A survey of flow at low pressures

The theory of internal flows at such low pressures that the Navier-Stokes equations are not valid is reviewed. In the extreme low pressure range (free molecular flow), where the flow rate is independent of pressure, the basic theory is well developed. However, the influence of channel lenght, cross sectional shape, or surface characteristics have not been totally defined. Slip theory, which extends the low pressure range of the Navier-Stokes equation by modifying the wall boundary conditions, is discussed. The theory provides a good basis for experimental data correlation, but is not adequate to extend the viscous equations into the free molecular range. The empirical methods used to provide a smooth transition from slip to free molecular flow are reviewed, and a method of obtaining an equation for the total flow regime is illustrated. The extensive work in physical gas dynamic is discussed. Boltzmann's equation which has been solved numerically for small pressure gradients was found to be valid only in the viscous regime near the free molecular flow range.