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Calculating specific gravity 6
- Thread starter Melon00
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- #41
katmar,
That is the same definition as in the 4th ed of the handbook. Now that I think about it, I think he did say both at standard conditions, I just didn't catch it, because my attention was so focused on the air requirements. Thanks for taking the time to look it up in the handbook. They should have put it in the index in the back. Don't know why they didn't.
That is the same definition as in the 4th ed of the handbook. Now that I think about it, I think he did say both at standard conditions, I just didn't catch it, because my attention was so focused on the air requirements. Thanks for taking the time to look it up in the handbook. They should have put it in the index in the back. Don't know why they didn't.
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All:
Update: I took a control valve engineering course at Fisher Controls just last week, and I asked the question regarding gas specific gravity. The instructor stated that gas specific gravity is normalized for air at standard conditions, regardless of inlet conditions. I referred him to the Fisher Control Valve Handbook 4th edition, and he said that definition is incorrect, and that he would look into why it is defined that way.
Well, I just got an email back from him:
"Gas specific gravity, Gg = the ratio of the density of the flowing gas at inlet conditions to the density of air at STP. Thus, Gg is normalized to air and dimensionless.
Gg is defined correctly in the Valve Engineering Student Manual (however, I will include the "at inlet conditions" in our next revision); it is not correct in the Abbreviations and Terminology Table on page 112 of the Control Valve Handbook (4th Ed.).
Note that Gg occurs within the square root functionality of the flow equation, so small variations in Gg have little impact on calculated Cv requirements. In class, for example, we looked at a steam sizing exercise where I used an estimate of Gg = 2.0 for superheated steam and saw almost no difference in the Cv requirements when we used the corrected values from the superheated steam tables in the handbook.", and he stated he spoke to some coworkers at Fisher, and the definition in the handbook is incorrect, but didn't state why. He also noted, that even if you were to use the incorrect value of density, that it should make a big impact on the results of your calculations, as Cv calculations have specific gravity under a square root function, so the error amount is rooted as well."
I just thought I would share that with everyone.
Regards,
Trent
Update: I took a control valve engineering course at Fisher Controls just last week, and I asked the question regarding gas specific gravity. The instructor stated that gas specific gravity is normalized for air at standard conditions, regardless of inlet conditions. I referred him to the Fisher Control Valve Handbook 4th edition, and he said that definition is incorrect, and that he would look into why it is defined that way.
Well, I just got an email back from him:
"Gas specific gravity, Gg = the ratio of the density of the flowing gas at inlet conditions to the density of air at STP. Thus, Gg is normalized to air and dimensionless.
Gg is defined correctly in the Valve Engineering Student Manual (however, I will include the "at inlet conditions" in our next revision); it is not correct in the Abbreviations and Terminology Table on page 112 of the Control Valve Handbook (4th Ed.).
Note that Gg occurs within the square root functionality of the flow equation, so small variations in Gg have little impact on calculated Cv requirements. In class, for example, we looked at a steam sizing exercise where I used an estimate of Gg = 2.0 for superheated steam and saw almost no difference in the Cv requirements when we used the corrected values from the superheated steam tables in the handbook.", and he stated he spoke to some coworkers at Fisher, and the definition in the handbook is incorrect, but didn't state why. He also noted, that even if you were to use the incorrect value of density, that it should make a big impact on the results of your calculations, as Cv calculations have specific gravity under a square root function, so the error amount is rooted as well."
I just thought I would share that with everyone.
Regards,
Trent
Melon00, Thanks very much for coming back with that information. However, I remain convinced that the definition of Gg in the Abbreviations and Terminology Table on Page 112 of the Control Valve Handbook (4th Ed) is correct and that your instructor is wrong. To state it specifically - the Gas SG as required by the Fisher valve sizing equations is the ratio of the gas density to air density both taken at standard conditions.
The reason why I am convinced of this is that the valve sizing equation for gases on the top of the right hand column on page 120 must be compatible with the liquid sizing equation at the top of page 114.
The liquid equation is
Cv = q / (N1.FP[√]((P1-P2)/Gf))
= q / (N[√]([Δ]P/Gf))
Note that here Gf is based on the density of the liquid at the flowing temperature. I have absorbed all the "constants" into a single N.
The gas sizing equation from Page 120 is
Cv = q / (N.P1[√](x/(Gg.T1.Z1)))
Again I have combined the "constants" N7, FP and Y into the single constant N as they are not important in the comparison of the forms of equation.
Firstly let us look at the flow rate q. In the gas equation the units are scfm (See example on page 121). However, we need actual cfm to be compatible with the liquid equation (the conversion from cfm to gpm is absorbed into the constant). This relationship is
q(acfm) = q(scfm) x (T1.Z1/P1) x (PS/(TS.ZS)) (Eq A)
PS and TS are the pressure and temperature at standard conditions and ZS=1 so they can all be absorbed into the global constant N.
Now assuming that Gg is as defined in the Handbook and is at standard conditions we also need to convert it to actual SG (remember the liquid equation uses SG at flowing conditions).
Gg(act) = Gg(std) x (P1/(T1.Z1)) x (TS.ZS/PS)
Again, all the standard parameters can be absorbed into the constant.
Now, looking at the portion within the square root in the liquid equation
[Δ]P/Gg(act) = ([Δ]P.T1.Z1)/(Gg(std).P1)
But Fisher use
x = [Δ]P/P1 so
[Δ]P/Gg(act) = (x.T1.Z1)/Gg(std) (Eq B)
Substituting Equations A & B derived above into the liquid Cv equation we get
Cv = (q(std).T1.Z1/P1) / (N.[√]((x.T1.Z1)/Gg(std)))
= q(std) / (N.P1[√]((x/Gg(std).T1.Z1))
which is exactly the equation on page 120 and so the assumption of the gas density being at standard conditions is correct.
Katmar Software
Engineering & Risk Analysis Software
The reason why I am convinced of this is that the valve sizing equation for gases on the top of the right hand column on page 120 must be compatible with the liquid sizing equation at the top of page 114.
The liquid equation is
Cv = q / (N1.FP[√]((P1-P2)/Gf))
= q / (N[√]([Δ]P/Gf))
Note that here Gf is based on the density of the liquid at the flowing temperature. I have absorbed all the "constants" into a single N.
The gas sizing equation from Page 120 is
Cv = q / (N.P1[√](x/(Gg.T1.Z1)))
Again I have combined the "constants" N7, FP and Y into the single constant N as they are not important in the comparison of the forms of equation.
Firstly let us look at the flow rate q. In the gas equation the units are scfm (See example on page 121). However, we need actual cfm to be compatible with the liquid equation (the conversion from cfm to gpm is absorbed into the constant). This relationship is
q(acfm) = q(scfm) x (T1.Z1/P1) x (PS/(TS.ZS)) (Eq A)
PS and TS are the pressure and temperature at standard conditions and ZS=1 so they can all be absorbed into the global constant N.
Now assuming that Gg is as defined in the Handbook and is at standard conditions we also need to convert it to actual SG (remember the liquid equation uses SG at flowing conditions).
Gg(act) = Gg(std) x (P1/(T1.Z1)) x (TS.ZS/PS)
Again, all the standard parameters can be absorbed into the constant.
Now, looking at the portion within the square root in the liquid equation
[Δ]P/Gg(act) = ([Δ]P.T1.Z1)/(Gg(std).P1)
But Fisher use
x = [Δ]P/P1 so
[Δ]P/Gg(act) = (x.T1.Z1)/Gg(std) (Eq B)
Substituting Equations A & B derived above into the liquid Cv equation we get
Cv = (q(std).T1.Z1/P1) / (N.[√]((x.T1.Z1)/Gg(std)))
= q(std) / (N.P1[√]((x/Gg(std).T1.Z1))
which is exactly the equation on page 120 and so the assumption of the gas density being at standard conditions is correct.
Katmar Software
Engineering & Risk Analysis Software
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