The mass flow rate is computed from the one-dimensional choked-flow continuity equation: mass flow = density × area × velocity. The orifice area is in ft², converted from the diameter in inches by dividing \(\pi d^2/4\) by 144. The discharge coefficient \(C_d\) accounts for the vena contracta (the narrowing of the stream below the geometric orifice area) and friction losses. The factor 60 converts the per-second velocity to per-minute for consistent units.

\begin{equation}\label{eq:orifice-method-mass-flow} \dot{m} = \rho^* \cdot \frac{\pi d^2}{4 \cdot 144} \cdot V^* \cdot 60 \cdot C_d \end{equation}

Symbols

\(\dot{m}\)	Mass flow rate of leaked air through one orifice \([\unit{ \pound\per\minute}]\)
\(\rho^*\)	Air density at the sonic throat \([\unit{ \pound\per\cubicFoot}]\)
\(d\)	Orifice (leak opening) diameter \([\unit{ \inch}]\)
\(144\)	Unit conversion: square inches per square foot \([\unit{ \squareInch\per\squareFoot}]\)
\(V^*\)	Sonic velocity at the orifice throat \([\unit{ \foot\per\second}]\)
\(60\)	Seconds per minute conversion \([\unit{ \second\per\minute}]\)
\(C_d\)	Orifice discharge coefficient \([\unit{ \unitless}]\)