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Calculating specific gravity
6

Calculating specific gravity

Calculating specific gravity

(OP)
How do you calculate the specific gravity of a vapor, using USC units?

RE: Calculating specific gravity

using USC units?  

RE: Calculating specific gravity

(OP)
Yes, United States Customary (USC) units, i.e. feet, pounds, gallons.

RE: Calculating specific gravity

3
For a vapor, the SG is simply the ratio of the molecular weight of the gas to the molecular weight of air.  It is dimensionless and so is not dependent on the system of units you choose to use.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Calculating specific gravity

(OP)
I thought it was the density of the vapor versus the density of air, is this not the case? Either way, I would assume dry air at standard conditions, correct? If so, what IS the appropriate value of dry air at standard conditions, in USC units?

RE: Calculating specific gravity

Melon,

katmar gave you the correct method.

RE: Calculating specific gravity

Melon is also correct. He just doesn't realize that the density of a gas is directly proportional to it's molecular weight.  

RE: Calculating specific gravity

melon00,

Air @ 60 deg F 14.7 psia would be approx. 0.076 lb/cu ft.

See 'Control Valve Handbook' Chapter 10 Engineering Data, and Chapter 12 Conversions and Equivalents, for other useful properties of air.  CVH published formerly by Fisher Controls, now Emerson Process Management, in 3.1MB pdf.

RE: Calculating specific gravity


The Fan Engineering handbook, 8th Ed., Buffalo Forge Company, defines "standard air":

Dry air, 0% humidity, 29.921 in. Hg, 70oF, density = 0.075 lbm/ft3.

Moist air, 50% humidity, 29.921 in. Hg, 68oF, density = 0.075 lbm/ft3.

RE: Calculating specific gravity

(OP)
Thanks to all that posted a reply, this helps a lot. I wouldn't have put two and two together about the molecular weight and density being directly proportional. I would have thought that the density would be affected by pressure on compressible fluids, and molecular weight would not be affected. I am an electrical guy, and these concepts are very fuzzy for me.

RE: Calculating specific gravity

Maybe I am wrong, but I don't thing that the Specific Gravity of a vapor is ratio of the gas MW over the MW of air.
I think it is the ratio of the vapor density at its operating conditions (diferent Press and Temp) over the density of the air at Normal or Standard conditions...

Not true?

RE: Calculating specific gravity

homayun, the MW ratio may not be logical, but it is the definition. I prefer to avoid all equations that are formulated around a vapor SG. It is much better to work with proper dimensions like mass density, compressibility etc.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Calculating specific gravity

(OP)
Homayun, I agree with you.

Katmar, could you provide a link to your reference for the definition of specific gravity.

RE: Calculating specific gravity

Gas specific gravity isn't necessarily the most useful when considering fuel gases. There it is the relative density that is often used, that is, the ratio of the test gas density to the density at the same conditions of a reference gas.
In other words, the (MW of the test gas)/(MW reference gas).

JMW
www.ViscoAnalyser.com
 

RE: Calculating specific gravity

I think the calculation method might depend on what information you know to start with.

Regards,

athomas236

RE: Calculating specific gravity

Melon,
The ratio of molecular weights goes back to the ideal gas laws.  
One (gram) mole of any ideal gas displaces 22.4 liters at standard conditions.  
So if you have 22.4 liters of a gas with a molecular weight of 15, and 22.4 liters of air with an effective molecular weight of 29, the density of the light gas is 15G/22.4L and the density of air is 29g/22.4L.  
The SG of the gas is (15/22.4)/(29/22.4)
Cancel the 22.4s and you get 15/29; the ratio of the molecular weights.   

RE: Calculating specific gravity

(OP)
jmw:

I don't really have a choice on using specific gravity. I am trying to calculate the maximum flow through a regulator at wide-open conditions. Fisher controls has a website full of equations dedicated to this:

http://www.fisherregulators.com/technical/sizingcalculations/#GasandSteamSizingSummary

They use specific gravity, but I want to be clear on how to calculate it. I think that is what athomas236 was meaning when they said, it depends on what info you know to start with.

JimCasey:

My problem with your info is that gas is a compressible fluid, i.e. a gas under standard conditions will displace a different amount of liquid under pressured conditions. If what you say is correct, does that mean that the specific gravity of a gas doesn't change under different pressure/temperature combinations? Can anyone else concur?

RE: Calculating specific gravity

The flow of the gas through the orifice is directly proportional to the specific gravity.  This is the ratio of the mole weights as described earlier.  Fisher's regulator charts compensate for the differing pressures.  Simply put, you will be able to flow more fuel gas at a 0.65 gravity than air at a 1.0 gravity.

RE: Calculating specific gravity

Homayun,

Gas SG can't be the ratio of gas density at actual conditions to air density at standard condition. In that case gas SG closely follows its actual density as the air density at standard conditions is about 1.2 bar.

Did some calculations for 10 gases at pressures ranging from 0 to 100 bar g (more or less close to ideal conditions) and SG values by pressue definition (i.e actual gas density/air density at gas conditions) differ after second decimal when compared with SG values by molecular weight definition.

 

RE: Calculating specific gravity

(OP)
quark:

"Gas SG can't be the ratio of gas density at actual conditions to air density at standard condition. In that case gas SG closely follows its actual density as the air density at standard conditions is about 1.2 bar."

I am assuming you meant 1.2 kg/m³, and not 1.2 bars for the density of air at standard conditions. Also, please note that I asked for USC units, and not SCI units.

"Did some calculations for 10 gases at pressures ranging from 0 to 100 bar g (more or less close to ideal conditions) and SG values by pressue definition (i.e actual gas density/air density at gas conditions) differ after second decimal when compared with SG values by molecular weight definition."

I ran my own numbers and found a much bigger difference than the second decimal place as you described. Here are my sample calculations, using steam as the example fluids.

Using MW to define SG:
Steam MW: 18.02
Air MW: 28.966
SG = 18.02/28.966 = 0.622

Using density to define SG:
Steam density @ 114.7 psia/400 °F = 0.2338 lb/ft³
Air density @ standard conditions = 0.075 lb/ft³
SG = 0.2338/0.075 = 3.12

As you can see, there is quite a bit of difference between the two values. Just for fun, I wanted to see what the SG of steam at 14.7 psia would be:

Using density to define SG:
Steam density @ 14.7 psia/212 °F = 0.0373 lb/ft³
Air density @ standard conditions = 0.075 lb/ft³
SG = 0.0373/0.075 = 0.497

As you can see, there is a big difference in SG when the vapor is under pressure.

I spoke to a mechanical engineer here, and he stated that the MW version, that everyone on this forum keeps referencing, is only valid for ideal gases.
 

RE: Calculating specific gravity


Densities of gases at high pressures can be approximated by applying the theorem of corresponding states. This theorem states that gases under the same "reduced" conditions exhibit the same deviations from ideal behaviour.

The deviations can therefore be determined using the generalized compressibility factor [z] diagram, knowng the critical properties.

Take, for example, CO2 at 100 atm and 198oC.

Tr = 471.2÷304.3 = 1.55; Pr = 100÷73 = 1.37 → z = 0.9

thus density:

d = MP/zRT = 44×100/(0.9×0.08206×471.2) = 126.44 g/L

The NIST value is 124.64 g/L. The error = 1.4 %.

With the probable exception of NH3 with errors around 7%, the accuracy using the generalized compressibility diagram is better than 5% for pure substances.   

RE: Calculating specific gravity

Melon,

1.2 bar is a mistake and kg/cu.mtr is the correct unit. As SG is a dimensionless number, units are not important.

Taking your case of 114.7 psia and 400F steam, the density is 0.2338 lb/cu.ft (Z is 0.958)

The density of air corresponding to 114.7 psia (7.9 bara)pressure and 400F (204.4C) temperature is 5.78 kg/cu.mtr or 0.3608 lb/cu.ft (Z value of air at 114.7 psia and 400F is 1 so you can safely assume that the condition is ideal)

So, SG = 0.2338/0.3608 = 0.648 (air density should be at actual conditions)

By MW definition, it is 18/29 = 0.6206

When you are using MW definition, you are assuming that both gases are at ideal condition. The error for considering steam as ideal at this condition is approximately 7%.

When you take steam at 14.7 psia and 212F (1 bara and 100C), air density is 0.95 kg/cu.mtr or 0.0593 lb/cu.ft

So, SG by density ratio at actual conditions = 0.0373/0.0593 = 0.629 (air is ideal and error of considering steam at ideal condition is about 2%.

Inaccuracy of steam as ideal gas

RE: Calculating specific gravity

Gentlemen,

Some definitions may be helpful.

ASTM D3588 defines the specific gravity (relative density) as the ratio of the density of a gas under specific conditions of temperature and pressure to the density of dry air, of normal CO2 content at the same pressure and temperature.

In addition, BS 7589, 1996 (which is the same as ISO 6976, 1995) states the relative density is the density of a gas divided by the density of dry standard air at the same specified conditions of pressure and temperature. the term ideal relative density applies when both gas and air are considered as fluids which obey the ideal gas law; the term real relative density applies when both the gas and air are considered as real fluids.

My interpretation of these definitions is the the specigic gravity/relative density do not change with the specified reference conditions of pressure and temperature.

Best regards,

athomas236

RE: Calculating specific gravity

(OP)
athomas:

Thanks for the specific definition and referencing your source of information.

Is your interpretation, the same as quarks directly above? Meaning, you don't think that the specific gravity is going to change under different pressure and temperature conditions?

RE: Calculating specific gravity

The relative density meter 3098 from Emerson Mobrey is used for fuel gases where the relative density is the density of the fuel gas to the density of a reference gas (not air) at the same temperature and pressure.
This is a commonly used measurement in hydrocarbon gas applications.

http://www.emersonprocess.com/Micromotion/products/densitometer-3098.html
Note: though they refer to it as a gas specific gravity meter it is more properly a relative density meter.
 

JMW
www.ViscoAnalyser.com
 

RE: Calculating specific gravity

Melon00,

I agree that based on the codes quoted quark is correct when he says "Gas SG can't be the ratio of gas density at actual conditions to air density at standard condition". I also agree that using the MW definition only applies to ideal gases.

Best regards,

athomas236

RE: Calculating specific gravity

Folks,
I've been watching this discussion with interest because it's a problem which vexed me a while ago.
I totally agree with the definitions given by athomas236 above.  The Gas SG is the ratio of gas density to air density at the same temperature and pressure conditions.  The point that I never got clear in my head was whether that means (a) you bring the gas density to "normal" conditions and divide by air density at normal conditions, which is a well known figure.  OR (b) divide the actual gas density by the air density to the actual conditions.  Now this might not sound like a big deal but try it, especially where the gas is non-ideal and actual conditions are a long way from "normal".

RE: Calculating specific gravity


The specific gravity is obtained by dividing the density of a gas by that of a reference gas (e.g., air at predetermined standard conditions) therefore it would change with T,P, as the density would.

I may be wrong, but it seems to me the main purpose of using specific gravities is to avoid using dimensional mass/volume units.

 

RE: Calculating specific gravity

25362,
No I don't believe that this is correct.  The Gas SG is not the gas density divided by reference gas (e.g. air) at standard conditions.  The definition is as written by athomas236 above.  The temperature and pressure at which the densities are quoted must be the same.  i.e. the density of the gas and reference gas (e.g. air) must be given at the same conditions and then ratiod.  Thus the Gas SG should be a constant.
[By the way, I absolutely hate using Gas SG and firmly believe in quoting densities at defined T&P]

RE: Calculating specific gravity

The most important lesson that can be learnt from all this discussion is that there is obviously no universal definition of the SG for a gas.  I have stated above that in my experience the SG is the ratio of the molecular weight of the gas to that of air.  I know that this is (or was?) a very widely used convention. athomas236 has referenced codes that define it differently, and I accept that he is correct.

The upshot of all of this is that whenever you see the term SG used, you need to check what that particular author intended it to mean.

Unfortunately this is typical of so many things in engineering.  We have had many discussions over standard conditions and normal conditions for gases - none of which are really standard or normal.  The SG for a liquid can be defined for a variety of different temperatures - for both the fluid and the water.  A valve Cv can be based on imperial or US gallons.

So rather than get all uptight over what the "right" definition is, we need to see what the definition is in the context that it was used.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Calculating specific gravity


I've seen both definitions for sp. gr. of gases, the one based on the air density at standard (whatever) conditions, and that mentioned by KenA. This discrepancy should be treated, as katmar so rightly says, in the right context. A becoming star for katmar's laudable message.

RE: Calculating specific gravity

Gentlemen,

I have watched this thread with interest as it has developed to over 30 replies and I have to admit to being surprised by the statement about getting "uptight over what the right definition is". The more than 30 replies to this thread suggests that people do want to know the right definition.

For me the important lesson to be learned is, if in doubt, look in codes and standards first.

Best regards to all

athomas236

RE: Calculating specific gravity

Hi all,

As per GPSA chapter 23 for Physical Properties:
"Relative Density (also termed specific gravity or gas
gravity) — is defined as the ratio of gas density (at the temperature and pressure of the gas) to the density of dry air (at the air temperature and pressure."

And also:
"The ideal gas relative density is the ratio of the molecular mass of the gas to the molecular mass of dry air."

Hence, when the specific gravity to be used in our calculations specified it as 'std conditions', we can calculate it as ratio of MW. If it is not specified as 'std conditions', we need to calculate it as ratio of density at actual conditions, in this case, the air referenced T and P should be defined or clarified.

Hope this help.

RE: Calculating specific gravity

Almost always, the gas flows are measured in STANDARD volume per time (Such as standard Cubic feet per minute or Standard Cubic meters per hour.  
Standard conditions are at atmospheric pressure and 60F. Therefore compression-induced density changes drop out and you're back to the ratio of moleccular weights.  

Compression of the gas is dealt with in the valve sizing equations.  

Another reason to give your application engineer FULL data when specifying a valve.  Nitrogen with 50 psi  Delta P is meaningless.  100F Nitrogen with 250 psi(g)  in, discharging to 200 psi(g)out, is vastly more specific.   

RE: Calculating specific gravity

Katmar is right on this, even if you are dealing with a gas (or one of its components) condensed at the reference conditions, it is the nature of approximate gas law calculations, for better or worse.



 

RE: Calculating specific gravity

Athomas236,
the real lesson is that when two people use the same term each may mean something different and thus it is important, where such differences of interpretation are known, to clarify the meanings.

I recall a pharmaceutical engineer who kept referring to brine solution and it was only when asked if that was sodium chloride brine that he answered that it was ethylene glycol and water.

JMW
www.ViscoAnalyser.com
 

RE: Calculating specific gravity

For sure, almost every requirement written can be interpreted.  It's the nature of the language itself, and the writer to be imprecise.

TTFN

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RE: Calculating specific gravity

(OP)
katmar,

I took your advice and spoke to a Fisher rep on this subject, since I am referencing Fisher equations. He said that specific gravity is the ratio of the densities of your fluid to air or water depending on your fluid's state. He then stated that the density of air is at standard conditions, regardless of the process conditions of the fluid. I will use this definition, since he sizes valves and regulators for a living, although, I happen to agree with the ASTM definition described by athomas236.

The main problem I had with referencing air at a specific pressure and temperature, is that there is no easy way to look up the density of air at, say 114.7 psia/400 °F. At least, I don't know an easy way.

Thanks to everyone for their prompt responses on this controversial issue.

RE: Calculating specific gravity

I have in front of me the Fisher Control Valve Handbook, 3rd Ed, 1999. On page 111 there is a table of terminology that gives the following definition for Gas Specific Gravity.

Gas specific gravity (ratio of density of flowing gas to density of air with both at standard conditions(1), i.e., ratio of molecular weight of gas to molecular weight of air), dimensionless.

(1) Standard conditions are defined as 60°F (15.5°C) and 14.7 psia (101.3 kPa).

The important part to note is the bit I have bolded in the definition viz. "both at standard conditions".  This means that your formula can only adjust the density on the basis of ideal gas behavior by using the temperature and pressure values for the flowing gas.  If you can find a formula that uses the actual density of the gas, rather than inferring the density from that of air and ideal gas behavior, that would be much better.  Unless of course your gas is at conditions where ideal gas behavior applies, and depending on the degree of accuracy that you need.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Calculating specific gravity

(OP)
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.

RE: Calculating specific gravity

(OP)
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

RE: Calculating specific gravity

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√(ΔP/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
  ΔP/Gg(act) = (ΔP.T1.Z1)/(Gg(std).P1)
But Fisher use
  x = ΔP/P1 so
  ΔP/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
http://katmarsoftware.com

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