Change in conductance of cylindrical orifice by beveling its edge and tapering its tube

Conductance of a thin cylindrical orifice is calculated farily accurately by an approximate equation. However, a practical orifice may have rounded edges and tapered shape. Influence of these deformation on the conductance was studied by Monte Calro simulation for thickness of the orifice L = 0-0.1r, where r was the radius of the orifice, beveled depth ΔL = 0-0.002r, angle of beveled edge 6 = θ=90 and difference of radius between inlet and outlet sides Δr= 0-0.002r. Results are 1) the conductance increases for 0.08% by beveling edge by 0.002r at the beveling angle of 45, and the increase was proportional to AL, 2) an increase caused by beveling both inlet and outlet sides was almost twice as large as that caused by beveling either side, 3) an increase caused by beveling either side at the beveling angle of 20 was more than a half of an increase at the angle of 90 (reducing orifice thickness ΔL), 4) an increase caused by tapering radius Δr was almost a half of the increase by enlarging the radius Δr. These results were explained by an approximate equation based on a simple model.