The formula derives from the continuity equation applied to a compressible fluid. The free-air flow rate \(Q\) is first converted to the actual compressed-air volumetric flow at operating pressure using Boyle's Law:

\begin{equation}\label{eq:boyles-law} Q_{compressed} = Q \cdot \dfrac{P_{atm}}{P_{line} + P_{atm}}\end{equation}

The required cross-sectional area at the design velocity is:

\begin{equation}\label{eq:cross-sectional-area} A_{ft^2} = \dfrac{Q_{compressed}}{v \cdot k_{60}}\end{equation}

Converting from ft² to in² by multiplying by \(k_{144}\):

\begin{equation}\label{eq:pipe-sizing-area} A = \frac{k_{144} \cdot Q \cdot P_{atm}}{v \cdot k_{60} \cdot (P_{line} + P_{atm})} \end{equation}

Symbols

\(A\)	Minimum required internal cross-sectional area \([\unit{ \inch\squared}]\)
\(k_{144}\)	Square inches per square foot (144) \([\unit{ \inch\squared\per\squareFoot}]\)
\(Q\)	Volumetric free-air flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(P_{atm}\)	Atmospheric (absolute) pressure \([\unit{ \psia}]\)
\(v\)	Maximum allowable compressed-air design velocity \([\unit{ \foot\per\second}]\)
\(k_{60}\)	Seconds per minute (60) \([\unit{ \second\per\minute}]\)
\(P_{line}\)	Operating gauge pressure in the pipe \([\unit{ \psig}]\)

Note

\(P_{line} + P_{atm}\) converts gauge pressure to absolute pressure (Boyle's Law requires absolute pressures). The combined factor \(k_{144} / k_{60} = 2.4\) converts the area from ft²·min/s to in².