Approximate Calculation of Expansion of Gas from Nozzles into High Vacuum

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Abstract
The exact calculation of the density of a steady-state gas flow by means of the Boltzmann function generally leads to great mathematical difficulties, in the case of an expanding gas passing from the viscousflow region into the molecular flow region. An approximate solution can be found by replacing the actually continuous transition from viscous to molecular flow with a suitably defined discontinuity surface. Molecules that leave the viscous region through this surface continue to fly in straight lines with their respective velocities. By adopting this conception, the density at each point of the molecular-flow region can be found by integration. The general procedure is specialized for the case of the two-dimensional flow and can be applied to the supersonic flow around a corner in vacuum.

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