Cv and K values

[howkers]

I work with systems engineers who use the Crane 410M book for resistance calculations using resistance coefficient K.

First question is K dimensionless and the same value for calculations in US gallons/minte and litres/min.

Second question. A lot of the valve manufacturers quote flow coefficient Cv for US gal/min for psi at 60degrees. Is there a source for a conversion formula to give the systems guys a K value from the valve bore and Cv value.

TIA

Bill

 

[MortenA]

I use a software package called flowmaster. Their reference manual has the following conversion formula:

K=0.2168*10^9*PI*D^4/Cv^2

where D is the nominal diameter

Best regards

Morten

 

[TD2K]

Take a look in Crane around page 2-10. My US units copy is at work but I believe it has an approximate conversion on/around that page.

 

[TD2K]

Now that I'm at work, the relationship is:

Cv = 29.9 * d^2 / (K)^0.5

 

[EGT01]

Howkers,

K is dimensionless and seems that you should be able to use it regardless of the units of the flow equation you use it in. For example, K = f * L/D

I would point out that there is a metric version of Cv that valve manufacturers use, it is Kv. Kv is in units of m3/h at 1 bar differential

The relationship between Cv and Kv is
Cv = 1.16 * Kv

http://www.control.com/952641863/index_html

 

[MortenA]

K and Kv is not the same. K is the dimensionless loss coefficient. Its mostly used in continental european engineering.

Best regards

Morten

 

[MortenA]

EGT01:

Sorry - you already knew that K is dimensionless.

TD2K

at least we use the same dimensions - but the constant is different. From studying my reference i have notised that my nominal diameter is in meter - this may be the root cause of the difference.

Best regards

Morten

 

[EGT01]

MortenA,

No problem, it was probably good to clarify that point since the two variables use such similar letter designations. I hope I haven't confused the issue by mentioning Kv.

But let's go back to the resistance coefficient equations. I have a copy of Crane in "US" units so I recognize the equation TD2K gives. Rearranging gives

K = 894 * d^4 / Cv^2, where d is in inches

Taking this equation when the diameter (let's say Dm) is given in meters and converting I get,

K = 894 * (Dm * (39.37 in/1 m))^4 / Cv^2
= 2.1478E9 * Dm^4 / Cv^2, where Dm is in meters

If you take PI out of the constant I don't get the same as you have given but if you take PI^2 out then it is close. Can you recheck your reference or does someone have a copy of Crane in metric that can check this? Otherwise, checking for example d = 2 inches and Cv = 46 and plugging the appropriate numbers into each equation, I get different results for K which is contrary to what I stated earlier.

 

[TD2K]

Crane's metric version on page 3-4 for equations has (with some re-arranging)

K = 8.94e-10 * Dm^4/Cv^2 and Cv rating is wrt USgpm.


(the actual shown relation is Cv = 29.9*d^2/K^0.5 where d is in millimetres).

 

[EGT01]

Now, I'm really confused.

TD2K,
Can you revisit your rearrangement of the actual shown relation where d is given in millimeters? For example, if Dm is in meters and d is in millimeters

d = Dm * (1000 mm/1 m)
d^4 = (Dm * (1000 mm/1 m))^4 = Dm^4 * 1000^4 = Dm^4 * 1E+12

Shouldn't the rearrangement be

K = 894 * 1E+12 * Dm^4 / Cv^2

which is closer to the same ball park as MortenA's equation.

Otherwise, I guess I'm surprised to see that

Cv = 29.9 * d^2 / K^0.5

is the same equation whether d is in inches or millimeters!

In that case, for a given Cv, it looks like K will be different for metric units versus US units and that doesn't seem consistent.

Cv can be expressed as K and K can be expressed as equivalent length, K = f * L/D. For a given equivalent length and pipe diameter, the ratio L/D will be the same no matter whether we use metric or US. Unless the friction factor value changes depending on the unit system, K will be the same right? What am I missing?

 

[MortenA]

EGT01

Try rearraging the equation:

Cv = 29.9 * d^2 / K^0.5 <=>

Cv^2=894*d^4/K <=>

K=894*d^4/Cv^2

Same dimensions - different constant when comparing with "my" equation (in an earlier post).

Now since "my" equation referes to d in mm and there is 25.4 mm to the inch this give

K= .372*10^9*d^4/Cv^2

if you choose to "convert" from d in IN to d in mm - faily close.

Best regards

Morten

 

[EGT01]

Morten,

I hate to keep pressing the issue, but it appears that I am performing the units conversion differently than what you and TD2K are doing and this is causing a significant difference in the order of magnitude of our resulting constants. Then again, I could be just misunderstanding your methods and not comparing your results correctly to mine. Please check the following and let me know if there is anything wrong with my approach.

Starting with the form of the rearranged equation to which I think we all agree, I will start with the units that my US version of Crane's TP410 gives

K = 894 * Din^4 / Cv^2 where
Din = diameter in inches
Cv = valve flow coefficient, gpm/psi differential

For Dmm = diameter in millimeters
Din * 25.4 mm/in = Dmm
or
Din = Dmm * 1 in/25.4 mm

Then K = 894 * (Dmm * 1 in/25.4 mm)^4 / Cv^2
K = 894 * (1/25.4)^4 * Dmm^4 / Cv^2
K = 2.1478E-3 * Dmm^4 / Cv^2

Now, if we want to convert from millimeters to meters
Dm = diameter in meters
Dmm * 1 m/1000 mm = Dm
Dmm = Dm * 1000 mm/1 m

Then K = 2.148E-3 * (Dm * 1000 mm/1 m)^4 / Cv^2
K = 2.1478E-3 * 1000^4 * Dm^4 / Cv^2
K = 2.1478E+9 * Dm^4 / Cv^2

So the equations for K in terms of Cv (gpm/psi differential) and diameter in inches, millimeters and meters should be

K = 894 * Din^4 / Cv^2
K = 2.1478E-3 * Dmm^4 / Cv^2
K = 2.1478E+9 * Dm^4 / Cv^2

As a check, if Cv = 46 and Din = 2
then Dmm = 50.8 and Dm = 0.0508

K = 894 * 2^4 / 46^2 = 6.76
K = 2.1478E-3 * 50.8^4 / 46^2 = 6.76
K = 2.1478E+9 * 0.0508^4 / 46^2 = 6.76

Regards,

Ellis

 

[MortenA]

EGT01:

Your right - I must have made a calculation mistaek. This is also 100% consisten with my source (they propably copied it from Crane anyway ) since my source says: 0.2168*10^9*PI^2 = 2.14*10^9 and NOT 0.2168*10^9*PI is i first posted. Sorry for that mistake. Could have cleared out a lot of doubts.

Best regards

Morten