Hypersonic Adiabatic Impact Pressure of a Rarefied Gas

Abstract

A solution to the Boltzmann equation for the Pitot tube problem is formulated. The distribution function is taken as a sum of two separate distribution functions, one of which is characteristic of the molecules coming from the free stream and the other of the molecules emerging from the tube wall. Each distribution function is further divided into quadrants in the velocity space. The local variables are the number densities in these quadrants and are determined by taking appropriate moments of the Boltzmann equation. Governing equations for the flow of a rarefied gas in an impact tube under hypersonic and adiabatic conditions are derived. Approximate closed form solution to these equations is obtained. The results are in close agreement with other theories for the free molecule limit and with experimental data for finite mean free paths.