where: q v {\displaystyle q_{v}{}} = volumetric flow rate (at any cross-section), m³/s q m {\displaystyle q_{m}} = mass flow rate (at any cross-section), kg/s C d {\displaystyle C_{d}} = coefficient of discharge, dimensionless C {\displaystyle C} = orifice flow coefficient, dimensionless A 1 {\displaystyle A_{1}} = cross-sectional area of the pipe, m² A 2 {\displaystyle A_{2}} = cross-sectional area of the orifice hole, m² D {\displaystyle D} = diameter of the pipe, m d {\displaystyle d} = diameter of the orifice hole, m β {\displaystyle \beta } = ratio of orifice hole diameter to pipe diameter, dimensionless V 1 {\displaystyle V_{1}} = upstream fluid velocity, m/s V 2 {\displaystyle V_{2}} = fluid velocity through the orifice hole, m/s p 1 {\displaystyle p_{1}} = fluid upstream pressure, Pa with dimensions of kg/(m·s² ) p 2 {\displaystyle p_{2}} = fluid downstream pressure, Pa with dimensions of kg/(m·s² ) ρ {\displaystyle \rho } = fluid density, kg/m³