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
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
JMW
www.ViscoAnalyser.com
RE: Interesting Equation
How do you get a velocity as a result ?
RE: Interesting Equation
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
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
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
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
Good luck,
Latexman
RE: Interesting Equation
David
RE: Interesting Equation
Good luck,
Latexman
RE: Interesting Equation
Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso
RE: Interesting Equation
David
RE: Interesting Equation
meanwhile, i'll send your request to a principal process engr; perhaps he may know the origin.
-pmover
RE: Interesting Equation
David
RE: Interesting Equation
Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso
RE: Interesting Equation
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
I didn't notice that. I'm going to have to think about why that is.
David
RE: Interesting Equation
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
"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
RE: Interesting Equation
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
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.
RE: Interesting Equation
JMW
www.ViscoAnalyser.com