Average pressure in gas pipe
Average pressure in gas pipe
(OP)
Hi Firends,
This is my first post. Please tell me if made any mistake in the explanation of my problem.
There is a high pressure gas pipe of uniform CSA - fixed installation - carrying nitrogen from a cylinder to nozzle. I need to calculate the average pressure in a certain section AB of the pipe. The parameters that I have in hand are:
* The pressure at both the ends of section AB
* Temperature of the gas
* Design flow rate through the section AB
I assume that the average pressure is simply the average of the pressure at the two ends. I am a beginner in this area. So I am not sure if my assumption is correct. When I googled, I saw how to calculate the average pressure inside a container, but I think that would not suit my case.
Your advice on this is greatly needed.
TIA,
Caddy
This is my first post. Please tell me if made any mistake in the explanation of my problem.
There is a high pressure gas pipe of uniform CSA - fixed installation - carrying nitrogen from a cylinder to nozzle. I need to calculate the average pressure in a certain section AB of the pipe. The parameters that I have in hand are:
* The pressure at both the ends of section AB
* Temperature of the gas
* Design flow rate through the section AB
I assume that the average pressure is simply the average of the pressure at the two ends. I am a beginner in this area. So I am not sure if my assumption is correct. When I googled, I saw how to calculate the average pressure inside a container, but I think that would not suit my case.
Your advice on this is greatly needed.
TIA,
Caddy





RE: Average pressure in gas pipe
delta P/g + 1/2 velocity ^2/g + height = constant
Thus, to have flow thru a horizontal pipe (height = 0) of constant cross-sectional area, velocity of the fluid is related to pressure drop and density of the fluid.
Since you have the delta P, the average pressure over the length of section AB would be (Pa + Pb)/2
RE: Average pressure in gas pipe
I was not quite sure if the average of the terminal pressures will give the average pressure in the pipe. Since the system involves high pressure, I thought, the change in pressure over the length of the pipe might be non-linear and hence some complicated formula might be involved in the calculation. Thank you for the reply.
Regards,
Caddy
RE: Average pressure in gas pipe
IF the losses are however reasonably small you can neglect the effect I've just described and use the approach you asked about.
RE: Average pressure in gas pipe
We're assuming you don't have a shock wave in the section in question, in which case, you'd have big variations in pressure.
RE: Average pressure in gas pipe
Shock waves are not a concern because the calculations are for the system in steady-state. Moreover the system does not have an external source to feed it other than its own nitrogen cylinders.
As TD2K said, I was concerned how the plot of pressure loss versus the distance from the inlet would look like. If the effect of temperature is neglected, I think the plot will be a straight line(I am not sure, though). Then one could use the average of the end pressures as the average pressure of the section. Otherwise the formula must be modified based on the shape of the curve.
The length of the pipe section could vary from just a few feet upto about 200 feet. I needed the average pressure to calculate the average density of the gas in that section. Since the pressure loss for longer pipe sections are not negligible, I thought it might be appropriate to clarify my approach to find the average pressure.
RE: Average pressure in gas pipe
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RE: Average pressure in gas pipe
Pavg=(2/3)*(P13-P23)/(P12-P22)
This equation is quite common in the natural gas industry, especially in the natural gas transmission field.
About 25 years ago, I looked up the original paper that introduced the Weymouth equation. I found that Prof Weymouth also derived the average pressure equation in the same paper. I guess you can call this the Weymouth Aerage Pressure equation . (If anyone is interested, the reference is: Problems in Natural-Gas Engineering: Trans. Am. Soc. Mech. Eng., vol. 34, 1912, pp 185-206.)
RE: Average pressure in gas pipe
Interesting information. Here is another equation that was referenced by AGA and generally accepted for determination of average pressure in a pipe, which accounts for non-linearity of pressure drop over distance;
Pavg = 2/3[P1+P2 - (P1*P2)/(P1+P2)]
RE: Average pressure in gas pipe
Are the both end pressures measured?
OR is one pressure measured and the other calculated--If so, what formulas/assumtions are used for the calculation?
Are the temperature measured or calculated--If calculated what formulas, etc?
RE: Average pressure in gas pipe
I have seen that equation before. Although I have not done the algebra in a long time, I believe that they can be shown to be algebraically equal.
RE: Average pressure in gas pipe
a3-b3 = (a-b)(a2+ab+b2)
So, (P13-P23)/(P12-P22) = (P1-P2)(P12+P1P2+P22)/(P1-P2)(P1+P2) = (P12+P1P2+P22)/(P1+P2)
So the algebraic sign of P1P2 should be + rather than -
I wish I had the paper with me.
Regards,
RE: Average pressure in gas pipe
If you multiply and divide the right-hand side of the equation metengr wrote by (P1-P2) then you will come to the equation RGasEng has written.
Thank you everybody for the posts. Since the result of average pressure calculations are used for further calculation of other parameters of the system, I wanted it as precise as possible and at the same time trying to not go beyond what is needed. Since the latest equation cares for non-linearity also which is exactly what I was looking for and also is an accepted standard practice in the industry I am very happy.
RE: Average pressure in gas pipe
RE: Average pressure in gas pipe
Metengr's formula for the average has apparently been evaluated at 4/3 the arithmetic average less 1/3 the harmonic average between P1 and P2, as follows:
RE: Average pressure in gas pipe
Thanks in advance.
RE: Average pressure in gas pipe
To quark,
I got the results I mentioned by playing around with metengr's formula, having noticed the arithmetic mean (AM) and the harmonic mean (HM) of P1 and P2 are both involved.
The average pressure I found = 4/3(AM)-1/3(HM) may be (I'm hypothesizing) the result of applying numerical methods such as the trapezium rule or Simpson's rule to treat either experimental results or a friction drop formula and its curve.
RE: Average pressure in gas pipe
For the operating ranges usually encountered in transmission practice; i. e., pressures below 1000 psia and temperatures of 60° F or higher, the variation of z with P is nearly linear, so that the compressibility factor may be represented by a function of the form
Z=1/(1+aP)
where a is a Constant dependent on T. The mean pressure (Pm) which must be used can be determined as follows:
(1/Zavg)∫P1P2 PdP = ∫P1P2 (P/Z)dP
or
(1+aPm) ∫P1P2 PdP = ∫P1P2 P (1+aP) dP
Upon integration
(1+aPm)(P1 2 - P2 2)/2 = (P1 2 - P2 2)/2 + a(P1 3 - P2 3)/3
or
Pm = 2/3(P1 2 - P2 2)/( P1 3 - P2 3)
If full integration of the general energy balance is desired, however, for the sake of extreme accuracy or where a computer program is involved, the variation of P and T and the consequent variation of z along the line can be accounted for by graphical or numerical techniques. Graphical integration could be effected by plotting P/ZT against P, and subsequently determining the area under the curve between the initial and terminal values of P. An additional possibility would involve the use of an analytical or virial equation of state.
RE: Average pressure in gas pipe
Last equation should be:
Pm = 2/3(P1 3 - P2 3)/( P1 2 - P2 2)
RE: Average pressure in gas pipe
(1/Zavg)?P1P2 PdP = ?P1P2 (P/Z)dP
Isn't the mean pressure the integaral of Pdx (limits x1 and x2) divided by x2-x1 where x is the length ?
RE: Average pressure in gas pipe
I don’t know why you would introduce length in calculating the average pressure. I don’t mean to be sarcastic, BUT(
RE: Average pressure in gas pipe
If the pressure distribution is integrated over the length,
the resulting units are pressure*length units. If one divides by a length the resulting units are in terms of pressure. ---The mean pressure--
RE: Average pressure in gas pipe
You are indeed correct….. I did my last calculus more than 30 years ago, so I may not be of much help to you. I think to do what you are suggesting you need to specify P as a function of x before integrating. You could probably use the flow equation as your pressure distribution function but one purpose of evaluating the average pressure is to plug it into the flow equation to correct for elevation. I don’t know if your method would make this any easier.
RE: Average pressure in gas pipe
RE: Average pressure in gas pipe
I have seen some of your posts on heat transfer and I have learned a great deal from them. I also saw your prior post in this thread and paid it little attention to it because it did not contribute to the original subject. I always try to help when I can but allow me to suggest respectfully that if you require answers to your questions or if you wish to pursue tangential issues you should start new threads.
RE: Average pressure in gas pipe
I assume that the average pressure is simply the average of the pressure at the two ends. I am a beginner in this area. So I am not sure if my assumption is correct."
I am under the impression that you now agree that the avg or mean pressure involves integration of pressure over length. Further to have the pressure distribution,one then can use the formulas and assumptions used in obtaining end pressures. Where are the tangential issues?
Respectfully
soday28
RE: Average pressure in gas pipe
at the first stage, it is right the average of the two ends.
But, that can change if there is:
- temperature variation
- Speed variation
- Pipes dimension variation (bends or ventury parts)
- modification of the nitrogen.
the is no statistics on that. We can have an exact calcul.
RE: Average pressure in gas pipe
RE: Average pressure in gas pipe
There really is no way to insert equations per se. The equations that you see are formatted text. Eng-Tips uses the TGML compiler to format text. If you look at the bottom of the reply box, you'll see a check box that says Process TGML. Leave the check box checked but click on Process TGML. You'll get a menu of TGML formats. Formatting text is similar to writing computer code; just follow the rules and it gets easier with practice. In most cases you can copy and paste the format examples and insert your text. As an example, I formatted the Colebrook equation below to show what it looks like before and after it is processed. Note, in the before posting example, I substituted | for [ for illustrative purposes so that the TGML compiler would not process the formatting code.
Colebrook Equation before posting
1/|√]f= -2Log{(k|sub]e[/sub]/3.7D)+(2.51/N|sub]Re[/sub])(1/|√]f)}
Colebrook Equation after posting (replacing | with [ )
1/√f= -2Log{(ke/3.7D)+(2.51/NRe)(1/√f)}
RE: Average pressure in gas pipe
1/v= P(1+aP)/RT
For isothermal process dP/v= P(1+aP)/RT dP (****)
integral of dP/v from P1 to P=
1/(RT)[ P^2/2+aP^3/3 ] (%%%%%)
Mean pressure
u velocity, x distance p pressure f friction factor
v specif volume D diameter G mass flux flow/unit area
subscirpt 1 conditions at pipe inlet
Dynamic eq. of motion
udu/dx + v dp/dx +fu^2/(2D)=0 (1)
conserv. of mass u=Gv (2)
Divide (1) by U^2 and substitute (2) into (1)
du/u + 1/v(G^2) dP +fdx /(2D) =0 (3)
after multiplying by dx
du/u from (2)= dv/v
and (3) upon integration with f a constant becomes with substitution of (%%%%%) becomes
ln (v/v1)+1/(RTG^2 [P^2/2-P1^2/2+aP^3/3-aP1^3/3
+ f(x-x1)/2/D=0 or
-ln[p(1+aP)]-ln[p1(p11+aP1)]
+1/(RTG^2 [P^2/2-P1^2/2+aP^3/3-aP1^3/3+ f(x-x1)/2/D=0
The above is difficult to solve for P vs x.
However pick P substitute and get x
Use numberical integ and mean pressure may be obtained.
Hopefully others will check for algebraic mistakes in above formulae.
RE: Average pressure in gas pipe
I'm a little too rusty to check for algebraic mistakes. But one question: How do you deal with a ?
RE: Average pressure in gas pipe
To deal with a, there are charts of Z vs. reduced pressure (P/Pcritical) with reduced temp T/Tcritical as a varying parameter.
For 0<Reduced pressure< from 0 to about 0.8
along a constant reduce pressure line, the curves seem to be fairly straigt with a negative slope, ie "a" is minus
Reference, for example Gouq-Jen Su, Ind. Eng. Chem., 38, 802 (1946)
This refernce inclues Nitrogen Methane, Ethane, Ethylene Propane, n-Butane, Isopentane, n-Heptane, CO2, H20 AND
Reduced isotherms of 1, 1.1, 1.2, 1.5 and 2.
Regards
RE: Average pressure in gas pipe
Sorry for the late reply to your post on the 25th. I was trying to familiarise myself with the equations and calculations related to pressure. I think it might take me ages to learn them all.
Pressure at the inlet and density of the gas at the inlet are known. The flow rate of the gas is assumed to be constant and the value of flow rate is also available. Temperature is also assumed to be constant(Room temperature). I used the Darcy-Weisbach equation to calculate the exit pressure of the pipe.
With the above data in hand, I needed the average pressure in order to calculate the average density of the gas in the pipe section(Average density is needed in the Darcy-Weisbach equation). Since average pressure is dependent on the end pressures, one of which is already known, the Darcy-Weisbach equation will contain only one unknown(the other end pressure), and can be solved for that unknown. This was my theory.
But I did not realise that the compressibility of gas will make things so complicated. I need to mention that the nitrogen cylinders are custom-made high pressure nitrogen cylinders(usually 3000 psi, but sometimes upto to 4500 psi). I think even the sophisticated equtions of state are not suitable for this kind of situation(Please correct me if I am wrong). I am reading through books to see if there is some way out. If anyone could help
RE: Average pressure in gas pipe
I suggest looking into equations of state (eos)which are valid in the approximate range of temperatures and pressures of your interest.
Then the flow equations will have to be numerically solved--if the eos is to cubersome to handle with regard to integration, etc.
RE: Average pressure in gas pipe
What will your actual temperature range be?
RE: Average pressure in gas pipe
pg 34-36 illustrates Z vs P for N2. In the temp/press ranges that are specified, it appears that a linear curve fit is applicable with "a" being positive.
RE: Average pressure in gas pipe
See thread687-127478 (4 Jul 05 17:59), the ALLPROPS program may interest you. You can calculate compressibility factors.
RE: Average pressure in gas pipe
With reference to
The IR Compressed Air and Gas Data 2nd Ed. 5th printing
in the range of 3000-5000psi, and room temperature, the compressibility can be approximated in the form
Z=ap^2+bP +c
Substiture into pv=zRT and solve for v
v=RT(ap+b+c/P)
Referring to my previous posts relating to the integral of v*dP or integral of RT(ap+b+c/p)dp
which yields RT(ap^2/2+bp+c ln(p) [you must include limits of upstream and downsteam pressures].
If further info is needed contact me at sailoday_28@yahoo.com