decibels_method Namespace Reference

Compressed air leak flow estimation using ultrasonic decibel measurements. More...

Classes
struct	Input
	Input parameters for the decibels method compressed air leak calculation. More...
struct	Result
	Result of the decibels method leak flow rate calculation. More...

Functions
Result	calculate (const Input &input)
	Estimates compressed air leak flow rate and annual consumption using the decibels method.

Detailed Description

The decibels method estimates compressed air leak flow rate by applying bilinear interpolation to a pair of reference data points. An ultrasonic detector measures the decibel level at the leak and the line pressure is recorded. Two calibration reference points — each defined by a pressure, a decibel rating, and the corresponding flow rates at the adjacent pressure — bracket the measured values. Bilinear interpolation across the pressure and decibel axes yields the leak flow rate without requiring physical access to the leak point.

See also

Decibels Method Calculator

Function Documentation

calculate()

Result decibels_method::calculate

(

const Input &

input

)

The leak flow rate is determined by bilinear interpolation over two reference axes: line pressure and ultrasonic decibel level. Two calibration reference points bracket the measured values; each point supplies flow rates at two pressures, forming a 2×2 grid of known flow values. Standard bilinear interpolation across this grid yields the leak rate at the measured conditions.

Annual consumption scales the instantaneous leak rate by operating hours and the minutes-per-hour factor, then converts to kiloscf.

Leak Rate Estimate:

\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}

where:

\(Q_{leak}\)	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) \([\unit{ \decibel}]\)
\(Q_{11}\)	Flow rate at (P_1,\, L_1) — first_flow_a \([\unit{ \scfm}]\)
\(Q_{21}\)	Flow rate at (P_2,\, L_1) — second_flow_a \([\unit{ \scfm}]\)
\(Q_{12}\)	Flow rate at (P_1,\, L_2) — first_flow_b \([\unit{ \scfm}]\)
\(Q_{22}\)	Flow rate at (P_2,\, L_2) — second_flow_b \([\unit{ \scfm}]\)

Annual Consumption:

\begin{equation}\label{eq:decibels-method-annual-consumption} C_{annual} = \frac{Q_{leak} \cdot t_{op} \cdot 60}{1000} \end{equation}

where:

\(C_{annual}\)	Estimated annual air loss from the leak \([\unit{ \kscf}]\)
\(Q_{leak}\)	Compressed air leak flow rate \([\unit{ \scfm}]\)
\(t_{op}\)	Annual system operating time \([\unit{ \hour}]\)
\(60\)	Minutes per hour conversion \([\unit{ \minute\per\hour}]\)
\(1000\)	Standard cubic feet per kiloscf \([\unit{ \unitless}]\)

Note

The reference pressures pressure_a and pressure_b and reference decibel ratings decibel_rating_a and decibel_rating_b must bracket the measured line_pressure and decibels respectively. Extrapolation beyond the reference grid is mathematically valid but may reduce accuracy.

Parameters

[in]

input

Input

Returns

Result containing leak_rate_estimate [scfm] and annual_consumption [kscf].