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Interesting Equation

Interesting Equation

Interesting Equation

(OP)
I was looking through a company piping standard today and found a maximum allowable velocity of:

vmax=380 ft/sec * SG * T^0.5 / P^0.1

Temperature in Rankine, Pressure in psia, and SG relative to air.

The equation results in pretty reasonable numbers (higher pressures or lower temperatures allow lower velocities which makes sense if it is trying to limit momentum), but I can't figure out why it works.  Does anyone have a feel for where this empirical equation might have come from?

David

RE: Interesting Equation

Is this related to static electricity? There is an ASTM Standard somewhere I think - ASTM D4865 - 09?

JMW
www.ViscoAnalyser.com

 

RE: Interesting Equation

I am confused about the units for this equation...

How do you get a velocity as a result ?

   

RE: Interesting Equation

(OP)
They don't talk about static anywhere around the equation in the standard, but they wouldn't if the genesis of the equation was not available to the standards writer (which often the case when the standard is a revision of a revision of a revision of a dead guy's work).

The equation behaves like it is trying to limit momentum.  Static generation is a function of momentum (among other things), so that may be the genesis.

David

RE: Interesting Equation

(OP)
MJCronin,
It is an empirical equation so you just have to assume that all of the unit-conversion stuff is buried in the constant.  I hate having to unravel empirical equations, but too many times the only ball park analysis tool is these stacks of coincidences.

David

RE: Interesting Equation

No idea where it came from.

Are there limits or ranges given for the input variables?  For air at ambient conditions (520 R, 14.7 psia) it suggests 6623 ft/sec.  That ain't right!

Good luck,
Latexman

RE: Interesting Equation

(OP)
I think you slipped a decimal Latexman.  For 14.73 psia and 60F for air I get 6620 ft/min or 110.4 ft/sec.  

The range of max velocities I see in people's standards is usually between 80 ft/sec and 120 ft/sec.  This is the first max velocity for piping that I've seen that didn't feel totally arbitrary.

David

RE: Interesting Equation

Since the constant is 380 ft/sec, I figured the answer was in ft/sec.

Good luck,
Latexman

RE: Interesting Equation

(OP)
OK, so I screwed up, not you.  The constant is supposed to be 380 ft/min.  I never use ft/min for anything so I have a hard time not shifiting into automatic and typing ft/sec.

David

RE: Interesting Equation

"I never use ft/min for anything"  Me too.  That sucks, but it's easy to fix.  Use 6.33 ft/sec.  Now it makes sense (in my example)!

Good luck,
Latexman

RE: Interesting Equation

If I had to guess, I'd say it's related to noise limits.

Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso

RE: Interesting Equation

(OP)
Not a bad guess, makes more sense than my first thought which was erosion.

David

RE: Interesting Equation

perhaps contacting the responsible authority within the company with the piping standard can answer the question.  does the standard have a contact name?

meanwhile, i'll send your request to a principal process engr; perhaps he may know the origin.

-pmover

RE: Interesting Equation

(OP)
The guy that included that in the standard said that he had copied it from the previous standard.  The guy that wrote the previous standard is dead.

David

RE: Interesting Equation

First of all I've never seen this formula before, anyhow the term T^0.5 (T absolute temperature in Rankine) reminded me something related to speed of sound. So I think the origin could really be related to noise issues (as pointed out above by BigInch).
What puzzles me a bit is that SG is at numerator and not at denominator. I would be more prone to accept that an increase in specific gravity implies a reduction of the max allowable velocity....
 

RE: Interesting Equation

(OP)
ione,
I didn't notice that.  I'm going to have to think about why that is.

David

RE: Interesting Equation

Humm.  Gum in the works.

Anyway, noise limiting factors at those velocities should also be considered.

Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso

RE: Interesting Equation

the principal process engr responded with:

"That is not an industry standard equation. The correct eqations are as follows:
100/sqrt(rmix) (Continuous)     Ft/sec
125/sqrt(rmix) (Intermittent)     Ft/sec
160/sqrt(rmix) (Erosional)     Ft/sec"

i'd at least notify the company of this observation (i.e. not known within industry) and let them decide of any changes.

I'd also bet that the "author" of that eqn conducted an analysis and created the eqn to suit certain conditions needed for the work being done at the time.  hence, the reason it was not published.

fyi, i did compare the eqn with those listed above yesterday for a couple of conditions and the results were nearly that of the intermittent eqn.

Good luck Dave!
-pmover

RE: Interesting Equation

pmover is correct for erosional velocity. I believe it comes from the standard, API RP 14E.

RE: Interesting Equation

(OP)
pmover,
The API equation is a constant divided by the square root of density (you didn't say what "rmix" is, but I'll assume it is density of the mixture).  This "constant divided by the square root of density" equation is a liquid model which results in outrageous velocities for gas.  For example at 30 psia and 60F, a 0.65 SG gas gives the following values:

Continuous = 314 ft/sec (0.237 Mach)
Intermittent = 393 ft/sec (0.296 Mach, this is the highest velocity where many researchers will use incompressible flow assumptions)
Erosional = 503 ft/sec (0.379 Mach)

No one would intentionally design pipeworks with those velocities.

The company in question has not done any original research in a couple of decades.  The standards author that first included this equation got it from somewhere (granted, there is no assurance that somewhere along the line it wasn't modified via typo, which is why I started this thread to find out if anyone else had seen it so I could verify that it had been entered correctly).

David

RE: Interesting Equation

David you are correct.  API RP 14E erosional velocity doesn't look like it has much to do with the origin of your equation in your first post.

The equation from API RP 14E uses the erosional velocity equation in the context of two phase gas/liquid flow.

According to the "Handbook of Natural Gas Transmission and Processing," it states:"In most pipelines, the recommended value for the gas velocity in the transmission pipelines is normally 40 to 50% of the erosional velocity (Mohipour, 2002)"  

Also it states that if there is much CO2, velocities should be limited to less than 50 ft/sec.



 

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