Rayleigh's Problem for a Cylinder of Arbitrary Shape, II
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概要
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Continuing the previous work I (J. Phys. Soc. Japan 9 (1954) 611), the author discusses the frictional force on an arbitrary cylinder which is started to move suddenly from rest with uniform velocity W in the direction of its length. By using the WKB method, a new asymptotic expansion formula in powers of √<vt>/R is derived for the frictional drag τ on the cylinder with no corners; [numerical formula] where v is the kinematic viscosity, t is the time measured from the start, R is the local radius of curvature of the surface measured inwards, and ds is the line element along the surface. The first approximation gives the naturally expected value μW/√<πvt> for the frictional drag per unit area, which is the same as that for a flat plate of infinite breadth. As far as the second approximation the total frictional drag on the cylinder is the same as that on a circular cylinder with the same perimeter, and is in accord with the results recently obtained by Batchelor. The effect of the variation of the curvature along the surface on the local friction first appears in the fourth order of approximation. The correction due to the presence of corners is made in the second approximation, and some errors in Batchelor's paper are corrected. For the intermediate value of vt the drag calculated by these formulae shows a good agreement with that calculated by the formulae in powers of (vt)^<-1> as given in I.
- 社団法人日本物理学会の論文
- 1955-05-05
著者
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Hasimoto Hidenori
Department Of Physics Faculty Of Science University Of Tokyo
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Hasimoto Hidenori
Department Of Aeronautical Engineering Faculty Of Engineering Kyoto University
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- Rayleigh's Problem for a Cylinder of Arbitrary Shape, II