Rearranges the pneumatic valve flow formula to solve for the dimensionless valve flow coefficient Cv. Use this method when the required flow rate and operating pressures are known and a valve must be selected or verified. Select a valve whose catalog Cv rating equals or exceeds the calculated value.

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

Symbols

\(C_v\)	Dimensionless valve flow coefficient \([\unit{ \unitless}]\)
\(Q\)	Measured or required air flow rate \([\unit{ \scfm}]\)
\(k_{flow}\)	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: Cv is treated as dimensionless in this formula; the unit dependence is absorbed into the constant \(k_{flow}\). A higher Cv indicates a valve with lower flow restriction. Pressures must be in psia (absolute). Always select a valve with a catalog Cv at least as large as the calculated value to ensure the system can meet its flow requirements.