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Sphere Drag in Flows of Almost‐Free Molecules
dc.contributor.authorLiu, Vi‐Chengen_US
dc.contributor.authorPang, Sing‐Chinen_US
dc.contributor.authorJew, Howarden_US
dc.date.accessioned2010-05-06T22:22:31Z
dc.date.available2010-05-06T22:22:31Z
dc.date.issued1965-05en_US
dc.identifier.citationLiu, Vi‐Cheng; Pang, Sing‐Chin; Jew, Howard (1965). "Sphere Drag in Flows of Almost‐Free Molecules." Physics of Fluids 8(5): 788-796. <http://hdl.handle.net/2027.42/70574>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70574
dc.description.abstractA kinetic theory of sphere drag in the transition flows, based on the Boltzmann equation for the Maxwellian molecules, is presented. The exact binary collision integral, in the first order Knudsen iteration, is expanded as a function of Hermite polynomials in molecular velocity. The drag of a sphere at free stream temperature with molecular diffuse reflection is calculated. The results agree well with Millikan's measured values over a wide range of Knudsen number (0.5 < λ∕d < 10). It is found that the sphere drag of the almost‐free molecular flows normalized by the corresponding collisionless drag is essentially independent of the speed ratio for the present range of calculations.en_US
dc.format.extent3102 bytes
dc.format.extent676660 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleSphere Drag in Flows of Almost‐Free Moleculesen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Aeronautical and Astronautical Engineering, The University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70574/2/PFLDAS-8-5-788-1.pdf
dc.identifier.doi10.1063/1.1761321en_US
dc.identifier.sourcePhysics of Fluidsen_US
dc.identifier.citedreferenceG. N. Patterson, Molecular Flow of Gases (John Wiley & Sons, Inc., New York, 1956).en_US
dc.identifier.citedreferenceD. R. Willis, Rand Report R‐339 (1959).en_US
dc.identifier.citedreferenceR. M. L. Baker and A. F. Charwat, Phys. Fluids 1, 73 (1958).en_US
dc.identifier.citedreferenceZ. Szymanski, Arch. Mech. Stos (Warsaw) 8, 449 (1956); 9, 35 (1957).en_US
dc.identifier.citedreferenceR. A. Millikan, Phys. Rev. 22, 1 (1923).en_US
dc.identifier.citedreferenceV. C. Liu, J. Aeron. Sci. 25, 779 (1958); also J. Fluid Mech. 5, 481 (1959).en_US
dc.identifier.citedreferenceS. Chapman and T. G. Cowling, Mathematical Theory of Non‐Uniform Gases (Cambridge University Press, New York, 1951).en_US
dc.identifier.citedreferenceH. Grad, Commun. Pure Appl. Math. 2, 325 (1949). [Note: the definition of B(θ)B(θ) is different from Grad’s by a factor of B1B1].en_US
dc.identifier.citedreferenceFor the Maxwellian molecules, B1  =  B1(n)B1=B1(n) following the notations used in Ref. 8.en_US
dc.identifier.citedreferenceC. S. Wang Chang and G. E. Uhlenbeck, University of Michigan ERI Report M999 (1953); D. R. Willis, thesis, Princeton University (1959).en_US
dc.identifier.citedreferenceV. C. Liu, University of Michigan ORA Report 02885‐11‐F (1962).en_US
dc.identifier.citedreferenceR. Goldberg, thesis, New York University (1954).en_US
dc.identifier.citedreferenceJ. C. Maxwell, Collected Works (Dover Publications, Inc., New York).en_US
dc.identifier.citedreferenceThe suggestion of the reviewer is appreciated.en_US
dc.identifier.citedreferenceIn this comparison the same expression for the mean free path is used in calculating Knudsen numbers.en_US
dc.identifier.citedreferenceH. Grad, in Handbuch der Physik, edited by S. Flügge (Springer‐Verlag, Berlin, 1958), Vol. 12, p. 292.en_US
dc.identifier.citedreferenceThe only approximation introduced is at representation of the molecular flux of the reflected molecules other than the truncation of the Hermite expansion.en_US
dc.owningcollnamePhysics, Department of


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