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Wednesday, November 7, 2007


In previous post, i have informed the first errata in API Std 521, edition Jan 2007. As expected more reading on this code found another discrepancy compare to previous version. This discrepancy is mainly due to REMOVAL of specific heat ratio (k) in the Mach number and Critical pressure calculation.

Equation [23] & [24] and [25] & [26] in API RP 521, 1997 (previous revision) are used to calculate the Mach number and Critical pressure of gas in the pipe.

Mach number
In imperial unit,


In metric unit,


Critical pressure
In imperial unit,


In metric unit,


After the API RP 521 is updated, similar equations used to calculate Mach number and Critical pressure has minimum modification.

Mach number
In imperial unit,


In metric unit,


Critical pressure
In imperial unit,


In metric unit,


Detail review on above equations, the specific heat capacity ratio (k) has been removed from the original equation. Is this a correction or an error ?

I have made some literature surveys and conduct some derivation works. Two main findings :

  • API R 521 1993 – No specific heat capacity ratio (k) included in the equation. However, API has included the k factor into the equation when it revised to API RP 1997. Once again, when it revised recently to 2007, the k factor has been removed again.
  • Quick derivation showed that k factor should appear in the equation.
Details refer below :



Based on simple derivation works, it ended-up with inclusion of k factor in the equation.

This discrepancy has been highlighted to API committee manager attention and quick response indicated equations in current edition (2007) are correct where k factor should not appear in those equations. Due to manning issue, no detail basis disclosed. Details searching do not find any supporting documents.

k factor generally range from 1.09 to 1.41 for most gases. Inverse square-root of k would range from0.84 to 0.96. Inclusion of k in the equation would probably bring down Mach number and critical pressure. Both impacts are partially balancing each and minimum impact to flowrate.

After further discussion and anaylsis, it's found that considering isothermal flow, the k factor should be omitted from the Mach number and critical pressure calculation. Details derivation may refer to "Removal of Specific Heat ratio (k) in the Mach No. & Critical Pressure Calculation".

- Nov 8, 2007
: This issue is being discussed in CheResource forum (Click HERE to view)
- Sept 28, 2008 : Post updated with omission of k factor.

Further Reading :

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posted by Webworm, 6:28 AM


Anonymous P.Leckner said...

k should NOT be in the equation and it was an error in the previous edition. I'm happy to see it finally be corrected.

The equations given by API are specifically stated to be for ISOTHERMAL gas flow, NOT ADIABATIC gas flow. The ratio of specific heats is for ADIABATIC conditions, NOT ISOTHERMAL conditions.

September 12, 2008 at 3:19 PM  

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