ISA/IEC sizing question

[gsxra]

I am looking for the equation for delta P across a control valve. I am looking for non-choked, compressible, turbulent flow with or without fittings attached. I have the equation to solve for C, but I was hoping someone has this equation re-worked for DP.

Thanks
Josh

 

[BSQUAREDBUCKEYE]

I'm sure I know what you are asking. For turbulent non-compressible flow it would be Flow squared, times Specific gravity over Cv squared equals delta P.

For compressible flow you first have to determine the delta P to P1 ratio. Then Weight, Mass or Vapor basis and what kind of valve globe, ball or butterfly.

 

[gsxra]

I have the equation but I do not know the downstream pressure. I need the equation reworked to solve for delta P. The equation I have is C=W/(N6*Y*{x*p1*rho1)^.5)
Y=1/(3FkxT), x=DP/P1

 

[JimCasey]

Dusting off my high-school algebra:
If
Cv= _Q_________
1360*P1*Y*Sqrt(X/GTZ)
And X=DP/P1

Substitute for X

Cv= _Q_________
1360*P1*Y*Sqrt(DP/P1GTZ)


Sqrt(DP/P1GTZ)=Q/CV*1360*P1*Y

(DP/P1GTZ)= (Q/CV*1360*P1*Y)^2


DP=Q^2*GTZ/P1^3*Cv^2*1360^2*Y^2

Q is in SCFH
P1 is inlet pressure in PSIA
Y is the expansion factor,(1-(X/3FkXt))
X Pressure drop ratio defined above
G specifig gravity (MW/29)
T=Temp in degrees R
Fk is specific heat ratio (ideal gas: 1.4)
Xt is terminal pressure drop ratio-from Mfr's tables)
Z is compressibility (ideal gas=1)

 

[gsxra]

Jim,

But you still need to break Y out (because Y=1-X/(3FkxT)).
When I do that I get a cubic equation for DP.
If you use your equation or the ISA one I listed same result.
I was hoping someone had the equation solved for me.

Thanks

 

[fwcatr]

gsxra,

If you assume the valve to be choked, start by using a Y of 0.667 and see where that gets you.

If the valve is not choked, use a Y value between 0.667 and 0.93.

If you want Y broken out, assume Fk=1 for air, Xt~0.5 to 0.75 for a globe valve, and the x/Xt factor to be the Xt value or some pressure drop ratio lower than the Xt.

What type of control valve are you using?

Regards,
Fred

 

[gsxra]

I am setting up a model in MS Excel that represents pressure loss through components such as pipe, elbows, block valve, control valve. This is used to determine the design conditions for a startup vent for steam service.

As for the type of control valves: I have used Fisher, Masoneilan, Samson, CCI, ValvTechnologies Xactrols, etc.

I know what Fk and xT values I will be using. I was just hoping some would have the equation written to solve for DP.

 

[fwcatr]

If you have an inlet pressure and the xT value, you can calculate your downstream pressure and then the pressure drop.

 

[gsxra]

fwcatr,
Help me out. Knowing the formula is C=W/(N6*Y*[x*p1*rho1]^.5)
Y=1-(x/(3FkxT)), x=DP/P1, N6=63.3
Known:
W, N6, Fk, xT, P1. rho1, C
This leaves DP the only variable I don't have. But I don't remember my algebra that well to solve for DP.
When I solve for DP I get:
DP^3/(3*Fk*xT*P1)^2 - 2DP^2/(3*Fk*xT*P1) + DP = (W/C*N6)^2/rho1

 

[fwcatr]

What I was trying to say before is that if you have an arbitrary inlet pressure and the xT, then you have xT=(P1-P2)/P1abs (since the xT is just a pressure drop ratio). You should then have your pressure drop where the valve becomes choked.

As far as the equation goes, I wouldn't break up Y at first, use Y as 0.667 to begin with, or leave it as Y. When I went through the equation, I ended up with pressure drop on one side and W^2/(rho*C^2*N6^2*Y^2) on the other side, with the P1 term dropping off because it appears in the numerator and the denominator.