The leak flow rate is determined by bilinear interpolation over a 2×2 grid of reference flow values supplied by the ultrasonic detector manufacturer. The grid axes are line pressure (P) and ultrasonic decibel level (L). Two reference pressures (P₁ and P₂) and two reference decibel ratings (L₁ and L₂) define the grid corners; the measured line pressure P and decibel level L are interpolated within this grid.

The four reference flow values at the grid corners are:

• Q₁₁: flow at (P₁, L₁) — first_flow_a
• Q₂₁: flow at (P₂, L₁) — second_flow_a
• Q₁₂: flow at (P₁, L₂) — first_flow_b
• Q₂₂: flow at (P₂, L₂) — second_flow_b

The formula reduces to the known corner value when the measured point falls exactly on a reference corner, and to linear interpolation when the measured point lies on a reference edge.

\begin{equation}\label{eq:decibels-method-leak-rate} Q_{leak} = \frac{ (P_2 - P)(L_2 - L)\,Q_{11} + (P - P_1)(L_2 - L)\,Q_{21} + (P_2 - P)(L - L_1)\,Q_{12} + (P - P_1)(L - L_1)\,Q_{22} }{(P_2 - P_1)(L_2 - L_1)} \end{equation}

Symbols

\(Q_{leak}\)	Estimated compressed air leak flow rate \([\unit{ \scfm}]\)
\(P\)	Measured line pressure \([\unit{ \psig}]\)
\(L\)	Measured ultrasonic decibel level at the leak \([\unit{ \decibel}]\)
\(P_1\)	Reference pressure (pressure_a) \([\unit{ \psig}]\)
\(P_2\)	Reference pressure (pressure_b) \([\unit{ \psig}]\)
\(L_1\)	Lower reference decibel rating (decibel_rating_a) \([\unit{ \decibel}]\)
\(L_2\)	Upper reference decibel rating (decibel_rating_b) \([\unit{ \decibel}]\)
\(Q_{11}\)	Reference flow at (P_1,\, L_1) — first_flow_a \([\unit{ \scfm}]\)
\(Q_{21}\)	Reference flow at (P_2,\, L_1) — second_flow_a \([\unit{ \scfm}]\)
\(Q_{12}\)	Reference flow at (P_1,\, L_2) — first_flow_b \([\unit{ \scfm}]\)
\(Q_{22}\)	Reference flow at (P_2,\, L_2) — second_flow_b \([\unit{ \scfm}]\)