Flow formulas for gas - where does the factor "514" come from?

Formulas for gas and liquid media are available for calculating the flow rate, the pressure drop or the kv-value. While the formulas for calculating these values for liquid media are based purely on variables, additional factors are used in the formulas for gaseous media. These factors are generally not derived in the literature, which is a nuisance to any ambitious engineer, as they cannot understand which parameters are packed into these factors. This article attempts to get to the bottom of this.

Calculation for gaseous media:

[1]         https://www.samsongroup.com/document/t00050de.pdf

[2]         http://www.mankenberg.de/UPLOAD/pdf/s33_0.pdf

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