5 replies to this topic

[sheiko]

Hi,

Crane TP-410 proposes the following formula to calculate the resistance coefficient of valves:

K = 891*d⁴ / Cv² (or Cv = 29.9*d² / K^0.5), with:
K: resistance coefficient
d: valve bore, port or seat diameter (inch)
Cv: valve coefficient (USgpm/psi^0.5)

I find this method handy because valve manufacturers do not publish K-factor, while they do publish Cv.

But the problem I see is the definition of "d" in the equation.
This is an "effective" diameter for determining the friction loss, and should probably correspond to the minimum flow diameter within the valve (at the seat), but the exact definition isn't clear...that is why I have defined "d" above as valve bore, port or seat diameter...

So, could you please help me clarify what is is "d" in the above mentionned formula:
- is it the bore, seat or port diameter?
- And is this formula applicable to reduced bore valve? Otherwise shall we use the following: K_{reduced bore} = K_{full bore} + K_reducer + K_expander?

[katmar]

It may initially seem counter-intuitive, but the "d" in this formula has no link to any dimension of the valve. This is a useful fact because we often do not know the physical dimensions inside the valve. So you can use it for reduced bore valves as well. All you need to know is the Cv.

The reason for this is that if we are using the resistance coefficient K then we express the pressure drop as

delta P = K * (V^2) *(density/2)

This shows that the important thing to correspond with K is the velocity, and this depends only on the PIPE ID. So the "d" in the conversion formula is the ID of the pipe in which you are calculating the pressure drop.

[sheiko]

Thanks Katmar

[kkala]

There is evidence that mentioned "d" represents valve cage size (http://en.wikipedia....iki/Globe_valve) , as written in manufacturer catalogues. If cage size is not reported, valve body size could be used instead, since cage and body size seems to be identical in this case.
Not having Crane bulletin at hand, I looked into C.R. Branan's "Pocket Guide to Chemical Engineering" for a list of Cd=Cv/d^2, where d is the valve diameter (inches). This refers to control valves, but apparently holds for manual valves too. For every type of valve, Cd= Cv/d^2 looks practically constant and independent of valve diameter. Cd is a bit smaller, as noted, if the valve is placed between two reducers. Attached "CValve.xls" contains this valve data, in case you find it useful.
The second page of "CValve.xls" (named examples) has applied the above to the valves of two manufacturers, and has estimated the valve resistance coefficients using Crane's formula. Cd of globe valves is nearly constant (12.0 - 15.3) , except two distinct valves (18.6 - 21.5). Same is Cd of gate valves examined (59 - 65). Crane formula results in reasonable resistance coefficients K for globe and gate valves, which indicates that d has been considered by Crane on the same basis. The cage or body size (diameter) of the valve is written on the catalogues, I am not sure it is identical to bore size.
This method may be more useful in the absence of valve manufacturer's data, when you have to preliminary size a valve. It seems that cage size (not body size) determines Cv and that cage size can be equal to body size, or smaller by 1 or 2 pipe sizes. Meaning of cage size may not be clear to us, but helps specify the valve.
Note: C.R. Branan points out that method is preliminary and manufacturer's Cv will give precise results. His references (*) are "Handbook of Control Valves" by Instrument Society of America and "Specifying control valves" by Chalfin, Fluor Corporation, Chemical Engineering magazine, 14 Oct 1974. They may have more clarifications on d.

Attached Files

•  CValve.xls   38KB   186 downloads

Edited by kkala, 08 September 2011 - 09:32 AM.

[sheiko]

Thanks kkala, the file is really useful.

It is indeed true that Branan defines "d" as the valve size in his book.
This is apparently also the case in Crane paper. Example 4-2 (page 4-2) indeed considers "d" as the valve diameter. I had missed that.

[kkala]

New knowledge (at least for me) from this topic is that valve cage size d (lower or equal to valve body diameter) specifies Cv. For instance, consider equal percentage BEIER valves from CValve.xls of 2" cage size. Their body diameter can be 2", 2.5", 3", but all of them have Cv=46.65. Of course a valve (or all its series) may have a single cage size, then identical to valve body diameter.
Method of flow coefficient K calculated from Cv can be somehow reversed, without looking at valve supplier catalogues. Suppose you estimate for a globe valve on a 4" line that max Cv=120 (Cv for max controllable flow will be lower). We know from Branan (see CValve.xls) that Cv/d^2=11.5, so d=sqrt(120/11.5)=3.2". A valve of cage d= 3" would be suitable. No need to be conservative chosing d=4", Cv/d^2 is already concervative compared to commercial values. But the Cv/d^2 is just statistics, to be verified in detailed engineering through valve supplier's actual data.