\small \bold{\color{blue} \dot{m} = CA \ \sqrt[]{k \rho_{in} P_{in} { \left ( \frac{2}{k+1} \right ) }^{ \frac{k}{k-1}}} \ = \ CAP_{in} \ \sqrt[]{\left ( \frac{kM}{Z_{in} RT_{in}} \right ) { \left ( \frac{2}{k+1} \right ) }^{ \frac{k}{k-1}}} } |
\small {\color{black} \dot{m} } = mass flow rate, kg/s |
\small {\color{black} C } = discharge coefficient, dimensionless, usually 0.72. |
\small {\color{black} A } = discharge hole cross-sectional area, m^{2}. |
\small {\color{black} \rho_{in}} = real gas (total) density at total pressure P_{in} and total temperature T_{in}, kg/m^{3}. |
\small {\color{black} T_in } = absolute upstream total temperature of the gas, K. |
\small {\color{black} M } = gas molecular weight (dimensionless). |
\small {\color{black} R } = Universal Gas Law constant, (Pa.m^{3}) / (kgmol.K) = 8.314472.10^{3}. |
\small {\color{black} Z_{in}} = the gas compressibility factor at P_{in} and T_{in}. Ideal gas Z_{in} = 1. |