A formulation for the flow rate of a fluid passing through an orifice plate from the First Law of Thermodynamics

• The new equation does not contain a discharge coefficient or an expansion factor.
• The new equation does not require an iterative solution to obtain mass flow rate.
• The new equation fits the standard data as well as the existing equations.

This work presents a new equation to calculate the mass flow rate through an orifice plate for both natural gas and air samples using a thermodynamic approach. This simple equation does not contain the Reynolds number (viscosity does not appear), thus the calculation is explicit in the mass flow rate, not iterative. Because of its fundamental thermodynamic basis, the resulting expression does not include an expansion factor or discharge coefficient. The energy balance for the orifice plate coupled with experimental values of pressure, temperature, molar composition, densities, geometrical dimensions, and mass flow rates are available for several data sets covering distribution natural gas and air. A simple expression using dimensionless numbers: ΔP/P, diameter ratio (β), and heat capacity ratio (CP/CV) describes the kinetic energy changes calculated from the experimental values. The resulting mass flow rates for natural gas are within±0.4% (2σ  ) for 0≤(ΔP/P)≤0.30≤(ΔP/P)≤0.3.