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# Maximum Natural Gas Flow Through Orifice

natural gas fluid flow

20 replies to this topic
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### #1 ukrche

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Posted 10 May 2024 - 08:23 AM

Hello everyone,

I would like to answer the question of what the maximum volumetric flow of natural gas is theoretically possible given the conditions. For some context, a control valve on a natural gas feed line was upsized with the assumption that the valve was the constraint of flow in the system. After the valve was replaced to one of larger size, the maximum flow has shown to be less than before on a smaller control valve. The new valve design included an orifice plate downstream of the valve which is the suspected restriction.

To simplify the problem at hand, I would like to calculate the maximum flow possible on the outlet side while completely ignoring this upsized valve and orifice plate. This would rule out that the valve is the restraint and hopefully provide some understanding of the limits of the system.

The feed natural gas line is a six-inch pipe that distributes the flow to 18 one-inch diameter holes. Initially, I attempted to model this scenario as a nozzle in SolidWorks, where the inlet is the six-inch diameter feed at 165 psig, 70F that converges to an outlet with the sum of cross sectional area of the 18 outlet holes. The outlet condition was that the environmental/surrounding pressure is 35 psig. The simulation did not run- stating that the velocity of flow was supersonic. This in turn led me to believe that the problem could be answered by assuming compressible fluid choked flow. I used a Purdue question as a resource (https://engineering....zle_Reading.pdf), but the mass flow of the natural gas was 560.4 kg/min which then converted to 32,980 cf/min. This flow is high and I am not sure if my calculation is correct. The goal is to answer if 20,000 cf/min of natural gas is possible to be discharged on the outlet side. In this problem- I am excluding any major and minor losses, just to be able to answer what is the maximum discharge flow of NG out of these 18 holes, and does it exceed 20,000 cf/min.

I hope that sheds some light on this case. I will clarify what I can if I missed parts. Please guide me on what tools to use to answer this problem.

Thank you!

Sincerely,

ukrche

### #2 Pilesar

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Posted 10 May 2024 - 08:46 AM

The source conditions are well defined. Input the flowrate to your system and determine what the outlet pressure would be. If the outlet pressure is above 35 psig, then all is well. There will be convergence problems if you also specify the outlet pressure... some parameter must be allowed to float. A little trial and error to adjust the flowrate may be needed to get above the 35 psig outlet constraint.

Edited by Pilesar, 10 May 2024 - 08:48 AM.

### #3 latexman

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Posted 10 May 2024 - 09:37 AM

More details = better replies.  A well dimensioned and labelled sketch would have been nice.  Click "More Reply Options" or "Use Full Editor", and the file attachment functions are under the text box.  Some questions I have are, is the CV upstream or downstream of the 165 psig source pressure?  What's the spacing between the 18 1" holes in the 6" pipe.  Is the CV close or far away from start of the 1" holes?

As a first pass, calculate the flow thru a 1" hole (C ~ 0.6) with dp = (165 psi upstream - 35 psig downstream), then multiply that flow x 18.  Is that > 20.000 cfm?

### #4 ukrche

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Posted 10 May 2024 - 10:45 AM

More details = better replies.  A well dimensioned and labelled sketch would have been nice.  Click "More Reply Options" or "Use Full Editor", and the file attachment functions are under the text box.  Some questions I have are, is the CV upstream or downstream of the 165 psig source pressure?  What's the spacing between the 18 1" holes in the 6" pipe.  Is the CV close or far away from start of the 1" holes?

As a first pass, calculate the flow thru a 1" hole (C ~ 0.6) with dp = (165 psi upstream - 35 psig downstream), then multiply that flow x 18.  Is that > 20.000 cfm?

CV is downstream of 165 psig source pressure, so the pressure after the valve will be lower. The pressure drop will be dependent on the valve position as well that is why I am just ignoring the CV for now to find the max flow rate at the discharge. The 6" line feeds an 8" line that necks down 18 times to 18 1.5" lines that each neck down to 1". I would say the CV is relatively far away from the 1" holes.

I'm getting roughly 0.3 cfh for one 1" hole using Weymouth and AGA equations. Something doesn't seem right to me... not even one cubic foot per hour?

#### Attached Files

Edited by ukrche, 10 May 2024 - 01:43 PM.

### #5 latexman

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Posted 10 May 2024 - 01:51 PM

pi x 62/4 = 28 in2

18 x pi x 12/4 = 14 in2

The 1" holes should be most restrictive.

First pass, I'd calculate the upstream pressure needed to flow 1111 cfm thru a 1" orifice (C~0.6) with 35 psi backpressure.  If that upstream pressure < or << 165 psi, it'll probably work?

Tools?  I'd think Aspen+ or HYSYS could do it, but it'd be painful.  My company has an old DOS program that could solve it pretty easily, but that's proprietary.  I don't know other software on the market that could do it.  Maybe others will come along and recommend some.

### #6 snickster

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Posted 13 May 2024 - 01:29 AM

There are a lot of factors involved but I calculate that the maximum possible flowrate at the exit of the 1" at the terminal point, assuming 35 psig pressure at the terminal point, is anywhere between 30,000 to 50,000 SCFM assuming that there is sonic velocity at the terminal point of the 1" lines.  The lower value assumes flow just reaches sonic at the terminal point, the higher value assumes no friction loss at all in the piping and there is an isentropic expansion from 165 psig to sonic coditions at the terminal of the 1" lines such that the 1" pipe exit pressure is about 0.5 x (165 +14.7) psia.  The actual case is likely much closer to the lower value since there likely considerable pressure drop if 1" lines are long.

In any pipe the maximum flow possible is sonic velocity which always occurs at the exit or at the connection of a smaller pipe to a larger header.

You can calculate if sonic velocity will exist for a given flow rate using the ideal gas equation PVA=mRT

where

P is the pressure at pipe exit

V is sonic velocity SQRT(gkRT),

A is the outlet area of pipe

m is the mass flow rate

R is universal gas constant

T is the sonic flowing temperature

All must be in consistent units.

If the calculated pressure is below the exit terminal pressure than the flow is subsonic and the pressure at the exit is the terminal pressure.  If the calculated pressure is equal to or above the terminal pressure the flow is sonic and the actual pressure at the exit of the pipe just inside the tip is the pressure calculated.

Once you get the terminal pressure then you work backwards doing a pressure drop calculation all the way to the 6" header at the location of your control valve.  If the pressure calculated with friction loss is equal to your source pressure (165 psig) then the flow will be as you calculate with your assumed flow.  If it is less than your source pressure then the flow will be greater until it reaches a point where the pipe exit terminal pressure plus back pressure equals your source pressure.  If the pressure you calculate is more than your source pressure your actual flow will be less than you first assumed.

If you give me details of your system I can do a more thorough check of maximum flow - lengths of lines, wall thicknesses, materials, or any other details required for a hydraulic analysis.

Edited by snickster, 13 May 2024 - 01:35 AM.

### #7 latexman

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Posted 13 May 2024 - 06:04 AM

Hi Snickster,

What tool do you use for high speed, compressible flow?  Just curious.

### #8 breizh

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Posted 13 May 2024 - 07:11 AM

Hi,

You are not generous! At least you should provide minimum data on your stream. starting with the composition to get access to Molecular weight and  Compressibility factors for your condition (P,T) then easy to get the density of the NG at (P,T). I will use an EOS , for example PR

2nd step : I will calculate the conditions for  the NG at the outlet to reach  choked condition i.e max Mass flowrate

P upstream/P downstream  >  [(k+1)/2 ]^ (k/(k-1)) ?

3rd step: From there I will define the min and max condition on Pressure to reach choked flows

4th step : at those conditions I will calculate the mass flowrates ( equations in the PDF)  for 1" nozzle or for 18 nozzles to get your answer.

I let you the math.

Volumetric flow rate [ 18000 to 55000 )SCFM  for methane , P upstream ( 6.3 to  12.4) bars abs, the difference is due to head loss mainly due to Cv + orifice to still operate under choked flow.

Breizh

### #9 snickster

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Posted 13 May 2024 - 03:07 PM

Latexman.

I always did mostly hand calculations and excel spreadsheet calcs, for just general piping compressible flow and relief systems calculations.

Edited by snickster, 13 May 2024 - 03:08 PM.

### #10 snickster

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Posted 13 May 2024 - 03:38 PM

Without any further information available I have thought over your system and have the following observations:

It appears that what this is is a gas burner distribution system with very short 1" takeoffs from the 8" header that develop very little friction pressure drop.  The 6" and 8" headers are also relatively short and also produce small frictional pressure drops.  In such case the CV was producing the major pressure drop to control the flow to the burner.  I assume the pressure in the burner vessel is the 35 psig you mentioned which is the pressure at the exit of each 1" outlet.

In the original installation with the smaller valve, the valve was too small to pass the required flowrate even when wide open.  The pressure at the outlet of the 1" is 35 psig and with some friction loss and expansion to higher velocity between 8" and 1" pipes the pressure in the 8" would run a little higher, say 50 psig just for a guess.  With 50 psig in the 8" and basically 6" too downstream of the original control valve flow across the CV orifice was at sonic flow, with 165 psig upstream in accordance with predicted sonic flow occuring when:

P upstream/P downstream  >  [(k+1)/2 ]^ (k/(k-1))

So even with valve wide open the flow through the valve orifice was at choked sonic flow at a flow value lower than required.

A new larger valve was installed to increase the flow capacity of the valve.  However at the given flowrate the pressure drop in the 8" and 6" just downstream of the CV would have still be about 50 psig as the flowrate is what produces the backpressure from the 1" outlet to the location of the CV.  Therefore the person who designed the arrangement installed a restriction orifice plate to induce a pressure drop in order to maintain a backpressure on the CV so that the CV operates in the subsonic flow range.  This was done to make the CV operate in a good controllable range at about 70 to 80 open under full flow conditions under sub sonic flow through it's port.

However it appears that the sizing of the restriction orifice did not take into account that sonic flow would now be present in the bore of the restriction orifice and therefore the flow would be choked in the orifice itself limiting the flow, regardless of having a larger CV.  So the restriction orifice bore is too small and need to be resized considering that there will be choked sonic flow developed in the orifice itself which will limit the flow predicted if subsonic flow was assumed in the restriction orifice.

Edited by snickster, 13 May 2024 - 03:41 PM.

### #11 ukrche

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Posted 21 May 2024 - 06:04 PM

Without any further information available I have thought over your system and have the following observations:

It appears that what this is is a gas burner distribution system with very short 1" takeoffs from the 8" header that develop very little friction pressure drop.  The 6" and 8" headers are also relatively short and also produce small frictional pressure drops.  In such case the CV was producing the major pressure drop to control the flow to the burner.  I assume the pressure in the burner vessel is the 35 psig you mentioned which is the pressure at the exit of each 1" outlet.

In the original installation with the smaller valve, the valve was too small to pass the required flowrate even when wide open.  The pressure at the outlet of the 1" is 35 psig and with some friction loss and expansion to higher velocity between 8" and 1" pipes the pressure in the 8" would run a little higher, say 50 psig just for a guess.  With 50 psig in the 8" and basically 6" too downstream of the original control valve flow across the CV orifice was at sonic flow, with 165 psig upstream in accordance with predicted sonic flow occuring when:

P upstream/P downstream  >  [(k+1)/2 ]^ (k/(k-1))

So even with valve wide open the flow through the valve orifice was at choked sonic flow at a flow value lower than required.

A new larger valve was installed to increase the flow capacity of the valve.  However at the given flowrate the pressure drop in the 8" and 6" just downstream of the CV would have still be about 50 psig as the flowrate is what produces the backpressure from the 1" outlet to the location of the CV.  Therefore the person who designed the arrangement installed a restriction orifice plate to induce a pressure drop in order to maintain a backpressure on the CV so that the CV operates in the subsonic flow range.  This was done to make the CV operate in a good controllable range at about 70 to 80 open under full flow conditions under sub sonic flow through it's port.

However it appears that the sizing of the restriction orifice did not take into account that sonic flow would now be present in the bore of the restriction orifice and therefore the flow would be choked in the orifice itself limiting the flow, regardless of having a larger CV.  So the restriction orifice bore is too small and need to be resized considering that there will be choked sonic flow developed in the orifice itself which will limit the flow predicted if subsonic flow was assumed in the restriction orifice.

Snickster,

Your analysis of the system is correct in its entirety. It's impressive! Sizing of the restricting orifice was increased, and I am seeing similar flow to the prior maximum on the 4" CV but it is still shy about 800 cfm. Also, I was able to tap the line downstream of the orifice and it reads about 135 psig. Now the control valve was not entirely open at this time, so I take it with a grain of salt. I am trying to solve the question by using the book "Flow of Fluids through valves, fittings & pipe - Crane" as a resource. I am still having some difficulty coming to an answer that makes sense to me. For example, I solved the problem 7-21 in the book, but with conditions that match my scenario. If assuming that the feed pressure is 165 psig, ignoring the CV and orifice plate altogether, then the answer came to about 1440 cfm per 1" hole. I didn't account for any constrictions/expansions in between the 6" feed and the single 1" discharge, but the answer still appears to be too high of flow than what I would expect. That would be 26,000 cfm if multiplying by the 18 holes if the answer was true.

Also, I am attaching an image of what the multi-orifice plate was months before and the current. I'm sure that geometry plays a role when calculating this, so I will not even attempt doing that. I was thinking of installing a pressure gauge at the 1.5" line, and calculating from there to shorten the system. What do you think of this idea?

Thanks for your willingness to help me understand. I want to know how to answer this myself more than just knowing the answer, although I do want to know the answer.

Sincerely,

ukrche

#### Attached Files

Edited by ukrche, 21 May 2024 - 06:06 PM.

### #12 ukrche

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Posted 21 May 2024 - 07:06 PM

Hi,

You are not generous! At least you should provide minimum data on your stream. starting with the composition to get access to Molecular weight and  Compressibility factors for your condition (P,T) then easy to get the density of the NG at (P,T). I will use an EOS , for example PR

2nd step : I will calculate the conditions for  the NG at the outlet to reach  choked condition i.e max Mass flowrate

P upstream/P downstream  >  [(k+1)/2 ]^ (k/(k-1)) ?

3rd step: From there I will define the min and max condition on Pressure to reach choked flows

4th step : at those conditions I will calculate the mass flowrates ( equations in the PDF)  for 1" nozzle or for 18 nozzles to get your answer.

I let you the math.

Volumetric flow rate [ 18000 to 55000 )SCFM  for methane , P upstream ( 6.3 to  12.4) bars abs, the difference is due to head loss mainly due to Cv + orifice to still operate under choked flow.

Breizh

I appreciate you sharing the paper. Thanks!

Composition I am making assumptions because I do not know them. About 95% Methane and 5% Ethane. k=1.29 and a molecular mass of 20.

2nd step: I am unsure of what upstream pressure to use. I assumed 165 psig upstream like mentioned in the first post. This ratio for me came to be 5.5 which is >> than 1.826

3rd step: How to find the min max of pressure for choked flow?

4th step: I obtained a mass flow rate of 1.04 kg/s. Still- I am unsure of how to convert this mass flow to a volumetric flow. Obviously T and P play a role, but I do not know the pressure? It cant be the 35 psig.

### #13 snickster

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Posted 21 May 2024 - 08:17 PM

ucrche

I will need to digest your latest post and will post a reply probably tomorrow.

### #14 snickster

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Posted 21 May 2024 - 08:32 PM

I have some questions.

The valve you show is the control valve I assume.  Who is the manufacturer?  The diffuser plate at the outlet is what you refer to as the orifice which maintains a backpressure on the valve and there are no other orifice plates downstream of the valve? So this control valve looks like a butterfly valve?  It is 6" nominal size?

Where are you measuring the 135 psig downsteam of the valve?  How far downstream from the diffuser plate are you taking the measurements of the pressure?

When you say you are still 800 CFM short do you mean you are 800 CFM of the 20,000 CFM or at maximum flow of 19,200 CFM?  So you are flowing a maximum of 19,200 CFM with the control valve basically fully open?

How long are the 1" take offs from the 8" header pipe?

Edited by snickster, 21 May 2024 - 08:37 PM.

### #15 breizh

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Posted 21 May 2024 - 10:17 PM

Hi,

A set of calculators to support your work:

CheCalc ‐ Fluid Flow

A few documents about compressible flow and orifice , Natural gas equations

You may need some time to absorb the documents.

Breizh

### #16 ukrche

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Posted 21 May 2024 - 10:51 PM

I have some questions.

The valve you show is the control valve I assume.  Who is the manufacturer?  The diffuser plate at the outlet is what you refer to as the orifice which maintains a backpressure on the valve and there are no other orifice plates downstream of the valve? So this control valve looks like a butterfly valve?  It is 6" nominal size?

Where are you measuring the 135 psig downsteam of the valve?  How far downstream from the diffuser plate are you taking the measurements of the pressure?

When you say you are still 800 CFM short do you mean you are 800 CFM of the 20,000 CFM or at maximum flow of 19,200 CFM?  So you are flowing a maximum of 19,200 CFM with the control valve basically fully open?

How long are the 1" take offs from the 8" header pipe?

Shark Tooth butterfly valve by Yeary. No other orifice plates downstream, just the expansion at the 8" then the constrictions leading to the 18x 1" outlets. Yes, it is 6" nominal size.

The 135 psig is measured just a few feet downstream of the CV/orifice plate.

800 CFM short- I am referring to the new 6" valve with upsized bores on the orifice plate being 800 CFM short of the flow compared to the 4" valve without an orifice plate. Before modification of the orifice plate, the 6" was only getting ~14.5 KCFM at most. That is why I am interested in the maximum flow out of 18x 1" discharges, to determine if valve sizing has anything to do with the restricted flow. 4" valve was able to do 17.5 KCFM on a cold day, and the new 6" valve with increased bores on the orifices can only do 16.7 KCFM on a cold day.

The take offs from the 8" pipe neck down to 1.5" within 10 feet and then these neck down again to 1" just within 10 feet of the discharge.

Edited by ukrche, 21 May 2024 - 11:09 PM.

### #17 ukrche

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Posted 21 May 2024 - 11:01 PM

Hi,

A set of calculators to support your work:

CheCalc ‐ Fluid Flow

A few documents about compressible flow and orifice , Natural gas equations

You may need some time to absorb the documents.

Breizh

I will definitely need some time to read these. Thanks again Breizh.

### #18 snickster

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Posted 22 May 2024 - 11:56 PM

I did a some hydraulic checks of the system.

From the manufacturer's Cv value of 769 at 70% rotation for the 6” valve at 10 psi differential pressure the flow through the valve should be about 36,000 SCFM so the control valve is adequately sized.  This is the same differential pressure shown between P1 and Px on the restriction orifice data sheet you attached.

The restriction orifice data sheet shows a Cv valure of 142 and a differential pressure of 58.65 psi for the orifice plate.  At this value of Cv and pressure differential the flow would be only 14,900 SCFM through the plate.  I assume this was the undersized restriction orifice that was later increased in size to have a higher Cv.  This makes sense because this would be about how much the maximum flow would have been before the orifice was upsized. which is about what you indicate it was, but this is with about 85 psig in the 8" header downstream of the restriction orifice with 143.65 psig upstream of the orifice as shown in the data sheet sketch.  I assume that the Cv of 142 for the orifice was before it was upsized and I don't know what it is now for the upsized plate but I assume that the Cv is much higher than 142 now so pressure drop is much lower for a given flow so the plate pressure drop should no longer be limiting the flow.

I calculate with 16700 scfm in 18 - 1" discharges (927.8 scfm per 1") the resulting pressure in the 8" header will be about 60 psig.  This makes sense since per the orifice data sheet the original design conditions shown downstream of the orifice plate is 85 psig so I assumed someone did a calculation that determined that 85 psig would be a design pressure in the 8" header to maintain with pressure drop through valve and orifice at a flowrate over 20,000 scfm which I believe you were shooting for.

If you are really only getting 16,700 scfm flow now then the 8" header pressure should be about 60 psig if you do a calculation starting at the 1" outlets back to the 8" header as indicated above.  However, if you really have 135 psig in the 8" header and the flow is only 16,700 scfm total the thing I may see happening is that you have blockages in the 1" outlets which is causing a much higher pressure in the 8" header to develop.  This happens because the outlet pressure of the 1" just inside of the tip will increase for reductions in area at a given flow under sonic flow conditions at the pipe exit.  For instance, if the 1” pipe at exit were corroding and laminating so as to reduce the inside diameter by 1/8” all around the flow area would be reduced by about 1/2.  This may make sense since if the ends of the 1” pipes were exposed to the high furnace temperatures over time they could be corroding and laminating reducing the flow area.

So further questions I have are:

Are you sure the header pressure downstream of the orifice plate is really 135 psig at 16,700 scfm flow?

Do you know what the new Cv of the orifice plate is?

Do the 1” outlets discharge directly into the furnace or do they have some type of nozzle at the ends?  Are the 1" outlets exposed to high furnace temperatures?

I understand from your latest posts that each outlet has about 10 feet of 1” pipe and 10 feet of 1 ½” pipe, is this correct?

The data sheet for the control valve restriction plate shows upstream and downstream pressure at plate, and plate Cv.  It appears this data sheet was prepared by the valve manufacturer.  Someone on your end must have given the valve manufacturer design condition such as pressure, temperatures and flowrate.  In particular do you know what design flowrate did the manufacturer use for his valve and orifice sizing? What is the maximum flowrate that you need?  From the sketch on the data sheet the manufacturer used 154 psig upstream and 85 psig downstream of the valve/plate assembly.  Is this correct?

Edited by snickster, 23 May 2024 - 12:00 AM.

### #19 breizh

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Posted 23 May 2024 - 01:28 AM

Hi,

For those interested by technology.

Breizh

### #20 snickster

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Posted 23 May 2024 - 05:59 PM

UKRCHE

I did another check assuming that you really have 135 psig downstream of valve/orifice plate assembly at 16,700 scfm flowrate.  In this case I back calculated the new upsized Cv of the restriction orifice plate assembly to be = 218 assuming 160 psig upstream of the plate and downstream of the valve.

With this value of plate Cv and using 10 feet length of each segement of 1", 1 1/2", 8" and 6" (assuming all Sch. 40 carbon steel) for pipe friction losses and the values of the Cv given in the manufacturer's tables for the control valve I was able to calculate a maximum flowrate possible at resulting pressure in the 6" dowstream of the orifice plate as follows:

Maximum flowrate: 25,000 SCFM

Pressure at outlet of valve/plate assembly in 6" = 100 PSIG

This considers the control valve is wide open with a Cv of 1535 per manufactures tables and there is negligible pressure loss through the valve,  and 160 psig @ 80 deg F upstream supply pressure which is the pressure directly upstream of the orifice plate with no losses through the valve, and that there are no blockages or restrictions in the piping downstream of the control valve/plate assembly as discussed in my previous post.

Edited by snickster, 23 May 2024 - 06:12 PM.

### #21 breizh

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Posted 24 May 2024 - 06:00 AM

Hi,

Agree with snickster, I got a cv of 217.19 for the orifice multi holes assuming Cv of 1535 for the valve 6" full open, leading to a Delta P valve of 0.47 psi for 16700 scfm,

with

p1: 179.7 psia; px: 179.23 psia and p2 :149.7 psia

Breizh