Mass flow through a circular orifice and a two-dimensional slit at high Knudsen numbers

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Abstract
The local and total mass flow through a circular orifice and a two-dimensional slit with large upstream to downstream pressure ratio is calculated for large Knudsen number. The solution is obtained by performing one iteration on an integral form of the kinetic equation, starting with the free molecular solution for the distribution function. A relaxation model is used to describe the inter-molecular collisions. There is found to be a variation of approximately 40% in the local mass flow perturbation (from the free molecular value) across the orifice. For the slit the variations are smaller when the Reynolds number is less than 0·3, but are comparable for greater values. This Reynolds number, defined by with R the radius of the orifice or half-width of the slit and with the flow field quantities evaluated far upstream, appears to be a less ambiguous quantitative parameter than the inverse Knudsen number. The ratio of total mass flow to the free molecular value is given by [1+0·083 Re+o(Re)] for the orifice and [1−0·057 Re ln Re+0·055 Re+o(Re)] for the slit. There is agreement within experimental error between the theoretical results and available experimental data for the circular orifice when Re < 1.

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