The orifice/pressure method estimates flow rate using a quadratic equation fit to empirical flow-versus-pressure data for 12 standard nozzle types (indices 0–11). Each nozzle type has a distinct set of coefficients \(a\), \(b\), and \(c\) from the lookup table in Nozzle Coefficient Lookup Table. The single-nozzle flow rate is computed from the supply pressure; total flow rate and annual consumption then scale with the number of nozzles.

\begin{equation}\label{eq:compressed-air-reduction-pressure-flow-rate} Q_{nozzle} = a \cdot P^2 + b \cdot P + c\end{equation}

\begin{equation}\label{eq:compressed-air-reduction-pressure-total-flow} Q_{total} = Q_{nozzle} \cdot N_{nozzles}\end{equation}

\begin{equation}\label{eq:compressed-air-reduction-pressure-consumption} C = Q_{total} \cdot t_{op} \cdot 60\end{equation}

Symbols

\(Q_{nozzle}\)	Flow rate per individual nozzle \([\unit{ \cubic\foot\per\minute}]\)
\(a, b, c\)	Nozzle-type-specific quadratic coefficients (from lookup table) \([\unit{ \unitless}]\)
\(P\)	Compressed air supply pressure \([\unit{ \psi}]\)
\(Q_{total}\)	Total compressed airflow rate \([\unit{ \cubic\foot\per\minute}]\)
\(N_{nozzles}\)	Number of nozzles in the system \([\unit{ \unitless}]\)
\(C\)	Annual compressed air consumption \([\unit{ \cubic\foot\per\year}]\)
\(t_{op}\)	Annual operating hours \([\unit{ \hour\per\year}]\)
\(60\)	Unit conversion factor (minutes per hour) \([\unit{ \minute\per\hour}]\)

Note: The coefficients \(a\), \(b\), and \(c\) depend entirely on the selected nozzle type. All 12 nozzle-type coefficient sets are listed in Nozzle Coefficient Lookup Table.; This method differs fundamentally from the orifice method used in the Orifice Method Calculator. Here the flow source is a manufactured end-use nozzle whose exact orifice geometry may be unknown but whose flow characteristics have been empirically characterised; a pre-fitted quadratic curve is therefore more accurate than a geometry-based calculation. In the leak survey the source is an unintended opening of known diameter, so first-principles compressible-flow equations applied directly to the hole geometry give the best estimate.

See also: Nozzle Coefficient Lookup Table