Calculate Max Flow Through Failed PCV 1

[ChEMatt]

This is a continuation of thread1203-205528 which was closed.

I was given the following equation from a speciality gas vendor. I was wondering if anyone could identify the source:

[tt]
For Critical Flow:

Qg = Cv * P1
-------
2 * SQRT(Sg)

Where:

Qg = gas flow in SCFM (60°F and 14.7 psia)
Cv = flow coefficient for regulators and valves
P1 = Inlet pressure in psia

For sub-critical flow:

Qg = Cv * SQRT(deltaP * P2)
----------------------
SQRT(Sg)

deltaP = P1 - P2
P2 = Outlet pressure in psia[/tt]

Where did these formulas come from? I have my doubts that the gas company came up with them. They seem too simple to me. (I realize they ignore geometry factors.)

Onwards,

Matt

 

[ChEMatt]

Anyone have an idea about where this equation came from?

Thanks.

Onwards,

Matt

 

[CJKruger]

ChEMatt, a nice write-up for control valves equations are Masoneilan's Handbook OZ1000 from:

http://www.masoneilan.com/internet/pages/documentwarehouse/get.cfm?id=1555&a=0

 

[JLSeagull]

Cg is an obsolete factor from the Fisher sizing equations.

 

[tickle]

...and is a function of Cv and Xt (have a look in Fisher's control valve handbook and / or ISA paper on control valve sizing - i cannot remember)

 

[ChEMatt]

I appreciate the feedback, but Cg is not mentioned in either of my posts. Perhaps you got Qg and Cg confused?

I'm wondering about the source of the equation and whether or not it can be universially applied to gas flow sizing when a Cv is given.

I appreciate the link to the PDF. However, it looks like it is just a rehash of the ISA equations which are also given in Fisher's Control Valve Handbook. The equation does not appear in either publication that I can see.

I have never seen the above equation in any publication. That's why I'm trying to find it. It is quite simple and, if correct, would be very easy to use.

Anyone know the source?

Onwards,

Matt

 

[Latexman]

I think you would be better served by going back to your specialty gas vendor and ask for technical support (i.e. an engineer).

Good luck,
Latexman

 

[skearse]

Yeah, I agrree with Latexman. Nothing like that appears in Crane either; I would go back to the vendor and ask for some tech help. If these are the guys that supplied the PCV, and that's what they used to size the valve, then the source may not matter as much. If the valve came from another source, I'd check with the actual valve manufacturer since some of them seem to have their own 'tweaks' that they use to correlate Cv and flowrates.

 

[TD2K]

The first equation appears to be based on Fisher's ideal gas equation which is:

scfh = (520 / (SG * T))^0.5 * P1 * Cg * sin (blah blah blah).

I left my notes at the office so be gentle with me

The sin factor goes to 1 for critical flow so it goes away.
Cg is approximately 30 * Cv for many globe style valves.
scfh = scfm * 60

60 * scfm = (520 / (SG * T))^0.5 * P1 * 30 * Cv

scfm = [(520 / (SG * T))^0.5 * P1 * 30 * Cv] / 60

scfm = [(520 / (SG * T))^0.5 * P1 * Cv] / 2

If we assumed the speciality gas vendor assumed their products would be used at room temperature then T1 = 520R and we end up with

scfm = P1 * Cv / 2 * SG^0.5

Can't help you with the second equation.

 

[TD2K]

Your second equation is very similar to one published by VOGT for their valves except they use P1 instead of P2 (I haven't seen any formulas that use P2 for flow through a valve in this location of the formula, could this be a typo?). I don't know the background of VOGT's equation but you could ask them.

VOGT for flow has scfm = 22.6 * Cv * ((dP * P1)/T1 * Sg))^0.5

If I assume T1 is supposed to be at 60F as previously, the square root of 520 is 22.8. Round off to 1, change P2 to P1 and you have your equation.

 

[TD2K]

I did some more playing around with Crane.

Start with equation 3-20 for scfm q'm
Set Y = 1.0 (that's one thing that bothered me with VOGT's equation, an increasing dP didn't account for expansion effects)
Substitue Cv for K (equation 2-5 on pg 2-8). If you rearrange it, you get K = 894 * d^4 / Cv^2
If you substitute it into the equation for q'm, you get

scfm = 22.6 * Cv * (dP * P1 / (T1 * Sg))^0.5 which is VOGT's equation except P2 is replaced with P1.