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# Calculating Flow Coefficient Through 2 Valves in Series(7)

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 zimonmayo (Industrial) 24 Jul 12 6:57
 Hi Guys, I have been looking for a formula which can be used to calculate the overall Cv values for 2 valves installed in series and came across the following from http://www.engineeringtoolbox.com/adding-kv-cv-d_1.... The formula given reads as follows (I have substituted Kv for Cv): 1 / (Cvt)^2 = (1 / (Cv1)^2) + (1 / (Cv2)^2) Which can be re-expressed as the following: Cvt = (Cv1 x Cv2) / (Cv1^2) + Cv2^2)^0.5 So based on the above, for the valves I am dealing with (Cv of single valve @ 90˚ = 9482): Cvt = (9482 x 9482) / (9482^2 + 9482^2)^0.5 Cvt = 89,908,324 / (89,908,324 + 89,908,324)^0.5 Cvt = 89,908,324 / (179,816,648)^0.5 Cvt = 89,908,324 / 13409.573 Cvt = 6704.79 So based on the above the calculated total Cv for the 2 valves (ignoring pipework etc.) would be 6705 (rounded up). Does the above appear correct? The answer does seem like it would make sense!!!
 (2)  BigInch (Petroleum) 24 Jul 12 7:27
 First clue. Ever seen a real PID with series valves drawn like this? They have a hard time distinguishing between series and parallel. Cv for series assemblies add directly. If it ain't broke, don't fix it. If it's not safe ... make it that way.
 zimonmayo (Industrial) 24 Jul 12 8:09
 Hi BigInch, I'm not sure what your point is. The image you have embedded shows 2 valves installed in parallel, not in series. If you scroll down the web page I linked in my earlier post it shows and image of the valves installed in series, along with the calculation for this. Cv for parallel installations is a case of adding the 2 Cv values together, but not for series (nor would I expect this to be the case)
 BigInch (Petroleum) 24 Jul 12 8:28
 That's their diagram. Do you draw upside-down valves too? That's not the only thing wrong with that page. They have a hard time distinguishing between series and parallel. Cv for series assemblies add directly. If it ain't broke, don't fix it. If it's not safe ... make it that way.
 zimonmayo (Industrial) 24 Jul 12 8:53
 Hi BigInch, What do you mean by 'Cv for series assemblies add directly' - are you able to give us an example? If I was installing the valve I mention above in PARALLEL then the calculation would would be: Cvt = Cv1 + Cv2 Cvt = 9482 + 9482 Cvt = 18,964 Giving an overall Cv of 18,964.
 MatthewL (Chemical) 24 Jul 12 10:54
 zimonmayo, biginch is trying to get you to see that the formula you are using is WRONG! Your initial calculation is for PARALLEL flow, not SERIES flow. SERIES flow Cv is a simple sum of the respective Cv, where PARALLEL flow uses the formula you listed in the first post. The site you listed has the formulas reversed. Matt Quality, quantity, cost. Pick two.
 BigInch (Petroleum) 24 Jul 12 10:57
 YES MatthewL. You got it! Zimon. NEVER BLINDLY USE FORMULAS, ESPECIALLY THOSE YOU GET OFF THE INTERNET! If it ain't broke, don't fix it. If it's not safe ... make it that way.
 zimonmayo (Industrial) 24 Jul 12 12:10
 Thanks Guys, however I am still not convinced. I would say that in SERIES the valves are installed on the same line, one after ther other as follows: --->--->---- But in PARALLEL, the line / flow is split so there are 2 PARALLEL lines running alongside each other: --->--- --->--- This is how it is depicted on the web page I linked to which I believe is correct. Are you trying to tell me that the pressure drop through 2 valves on the same line is less than it would be through one valve? That wouldn't make any sense!
 DLite30 (Mechanical) 24 Jul 12 12:40
 The engtool box equations are correct. For the same overall differential pressure, you'll flow less through two series valves, and more through parralel set up, so your Cv for parrallel operation is greater than the Cv for series.
 Latexman (Chemical) 24 Jul 12 12:54
 If I want more flow all I gotta do is add another CV in the line in series? NOT! Good luck, Latexman
 zdas04 (Mechanical) 24 Jul 12 13:09
 I'm not a fan of engeeringtoolbox.com (too high an add to content ratio), but I don't see a problem either mathematically or conceptually with what I just read there. The equation above (except for an extra closing parenthesis) is a valid restatement of the initial equation (and I got the same answer as the OP). Logically, if I get a dP in the first valve then the second valve has a lower dP available so the answer should be less than either valve's Cv. David Simpson, PE MuleShoe Engineering "Belief" is the acceptance of an hypotheses in the absence of data. "Prejudice" is having an opinion not supported by the preponderance of the data. "Knowledge" is only found through the accumulation and analysis of data.
 Latexman (Chemical) 24 Jul 12 13:26
 I've seen and used CVs in parallel for turndown reasons. I don't think I've ever seen CVs in series. Good luck, Latexman
 MatthewL (Chemical) 24 Jul 12 14:20
 OK, one more time. Here is the pertinent info from engineeringtoolbox: Control Valves in Parallel The resulting Kv or Cv if two valves are installed in parallel can be calculated as Kvt = Kv1 + Kv2 (1) where Kvt = resulting Kv Kv1 = Kv valve 1 Kv2 = Kv valve 2 Control Valves in Series The resulting Kv or Cv if two valves are installed in series can be calculated as 1 / (Kvt)2 = 1 / (Kv1)2 + 1 / (Kv2)2 (2) The formulas are reversed! Series valves are ADDED together, just like any other fitting. If I have two normal valves on a pipe run, in series, and I am looking to find out the losses, I ADD them together, along with the pipe lengths, fittings, etc. that constitute the piping structure. If the valves are in PARALLEL, the losses are resolved by the second equation, which they have mistakenly put under series valves. Flow resistance is handled just like any other resistance (electrical, heat, mass, etc.), if the resistance is in series, the terms are added Rt = R1 + R2 + R3 + ... if in parallel, they are handled as 1/Rt = 1/R1 + 1/R2 + 1/R3 + ... Matt Quality, quantity, cost. Pick two.
 (2)  katmar (Chemical) 24 Jul 12 14:37
 zimonmayo, your formula is correct. The first concept to note is the a Cv is a "conductance" type of factor - i.e. a valve with a high Cv passes fluid more easily than one with a low Cv. Contrast this with the resistance factor K (the one used for pipe fittings like bends etc). A fitting with a high K value passes fluid less easily than one with a low K value. Now, we know that for pipe fittings in series we can add K values. We all do this every day. Cv and K are related by Cv = 29.9 x d2/√K (Ref Crane 410 Eq 3-16) To simplify the math assume constant d and we can make 29.9 x d2 = J and now Cv = J/√K or K = (J/Cv)2 The total resistance = KT = K1 + K1 = (J/Cv1)2 + (J/Cv2)2 The combined Cv = J/√KT And with a bit of manipulation you have the exact formula you quoted. There is a bit of confusion with people quoting the engineeringtoolbox formula. The Kv that they have used is the European version of Cv and not the resistance factor K. As I stated above, for resistance factors in series you can add the K values, but not the Kv values. It looks like zimonmayo understood this from the beginning, but many people (particularly those in the USA who don't often come across the European Kv) do get confused by the similarity. Katmar Software - Uconeer 3.0 http://katmarsoftware.com "An undefined problem has an infinite number of solutions"
 zdas04 (Mechanical) 24 Jul 12 14:48
 Yeah, the link in the OP has a hyperlink to the definition of Cv. The Cv number that goes into the equation is "flow rate (in gpm) that results in a 1 psi dP across the restriction". The definition of Kv is the same as Cv with metric units (something like flow in cubic m/min that results in a 1 bar dP) So as Katmar says, it is a conductive factor which means that parallel valves should be a direct add while series valves would be a cumulative effect to lower the Cv below the lowest value. David Simpson, PE MuleShoe Engineering "Belief" is the acceptance of an hypotheses in the absence of data. "Prejudice" is having an opinion not supported by the preponderance of the data. "Knowledge" is only found through the accumulation and analysis of data.
 zimonmayo (Industrial) 24 Jul 12 15:12
 Thanks guys. The earlier posts had me confused for a while there. This is the first time I'd come across this formula so wanted to check it was correct - as BigInch mentioned, not all formulae posted on the web can be trusted!! Cheers
 BigInch (Petroleum) 24 Jul 12 15:32
 I was thinking that I have to keep the same flowrate, so I can't keep the same overall differential pressure. ------------------------------------ OK, so this is the same equivalent pipe for a looped pipeline problem, but with valves. I agree that with the same differential pressure, there's more flow with two parallel valves, just as with 2 parallel pipes. --------------------------------------------------- Zimon, sorry I got off on the wrong perspective. I must apologize to the Toolbox too. To make amends, a spreadsheet. If it ain't broke, don't fix it. If it's not safe ... make it that way. http://files.engineering.com/getfile.aspx?folder=321b5cee-4590-4f0b-9bf0-81
 BigInch (Petroleum) 24 Jul 12 15:40
 When I stuff it, I do a good job at that too. If it ain't broke, don't fix it. If it's not safe ... make it that way.
 btrueblood (Mechanical) 24 Jul 12 15:49
 Still, that valve is upside down.
 GHartmann (Chemical) 24 Jul 12 15:58
 Yes there are some folks here steering the OP in the wrong direction. The Cv of two valves in series is NOT the some of the two Cvs. Someone is getting Cv confused with "K" pipe resistence factors. The original analysis is in factor correct.
 BigInch (Petroleum) 24 Jul 12 16:22
 Ya. I saw that upside down valve and couldn't believe anything on that website after that. If it ain't broke, don't fix it. If it's not safe ... make it that way.
 GHartmann (Chemical) 24 Jul 12 16:42
 Yea and spell "sum" as some. What would I ever do without spellcheck?
 GHartmann (Chemical) 24 Jul 12 16:43
 OOPS I meant I had the misspelling.
 zdas04 (Mechanical) 24 Jul 12 19:00
 GHartmann, Your spelling is absolutely the smallest of your problems. By the time you posted, everyone who had been confused had admitted their mistake and everyone was on the same page. Your chastising the people who made errors was kind of beating a dead horse. David Simpson, PE MuleShoe Engineering "Belief" is the acceptance of an hypotheses in the absence of data. "Prejudice" is having an opinion not supported by the preponderance of the data. "Knowledge" is only found through the accumulation and analysis of data.
 MatthewL (Chemical) 24 Jul 12 19:13
 Umm, not everyone, Dave. Just got back on and saw I made a bad assumption (you know what they say about assume, don't you? Only makes an a\$\$ out of u and me ) Sorry for leading you around the bush, zimonmayo, and thanks to all for catching it! Matt Quality, quantity, cost. Pick two.
 zdas04 (Mechanical) 24 Jul 12 19:22
 You know that the very best thing about eng-tips.com is that if you make a mistake, someone will catch it and get the train back on the tracks. Even people as active as some of the folks in this thread (probably the three or four most active members of the Piping forum) get it wrong sometimes. When they (we) do get it wrong, someone is in the middle of our error within the hour--where else can you get that? David Simpson, PE MuleShoe Engineering "Belief" is the acceptance of an hypotheses in the absence of data. "Prejudice" is having an opinion not supported by the preponderance of the data. "Knowledge" is only found through the accumulation and analysis of data.
 BigInch (Petroleum) 24 Jul 12 23:49
 It was interesting thinking of valves in that way. I've never had the need to replace two valves with an equivalent valve. I have done the equivalent pipe thing, but way back before the days of the PC when every extra step was a pain. The math of finding the equivalent valve is more complex then copying and pasting a duplicate. I still can't think of why it would it be necessary to find an equivalent valve. So Zimon, what are you up to? Why? If it ain't broke, don't fix it. If it's not safe ... make it that way.
 zimonmayo (Industrial) 25 Jul 12 5:05
 I was trying to calculate the Cv for a Double Block and Bleed Metal Seated Triple Offset Butterfly Valve which is basically 2 valves in one casting. I only have the Cv rating for a single disc / valve so this calculation should give me the Cv for the complete valve. Ok there is a section of valve body to take into account but this is minimal and is full bore so for the purposes of my application I am happy with the value obtained. If you want to see such a valve go to the Hobbs Valve website and look for their Double Block and Bleed Valve.
 Latexman (Chemical) 25 Jul 12 7:12
 Sounds like an open/closed type valve to me; not a throttling operation. So, it makes me wonder why the velocity head method (K) is not used. Then, the K's of the two valves can be added together for the K of the assembly. Good luck, Latexman

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