An Analysis of Flow through a Sharp-Edged Orifice in a Pipe under the Free-Molecule Flow Regime

Abstract

The characteristics of pipe-orifice flow in the free-molecule flow regime are analyzed by the kinetic theory of gases. Main attention is paid to number flux distributions of incident molecules on the pipe wall, which are given by simultaneous integral equations. The numerical solutions show that the interaction region between pipe flow and orifice one exists always at the vicinity of the orifice plate, and depends strongly on the ratio of the pipe-length to the pipe-diameter but weakly on the ratio of the orifice-diameter to the pipe-diameter. The analysis also shows that the conductance of a pipe-orifice having a finite pipe-length should be calculated exactly instead of bureau's approximate formula based on the assumption of no interaction, since the effects of the interaction become relatively large as the pipe-length decreases.