loss from the pipe to atmosphere.  The line when operating maintains 160-190 deg C.

The nitrogen on the other hand is about atmospheric when fed into this 'hot' line.  Did I make a mistake in assuming constant atmospheric (298 K) temperature for my gas.  Should I have done a heat transfer calculation to find what the temperature of the gas would actually be once in the pipe line ?

sam

### RE: Flow rate of N2 with know pressure

Sam,

If the N2 gets heated up as it flows to the column, the volumetric flow rate will not change much from what was calculated.  The mass flow rate will decrease though as the density decreases.  If you are after a max., you already have it.  The real flow will be less than what you calculated at 25 C, but, yes, you will have to estimate the heat gain if you need a more refined estimate.  You'll have to use an average temperature in the same equation you used, or use an equation that includes the heat gain, which you can find in Shapiro's book titled, "The Dynamics and Thermodynamics of Compressible flow".

Good luck,
Latexman

### RE: Flow rate of N2 with know pressure

Latexman--I'm glad to see some one referencing Shapiro.

Now-you didn't mention that the formulations are in Vol I.

Regards
Sailoday

### RE: Flow rate of N2 with know pressure

Sailoday,

An oversight on my part.  I have both volumes though.

Good luck,
Latexman

### RE: Flow rate of N2 with know pressure

(OP)
Cool...

I will refine my calculations with the input you all have contributed.  By the way, I want to than you all, its really great to have technical support such as this.

Thank you all once again, and I will definately have to get my hands on a copy of Shapiro's...sounds like a useful resource.

cheers,

sam

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