Plug Valve K Factors

[PEDARRIN2]

How do you deal with calculating the K factor (from Crane TP 410) of a plug valve where the area of the port is more than the area of the pipe size going to the valve?

Example is the Durco G432 plug valve (for natural gas). According to the literature, for the 1/4" to 1/2" valves, the %port size is greater than 100.

Would I do a pair of sudden/gradual enlargement/contraction?

I have never run into this and would appreciate any guidance.

 

[ione]

You should be able to get the flow coefficient of your specific valve from the valve supplier and then convert it to resistance coefficient.

You might want to take a glance at the page at the link below from the website of respectful member katmar:

http://www.katmarsoftware.com/articles/pipe-fitting-pressure-drop.htm#cv

 

[PEDARRIN2]

I have read that article - very helpful.

And I got the Cv from the manufacturer. My issue is Cv is traditionally defined in regards to flow of liquids of low viscosity (flow in gpm which produces 1 psig drop) - and Crane TP 410 indicates the relationship between Cv (liquid) and K factor, but not Cv(gas) with K.

The issue I have is how to translate a Cv (gas), which I have or can calculate to K factor.

Per Crane, q'h = 24700*Y*d^2/Sg*sqrt (delta P*density/K)

The equation I have used to relate q'h to Cv is

q'h = 1391*Cv*sqrt(P2*delta P/ (Sg*T)).

This comes from

http://www.fluidprocess.com/Atkomatic/pdf/Sizing.pdf

and I am assuming my pressure drop is less than the 55% for methane (natural gas)

So I put the two formulas on either side of an equal sign and solve until I get K.

Seems convoluted, but appears to be correct.

But I digress.

I use the information provided, but I like to know how it is derived.

I was wondering how to calculate the K factor for a plug valve when the port gets bigger.

 

[bimr]

The calculation of pressure losses in pipe fittings is an estimate. At best, the accuracy is +/- 10%. The Crane resistance coefficient method is basically a rule of thumb method, not a scientific calculation.

Scientists are the ones who start the process, and their work is sometimes theoretical in manner and extremely precise, but engineers doesn't really need to go that far to serve their purpose.

 

[katmar]

Unless you are working with high pressure drops with gases, the Cv and K values of a valve are effectively the same for low viscosity liquids and gases. I agree with you that the plug valve could be considered as a enlargement/contraction pair in much the same way as a tee used in the straight run through mode (i.e. not branching) has a K value > 0 because of the enlargement as the fluid passes the branch. But the K value that you will get will be very small (I guess in the region of 0.2 to 0.4) and the pressure drop should be negligible when the valve is fully open.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[PEDARRIN2]

So, in systems where the delta P is minor, a valve with a Cv = 1 would mean "1 gpm of liquid at standard conditions produces 1 psig drop" and " 1 scfh of gas produces 1 psig drop"?

 

[katmar]

I am not aware of any definition that gives a Cv for a gas as "1 scfh of gas produces 1 psi drop". As far as I know Cv (in US units) is always given per the 1 gpm and 1 psi definition. When you are working with a gas the flow rate calculated using the Cv formula would also be in actual gpm, but because we never measure gases in actual gpm an assortment of constants has to be added to convert the actual gpm to scfh.

There was a similar discussion a few years ago where I used the Fisher (Emerson) control valve handbook formulas to describe the conversion. See thread798-233225 The Fisher handbook gives a table of the constants to use for various conditions and systems of units. Last time I looked this handbook was a free download from the Emerson site. I see that Fisher's constants are slightly different from those in your reference. This could be because of different definitions of standard conditions for gases.

One thing to be aware of is that in the realms of control valve sizing for gases, the specific gravity of a gas is defined as the ratio of the molecular weight of the gas to the MW of air (28.96).

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[ione]

PEDARRIN2,

The definition of the flow coefficient Cv is univocal and it’s specifically referred to water at 60 °F as fluid flowing through the valve, so my answer to your question is no.
What changes when working with compressible fluids (natural gas in your specific case) is the equation that relates the Cv of the valve to the pressure drop and to volumetric flow rate passing through the valve.
The Cv value you have to enter inside the equation – for instance the one you’ve quoted in one of your previous posts q'h = 1391*Cv*sqrt(P2*delta P/ (Sg*T)) - is always the one provided by the supplier/mfg and that is referred to water at 60 F. It’s the equation that has been re-arranged in order to take into account the nature of the fluid you are dealing with.

 

[katmar]

My previous post was not clear - thanks to Ione for pointing out that the 1 gpm is water at 60°F.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[PEDARRIN2]

Just so I understand,

A published Cv relates to water at 60F - so if I want to find the Cv of the valve for natural gas (or any compressible fluid), I have to convert from the gpm indicated in the Cv value to scfh, taking into account differences in density at standard conditions.

 

[katmar]

No, the published Cv of the valve is the only Cv for that valve - irrespective of the flowing fluid. The different forms of the Cv equation cater for the different fluid phases, but the Cv value is always the same for a given valve. The Fisher handbook includes a table of constants that you plug into the various forms of the equation that allow you to work in different units, but the Cv value does not change.

Just to contradict myself, there is (was?) a form of Cv used by British companies that was based on the Imperial Gallon, and the Europeans have Kv, which is based on m³/h and bar. But if you are in the US and using US made valves these 2 situations can be ignored.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[PEDARRIN2]

I am still a bit confused and probably a bit slow on the uptake. I am trying to wrap my head around this.

I thought Cv was defined as the amount of flow in gpm that produces 1 psig drop in water at 60 F - so a valve with a Cv of 1 will produce 1 psig drop when water at 60 flows through it at 1 gpm.

So it would have units of gpm/psig - if I have 2 psig drop, I should only have 0.5 gpm flow.

So if I use Cv=1 in a compressible fluid equation, and put in 1 psig for the delta P, should I get the equivalent of 1 gpm of flow, once I change the units and take into account density?

 

[ione]

As already said the definition of the flow coefficient is univocal and it is referred to water service at 60 °F. So now forget the unit for a while and focus your mind on the value of the flow coefficient (just the number) of your specific valve. This is exactly what you have to put inside the equation that correlates the volumetric flow rate, the upstream and downstream pressure involved at the specific temperature etc. The equation itself is conceived to give you the flow rate in SCFM.
Please consider the worked out example at page 25 (for a gas application) of the attached paper, it could be informative.

 

[katmar]

I think you are just about there. Don't forget the square root for the pressure drop. From the sheet of formulas that you linked to earlier
F = Cv x [√]([Δ]P/S)
This gives Cv the units gpm/[√]psi

Being a bit pedantic - the g in psig is wrong. The pressure drop is a differential pressure and is sometimes written as psid, but should not be written as psig or psia.

Applying this formula to your example of the valve with Cv = 1, when you increase the differential pressure to 2 psi the flow will increase by the square root of 2 and will be 1.41 gpm.

Your last statement is correct. The value 1,391 in the Gas Flow equations on your sheet converts the gpm to SCFH, converts the SG relative to water to be relative to air, and includes the base temperature and pressure for the standard conditions (usually 520[°]R and 14.7 psia).

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[PEDARRIN2]

I am understanding better.

Thank you for the resource from Parker. It is definitely good.

Getting back to my original question, to convert Cv to K for friction loss calculations, I can use the Cv from the manufacturer in the equation K = 891*d^4/Cv^2, regardless of whether the process fluid is water or natural gas?

 

[katmar]

Yes, this is a useful way to be able to convert a valve Cv into a K value so that the valve can be treated along with any other pipe fittings in the Darcy-Weisbach equation. The K values (provided they all apply to the same pipe diameter) can simply be summed together.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[ione]

The flow coefficient (Cv) expresses the flow rate allowed by a valve at given pressure differential, while the resistance coefficient (K) represents the pressure differential created by a given flow rate of fluid which passes through a fitting (a valve in our case).

In short:

(Cv)^2 = const1 * (kinetic energy/pressure differential)

K = const2 * (pressure differential/kinetic energy)

Rearranging the two expressions above for pressure differential and equalling them, it is possible to find the correlation between the flow coefficient (Cv) and the resistance coefficient (K).

It turns out to be K = 891*D^4/(Cv)^2

Where Cv is indeed the published flow coefficient.

While what above is true for incompressible flow, for compressible non-critical flow it turns to be true in the measure you can assume the density of the fluid remains constant as it flows through the valve, that is under the same limitations over which the Darcy-Weisbach equation can be applied to compressible flow.