Interesting Equation 1

[zdas04]

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

v_max=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

 

[jmw]

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

JMW

http://www.ViscoAnalyser.com

 

[MJCronin]

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

How do you get a velocity as a result ?

 

[zdas04]

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

 

[zdas04]

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

 

[Latexman]

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

 

[zdas04]

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

 

[Latexman]

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

Good luck,
Latexman

 

[zdas04]

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

 

[Latexman]

"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

 

[BigInch]

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

 

[zdas04]

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

David

 

[pmover]

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

 

[zdas04]

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

 

[BigInch]

Similar variables to what appears here. I think it will plot as some proportion of mach number vs density

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

 

[ione]

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....

 

[zdas04]

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

David

 

[BigInch]

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

 

[pmover]

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

 

[CRG]

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