Accession Number : AD0424376
Title : ON AN INVESTIGATION OF MECHANICS OF RAREFIED GASES.
Descriptive Note : Final rept., 1 July 58-31 Mar 63,
Corporate Author : WEIZMANN INST OF SCIENCE REHOVOTH (ISRAEL)
Personal Author(s) : Pekeris,C. L.
Report Date : 10 JUL 1963
Pagination or Media Count : 43
Abstract : The linearized Boltzmann integral equation for the problem of propagation of sound was solved both for a Maxwell gas and for a rigid sphere gas. The solution is based on the eigenfunctions and eigenvalues of the collision operator. For the Maxwell gas 559 eigenvalues were computed. For the rigid sphere gas 30 coefficients of the series expansion of each of 105 eigenfunctions have been computed together with the corresponding eigenvalues. With these values the sound propagation and absorption coefficients have been obtained by successive approximations. Determinants up to order n = 483 were solved for the Maxwell gas and up to n = 105 for the rigid sphere gas. With the maximum order of 483 of the matrix solved for the Maxwell gas the values of the propagation parameters obtained show convergence to within 10 per cent for R > 0.6. For the rigid sphere gas convergence to within 2% is obtained for R > =.*. The theoretical results are in fairly good agreement with Greenspan's measurements of the speed and attenuation of sound in rarefied helium. It is shown that the kernel of the linearized Boltzmann integral equation for rigid sphere molecules is not square-integrable. (Author)
Descriptors : (*GASES, TRANSPORT PROPERTIES), (*RAREFIED GAS DYNAMICS, TRANSPORT PROPERTIES), VISCOSITY, PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, SPHERES, MOLECULES, DIFFERENTIAL EQUATIONS, SOUND, PROPAGATION, LINEAR SYSTEMS, ADSORPTION, THEORY, HELIUM, GASES, MECHANICS, SOUND TRANSMISSION
Distribution Statement : APPROVED FOR PUBLIC RELEASE