For Orifice plate #Application

${\displaystyle q_{m}={\frac {C}{\sqrt {1-\beta ^{4}}}}\;\epsilon \;{\frac {\pi }{4}}\;d^{2}\;{\sqrt {2\;\Delta p\;\rho _{1}}}}$

${\displaystyle \epsilon =1-(0.351+0.256\beta ^{4}+0.93\beta ^{8}){\bigg [}1-{\bigg (}{\frac {p_{2}}{p_{1}}}{\bigg )}^{\frac {1}{\kappa }}{\bigg ]}}$

${\displaystyle C=0.5961+0.0261\beta ^{2}-0.216\beta ^{8}+0.000521{\bigg (}{\frac {10^{6}\beta }{Re_{D}}}{\bigg )}^{0.7}+(0.043+0.080e^{-10{L_{1}}}-0.123e^{-7{L_{1}}})(1-0.11A){\frac {\beta ^{4}}{1-\beta ^{4}}}-0.031(M'_{2}-0.8{M'_{2}}^{1.1})\beta ^{1.3}}$ unless D < 71.2mm in which case this further term must be added to C: ${\displaystyle +0.011(0.75-\beta ){\bigg (}2.8-{\frac {D}{25.4}}{\bigg )}}$

where:
${\displaystyle C}$	= coefficient of discharge, dimensionless
${\displaystyle d}$	= orifice diameter, m
${\displaystyle D}$	= pipe diameter, m
${\displaystyle L_{1}}$	= ratio of distance of upstream tapping from upstream plate to pipe diameter, ${\displaystyle {\frac {l_{1}}{D}}}$
${\displaystyle p_{1}}$	= fluid absolute static pressure in plane of upstream tapping, Pa
${\displaystyle p_{2}}$	= fluid absolute static pressure in plane of downstream tapping, Pa
${\displaystyle q_{m}}$	= mass flow rate, kg/s
${\displaystyle Re_{D}}$	= pipe Reynolds number, ${\displaystyle {\frac {4q_{m}}{\pi \mu D}}}$
${\displaystyle \beta }$	= diameter ratio of orifice diameter to pipe diameter, dimensionless
${\displaystyle \Delta p}$	= differential pressure, Pa
${\displaystyle \epsilon }$	= expansibility factor, also called expansion factor, dimensionless
${\displaystyle \kappa }$	= isentropic exponent, often approximated by specific heat ratio, dimensionless
${\displaystyle \mu }$	= dynamic viscosity of the fluid, Pa.s
${\displaystyle \rho _{1}}$	= fluid density in plane of upstream tapping, kg/m³