Improved Expansion Factors for Nozzles, Orifices, and Variable-Area Meters

An explicit equation is developed for calculating jet area increase due to compressibility when the incompressible coefficient is known. If the latter is dependent on Reynolds number, Y must be also. When adiabatic theory is applied to this new jet area, instead of to the aperture as measured by solid boundaries, agreement between theory and experiment is much improved. Orifice data on natural gas and variable-area data on air are analyzed in the light of such theory and revised values of Y are proposed. Pursuit of the methods described should lead to improvement of an order of magnitude in the accuracy of fluid flow measurement with nozzles, orifices, and variable-area meters in the sub-critical compressible regime. The author recommends that all expansion factors, theoretical and experimental, should be based on the stagnation temperature as well as on a statement of the particular pressure to be used with stagnation temperature in determining the density to be used in calculating the flow. In any event, no expansion factor can be meaningful unless accompanied by a definition of the temperature and pressure instrumentation used in experiment or assumed in theory.