The speed of sound at the throat temperature follows from isentropic relations. The throat temperature is lower than the supply temperature by the factor \(2/(\gamma+1)\). Substituting into the sound-speed formula and using the gravitational conversion constant \(g_c = 32.2\) lbm·ft/(lbf·s²) to reconcile U.S. customary units gives the expression below. Note: the supply temperature \(T_R\) is used directly because the stagnation-to-throat temperature ratio \(2/(\gamma+1)\) is already absorbed into the leading coefficient.

\begin{equation}\label{eq:orifice-method-sonic-velocity} V^* = \sqrt{\frac{2\gamma}{\gamma + 1} \cdot R_{air} \cdot T_R \cdot g_c} \end{equation}

Symbols

\(V^*\)	Sonic air velocity at the orifice throat \([\unit{ \foot\per\second}]\)
\(\gamma\)	Ratio of specific heats for dry air (1.4) \([\unit{ \unitless}]\)
\(R_{air}\)	Specific gas constant for dry air (53.34 ft·lbf per lbm·°R) \([\unit{ \foot\lbf\per\lbm\per\degreeRankine}]\)
\(T_R\)	Air temperature in degrees Rankine \([\unit{ \degreeRankine}]\)
\(g_c\)	Gravitational conversion constant (32.2 lbm·ft per lbf·s²) \([\unit{ \lbm\foot\per\lbf\per\second\squared}]\)