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Cv conversion to other units 1
- Thread starter foxtrot
- Start date
As noted in Crane Technical Manual 410, "The Cv coefficient of a valve is defined as the flow of water at 60F, in gallons per minute, at a pressure drop of one pound per square inch across the valve."
From that description, I'd think you could convert to any units you like (eg, liters per hour per inches of mercury, cubic centimeters per second per atmospheres, etc).
From that description, I'd think you could convert to any units you like (eg, liters per hour per inches of mercury, cubic centimeters per second per atmospheres, etc).
MikeHalloran
Mechanical
Uh, yes, you can make conversions, but you have to be careful, because the units of Cv are NOT gpm/psi.
The units of Cv are gpm/sqrt(psi).
It's unfortunate that the usual statement of Cv's definition does not make that clear.
One complementary common metric equivalent that you might actually run into is
mbar/(m^3/hr)^2
Mike Halloran
Pembroke Pines, FL, USA
The units of Cv are gpm/sqrt(psi).
It's unfortunate that the usual statement of Cv's definition does not make that clear.
One complementary common metric equivalent that you might actually run into is
mbar/(m^3/hr)^2
Mike Halloran
Pembroke Pines, FL, USA
In my experience there are three common "Cv's" that are used to size valves and that are found in valve suppliers' catalogs. These are
1. "American" Cv - uses US gpm and psi
2. "English" Cv - uses Imperial gpm and psi
3. "European" Kv - uses m3/h and bar
I have included these three in my units conversion program Uconeer which can be downloaded for free from my web site at
If there are others that are actually used in industry please let me know and I will add them to Uconeer.
1. "American" Cv - uses US gpm and psi
2. "English" Cv - uses Imperial gpm and psi
3. "European" Kv - uses m3/h and bar
I have included these three in my units conversion program Uconeer which can be downloaded for free from my web site at
If there are others that are actually used in industry please let me know and I will add them to Uconeer.
- Thread starter
- #5
Thanks to all for the input.
Katmar, I downloaded your conversion program--thanks for making it available.
Another question: what is the differance between Liters/minute and Normalized liters/minute?--I see that in Europe both seem to be used rather than Cv for pneumatic valves (along with orfice sizes and effective sectional area in the orient)--is there any way to tie all of these together so that it's a bit easier to make comparisons?
Katmar, I downloaded your conversion program--thanks for making it available.
Another question: what is the differance between Liters/minute and Normalized liters/minute?--I see that in Europe both seem to be used rather than Cv for pneumatic valves (along with orfice sizes and effective sectional area in the orient)--is there any way to tie all of these together so that it's a bit easier to make comparisons?
MortenA:
In building engineering services work in the UK, Kv is based on m3/hour and bar. The dimensionless coefficient to which you refer is that which tells us how many velocity pressures we lose in a fitting; this is not the same as Kv. Maybe it's different in the petroleum industry?
Regards,
Brian
In building engineering services work in the UK, Kv is based on m3/hour and bar. The dimensionless coefficient to which you refer is that which tells us how many velocity pressures we lose in a fitting; this is not the same as Kv. Maybe it's different in the petroleum industry?
Regards,
Brian
Morten,
The Kv that I listed, and which is included in Uconeer, is exactly analogous to Cv. The formula is identical, except for the units as noted above. In both cases the liquid density is given as SG relative to water, so that does not change. It is in common use in Germany.
The confusing issue is that the symbol "K" is also used in pressure drop calculations of fittings (including valves) and as you note this is a dimensionless factor that relates the number of velocity heads to the fitting.
For valves of the same type, but different sizes, the K values will be virtually the same. However the Kv (and Cv) of the larger valve will be greater than the Kv of the small valve. It is easy to convert between K and Kv (or Cv) and I'm fairly sure Crane 410 discusses it (unfortunately I do not have my copy with me right now).
regards
katmar
The Kv that I listed, and which is included in Uconeer, is exactly analogous to Cv. The formula is identical, except for the units as noted above. In both cases the liquid density is given as SG relative to water, so that does not change. It is in common use in Germany.
The confusing issue is that the symbol "K" is also used in pressure drop calculations of fittings (including valves) and as you note this is a dimensionless factor that relates the number of velocity heads to the fitting.
For valves of the same type, but different sizes, the K values will be virtually the same. However the Kv (and Cv) of the larger valve will be greater than the Kv of the small valve. It is easy to convert between K and Kv (or Cv) and I'm fairly sure Crane 410 discusses it (unfortunately I do not have my copy with me right now).
regards
katmar
foxtrot,
Because gases expand and contract with changes in pressure and temperature the convention has arisen to refer the volumes back to reference conditions. The reference conditions are called either "standard" or "normal" conditions. Unfortunately there is nothing standard or normal about these conditions and there are literally dozens of conflicting definitions for both terms.
If you do an Advanced Search in Eng-Tips for the terms "standard conditions", "Normal conditions", SCFM etc you will find lots of discussion on this. Another excellent resource on the subject is Milton Beychok's site (Milton is one of the "elder statesmen" on this forum). See
This means that your normalised liters are refered back to some defined state. "Normal" usually refers to 0 deg C and either 1 atm or 1 bar, but you should check with the source of the data.
Uconeer includes a conversion utility for this (Use the fan icon on the toolbar). Note that to convert from one volumetric definition to another you go via the mass based quantity - thanks goodness the mass of a gas is unaffected by temperature and pressure!
regards
katmar
Because gases expand and contract with changes in pressure and temperature the convention has arisen to refer the volumes back to reference conditions. The reference conditions are called either "standard" or "normal" conditions. Unfortunately there is nothing standard or normal about these conditions and there are literally dozens of conflicting definitions for both terms.
If you do an Advanced Search in Eng-Tips for the terms "standard conditions", "Normal conditions", SCFM etc you will find lots of discussion on this. Another excellent resource on the subject is Milton Beychok's site (Milton is one of the "elder statesmen" on this forum). See
This means that your normalised liters are refered back to some defined state. "Normal" usually refers to 0 deg C and either 1 atm or 1 bar, but you should check with the source of the data.
Uconeer includes a conversion utility for this (Use the fan icon on the toolbar). Note that to convert from one volumetric definition to another you go via the mass based quantity - thanks goodness the mass of a gas is unaffected by temperature and pressure!
regards
katmar
This is all really good information, but empirical equations are often quite illogical and very loose with units. Temperature is one important area of slack performance by developers. Many Oil & Gas empirical equations expect temperature in degrees F. We all know that you can't multiply a temperature in F (or C) in an equation and get consistent results, but the authors of empirical equations often state "this equation is valid in the range of 60F to 150F and should not be extrapolated outside that range" and then we all ignore the valid range (if we even know about it). The first time someone tries to use the equation at 0F it explodes and at -10F if gives invalid results.
I've spent many unpleasent hours trying to convert constants from one set of units to another with inconsistent results.
Where I've ended up is that I convert all input units to what the authors of the empirical equations specify and then convert the result to the units that I want. It is kind of a pain, but I end up not having to try to figure out why MathCad won't let me take the log of psi or losing the fact that I took a fifth root of inches and multiplied it times ft[sup]2.5[/sup].
Some empirical equations are simple enough that simply changing the constant will work. Others are more subtle. I would suggest using my technique to verify the results you get from messing with the constants before you base an important decision on your arithmetic.
David Simpson, PE
MuleShoe Engineering
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.
The harder I work, the luckier I seem
I've spent many unpleasent hours trying to convert constants from one set of units to another with inconsistent results.
Where I've ended up is that I convert all input units to what the authors of the empirical equations specify and then convert the result to the units that I want. It is kind of a pain, but I end up not having to try to figure out why MathCad won't let me take the log of psi or losing the fact that I took a fifth root of inches and multiplied it times ft[sup]2.5[/sup].
Some empirical equations are simple enough that simply changing the constant will work. Others are more subtle. I would suggest using my technique to verify the results you get from messing with the constants before you base an important decision on your arithmetic.
David Simpson, PE
MuleShoe Engineering
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.
The harder I work, the luckier I seem
David,
I agree completely with your sentiments. I have also wasted many hours converting formulas. But there are a few bad ones that I continue to use. Two of my favorites :-
My rule of thumb for liquid piping : Take the flowrate in liters per second, multiply by 1.5 and then take the square root to give the pipe size in inches. I think I originally found it in gpm, and did the conversion to l/s - but that is lost in the mists of time.
Go-anywhere steam tables : Take the pressure in bar absolute and take the fourth root (i.e. press square root twice on your calculator), multiply by 100 to give the steam temperature im degrees C. Example - 100 PSIG = 7.9 bar abs gives 167.7 C. Steam tables give 169.9 C. Good enough for in-plant estimates.
katmar
I agree completely with your sentiments. I have also wasted many hours converting formulas. But there are a few bad ones that I continue to use. Two of my favorites :-
My rule of thumb for liquid piping : Take the flowrate in liters per second, multiply by 1.5 and then take the square root to give the pipe size in inches. I think I originally found it in gpm, and did the conversion to l/s - but that is lost in the mists of time.
Go-anywhere steam tables : Take the pressure in bar absolute and take the fourth root (i.e. press square root twice on your calculator), multiply by 100 to give the steam temperature im degrees C. Example - 100 PSIG = 7.9 bar abs gives 167.7 C. Steam tables give 169.9 C. Good enough for in-plant estimates.
katmar
Katmar,
Steam is pretty safe to do your empirical equation since you don't often have useable steam at 0C.
My favorite doesn't translate at all. To calculate the volume of a 1000 ft of pipe (in 42 galon barrels) you only have to square the ID (in inches) of the pipe. The result is about 3-4% higher than you get by actually calculating the volume (since I use this for calculating hydrotest volumes the extra works out well for trucks that may not be as full as advertised). This is much more of a coincidince than a physical relationship and it only works for inches, feet, and barrels. If you use meters, mm, and liters the number is some other relationship.
David
Steam is pretty safe to do your empirical equation since you don't often have useable steam at 0C.
My favorite doesn't translate at all. To calculate the volume of a 1000 ft of pipe (in 42 galon barrels) you only have to square the ID (in inches) of the pipe. The result is about 3-4% higher than you get by actually calculating the volume (since I use this for calculating hydrotest volumes the extra works out well for trucks that may not be as full as advertised). This is much more of a coincidince than a physical relationship and it only works for inches, feet, and barrels. If you use meters, mm, and liters the number is some other relationship.
David
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1
- #15
David,
We should not feel sad about this. I have accepted that I am a techno-junkie nerd and that I get my kicks from things that "normal" people would find boring. Years ago I was working my way up the corporate ladder and had got to a purely management position with virtually no technical work. I was bitterly unhappy - to the point of feeling physically sick on my way to work every morning. I realized that I had to get back into the technical realm. Perhaps I do no earn as much as I would have if I had remained on the corporate ladder, but at least I look forward to my work every day now.
yours in engineering
katmar
We should not feel sad about this. I have accepted that I am a techno-junkie nerd and that I get my kicks from things that "normal" people would find boring. Years ago I was working my way up the corporate ladder and had got to a purely management position with virtually no technical work. I was bitterly unhappy - to the point of feeling physically sick on my way to work every morning. I realized that I had to get back into the technical realm. Perhaps I do no earn as much as I would have if I had remained on the corporate ladder, but at least I look forward to my work every day now.
yours in engineering
katmar
To foxtrot and others,
I have found the reference in Crane 410 for converting between Cv (valve coefficient) and K (dimensionless resistance coefficient). In my 1988 Metric edition (410M) it is equation 3-16 on page 3-4. For those who don't have Crane 410 handy the conversion is
Cv = 29.9 * d^2 / sqrt(K)
Cv is USgpm and psi
d is pipe inside diameter in inches
K is dimensionless resistance coefficient
This allows you to express the flow characteristic of any fitting (eg an elbow) as a Cv value, but Cv's are usually only used for valve sizing. It is probably more useful in reverse - i.e. to express a valve with a known Cv as a K value to allow you to sum all the K's to get an overall pressure drop for a pipeline.
katmar
I have found the reference in Crane 410 for converting between Cv (valve coefficient) and K (dimensionless resistance coefficient). In my 1988 Metric edition (410M) it is equation 3-16 on page 3-4. For those who don't have Crane 410 handy the conversion is
Cv = 29.9 * d^2 / sqrt(K)
Cv is USgpm and psi
d is pipe inside diameter in inches
K is dimensionless resistance coefficient
This allows you to express the flow characteristic of any fitting (eg an elbow) as a Cv value, but Cv's are usually only used for valve sizing. It is probably more useful in reverse - i.e. to express a valve with a known Cv as a K value to allow you to sum all the K's to get an overall pressure drop for a pipeline.
katmar
Montemayor
Chemical
Harvey:
Please excuse this belated post. As you know, I was bedridden for 6 weeks and am now getting back to half-normal speed. I couldn’t read this thread and let the opportunity go by to pop yet another engineering balloon – this time, the error in one of my favorite Crane Tech Paper #410 equations: the conversion of Cv to K.
As you have correctly cited, Crane gives us the equation for Cv:
Cv = 29.9 * d^2 / sqrt(K)
However, they screwed things up by not leaving well enough alone. They proceeded to solve for K with the following:
K = (891) * d^4 / (Cv)^2 (which is not correct)
The correct equation for K is, of course,:
K = (894.01) * d^4 / (Cv)^2
There are some more errata in Crane’s which I have noted in my copies (I still have my original 1957 printing) and this raises the subject that I would like to bother you with: you recently wrote an interesting post on your disenchantment with the “K’s” as used in Crane and although I read the thread, I have not been able to find it lately. Could you help me by remembering which thread it was that you expounded some very interesting and experienced finding on the information found in Crane’s regarding the use of “K’s” in calculating head loss?
As I recall, your findings dove-tailed with my past experience in using Crane’s data and equations and I want to relate this information to another engineer I am helping out. I know this changes the theme of this thread, but I thought it would get your attention and I always enjoy discussing fluid mechanics with you anyway.
Best Regards,
Art Montemayor
Please excuse this belated post. As you know, I was bedridden for 6 weeks and am now getting back to half-normal speed. I couldn’t read this thread and let the opportunity go by to pop yet another engineering balloon – this time, the error in one of my favorite Crane Tech Paper #410 equations: the conversion of Cv to K.
As you have correctly cited, Crane gives us the equation for Cv:
Cv = 29.9 * d^2 / sqrt(K)
However, they screwed things up by not leaving well enough alone. They proceeded to solve for K with the following:
K = (891) * d^4 / (Cv)^2 (which is not correct)
The correct equation for K is, of course,:
K = (894.01) * d^4 / (Cv)^2
There are some more errata in Crane’s which I have noted in my copies (I still have my original 1957 printing) and this raises the subject that I would like to bother you with: you recently wrote an interesting post on your disenchantment with the “K’s” as used in Crane and although I read the thread, I have not been able to find it lately. Could you help me by remembering which thread it was that you expounded some very interesting and experienced finding on the information found in Crane’s regarding the use of “K’s” in calculating head loss?
As I recall, your findings dove-tailed with my past experience in using Crane’s data and equations and I want to relate this information to another engineer I am helping out. I know this changes the theme of this thread, but I thought it would get your attention and I always enjoy discussing fluid mechanics with you anyway.
Best Regards,
Art Montemayor
I was looking in Marks' Handbook for MEs and I did not find this conversion, although I did not look very hard. If you happen to know what page it would be I'd be very gratefull.
Second question, what is "d" when looking at a valve. Let's take for example a valve with the following characteristics: Orifice Dia = .25", pipe size NPT = .38",and Cv = 1.00. Would d be the .25 or the .38?
Cooperjer
Cooperjer
Mechanical Engineer
Second question, what is "d" when looking at a valve. Let's take for example a valve with the following characteristics: Orifice Dia = .25", pipe size NPT = .38",and Cv = 1.00. Would d be the .25 or the .38?
Cooperjer
Cooperjer
Mechanical Engineer
jsummerfield
Electrical
Refer to ISA-75.01.01 Control Valve Sizing Equations or IEC 60534-1. Also, from ISA 75.05.01
3.28 capacity: the rate of flow through a valve usually stated in terms of CV or KV.
John
3.28 capacity: the rate of flow through a valve usually stated in terms of CV or KV.
John
Art,
I am pleased you are back and active here again. I think the thread to which you are referring is thread798-135792 It was in the Chemical process engineering forum, which is probably why it did not result in much discussion.
My objection to the Crane 410 "K" values was that they are not applicable to laminar flow calculations, but Crane example 4-7 explicitly shows them being used for laminar flow. I recently got involved with some calculations for a liquid fertiliser plant where CMS (condensed molasses solids) was being pumped. The very high viscosities involved make this a definite laminar problem, and I found huge discrepancies between the various methods.
What really surprised me was that the "equivalent length" method, which tends to be looked down upon as an inferior short-cut method, was far better then using turbulent flow "K" values.
I put together a few examples to illustrate this, using a Sched 40 standard radius 90 degree welded elbow. The two fluids are water at 2 m/s (Reynolds = 205000) and molasses (visc = 4000 cP, Reynolds = 10.1).
For water I got:
Constant K = 0.3, press drop = 0.600 kPa
Equivalent length = 20, press drop = 0.749 kPa
Hooper 2-K method K = 0.316, press drop = 0.632 kPa
Darby 3-K method K = 0.335, press drop = 0.670 kPa
For molasses I got:
Constant K = 0.3, press drop = 0.019 kPa
Equivalent length = 20, press drop = 8.193 kPa
Hooper 2-K method K = 79.5, press drop = 5.136 kPa
Darby 3-K method K = 79.5, press drop = 5.136 kPa
In both cases the equivalent length method gives results that are a bit high, but in the ball-park. For laminar flow the Constant K method is out by a factor of 265. This is way beyond acceptable.
Back to the Cv to K conversion. I think the discrepancy you point out between the two Crane formulas is just rounding error. In my notes, where I worked to 4 significant digits I got a value of 29.83 in place of Crane's 29.9, and a value of 889.8 in place of their 891.0. In view of the other likely uncertainties I don't think it is too critical.
regards
Harvey
I am pleased you are back and active here again. I think the thread to which you are referring is thread798-135792 It was in the Chemical process engineering forum, which is probably why it did not result in much discussion.
My objection to the Crane 410 "K" values was that they are not applicable to laminar flow calculations, but Crane example 4-7 explicitly shows them being used for laminar flow. I recently got involved with some calculations for a liquid fertiliser plant where CMS (condensed molasses solids) was being pumped. The very high viscosities involved make this a definite laminar problem, and I found huge discrepancies between the various methods.
What really surprised me was that the "equivalent length" method, which tends to be looked down upon as an inferior short-cut method, was far better then using turbulent flow "K" values.
I put together a few examples to illustrate this, using a Sched 40 standard radius 90 degree welded elbow. The two fluids are water at 2 m/s (Reynolds = 205000) and molasses (visc = 4000 cP, Reynolds = 10.1).
For water I got:
Constant K = 0.3, press drop = 0.600 kPa
Equivalent length = 20, press drop = 0.749 kPa
Hooper 2-K method K = 0.316, press drop = 0.632 kPa
Darby 3-K method K = 0.335, press drop = 0.670 kPa
For molasses I got:
Constant K = 0.3, press drop = 0.019 kPa
Equivalent length = 20, press drop = 8.193 kPa
Hooper 2-K method K = 79.5, press drop = 5.136 kPa
Darby 3-K method K = 79.5, press drop = 5.136 kPa
In both cases the equivalent length method gives results that are a bit high, but in the ball-park. For laminar flow the Constant K method is out by a factor of 265. This is way beyond acceptable.
Back to the Cv to K conversion. I think the discrepancy you point out between the two Crane formulas is just rounding error. In my notes, where I worked to 4 significant digits I got a value of 29.83 in place of Crane's 29.9, and a value of 889.8 in place of their 891.0. In view of the other likely uncertainties I don't think it is too critical.
regards
Harvey
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