Impact pressure probe in free molecular flow

The impact pressure probe in free molecular flow is studied theoretically on the assumption that the gas entering the tube has a Maxwellian distribution and that the molecules are reflected diffusely at the tube wall. The case is considered in which the tube length is very large compared with its diameter. An asymptotic theory for a long tube is employed in the analysis to obtain the pressure at the gage volume attached to one end of the tube. Numerical calculations are made on the properties of the probe for speed ratios up to 5.0 and angles of attack ranging from 0 to 180 deg. A comparison with previous work based on the Clausing approximation makes it clear that the error due to this approximation increases with the speed ratio, reaching about 10% at a speed ratio of 5.0. An explicit formula for the gage pressure is also obtained in the case of small speed ratios.