Computes the theoretical air flow rate for a valve with Cv = 1 using the simplified compressible-flow pneumatic valve formula. This formula is valid for subsonic (non-choked) flow of dry air at standard conditions (60°F, 14.696 psia) and is commonly used for conservative valve sizing in industrial compressed air systems.

The factored form used in the calculation is algebraically identical to the square-of-pressures form: \(\sqrt{(P_{in} - P_{out})(P_{in} + P_{out})} = \sqrt{P_{in}^2 - P_{out}^2}\).

\begin{equation}\label{eq:pneumatic-valve-flow-rate} Q = k_{flow} \cdot \sqrt{(P_{in} - P_{out}) \cdot (P_{in} + P_{out})} \end{equation}

Symbols

\(Q\)	Air flow rate through the valve (Cv = 1) \([\unit{ \scfm}]\)
\(k_{flow}\)	Empirical air flow constant for dry air at standard conditions (0.6875) \([\unit{ \scfm\per\psi}]\)
\(P_{in}\)	Inlet (upstream) absolute pressure \([\unit{ \psi}]\)
\(P_{out}\)	Outlet (downstream) absolute pressure \([\unit{ \psi}]\)

Note: The constant \(k_{flow} = 0.6875\) is empirically derived from isentropic flow theory for dry air (specific heat ratio \(\gamma = 1.4\)) at standard conditions. Pressures must be in psia (absolute). For a valve with a specific Cv, multiply \(Q\) by that Cv value.