By Boresi and Schmidt

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L A G E R S T R O M Introduction. The present paper and Réf. 1 are essentially based on Ref. 2. Some of the basic ideas of Ref. 2 have been described and applied in Ref. 3; pp. 872-877 in particular may serve as an introduction to the present paper and to Réf. 1. A concrete application of the ideas described below is given in Réf. 1. We consider viscous incompressible stationary flow past an arbitrary finite body in two or three dimensions. The following notation is used q = velocity, ρ = density = constant, ρ = pressure, ν = kinematic viscosity, L = characteristic χ2 length of body, (x<) = Cartesian coordinates, χ = xl7 = Σ ί - ι χ where η is the dimension of the space.

43, N o . 2, 3 8 1 - 4 0 7 (April 1 9 4 2 ) . [ 2 ] R. V O N MISES and K . O . FRIEDRICHS, Fluid Dynamics, Chapter I V (Brown University [Notes], Summer, 1941). [3] G. E. L A T T A , Singular Perturbation Problems, Thesis, Calif. Inst, of Technol. (1951). [4] M. D . V A N D Y K E , Private communication. [5] P. A . LAGERSTROM, Private communication. 41 FLUID M E C H A N I C S A N D S I N G U L A R V o l . V , 1954 PERTURBATIONS T h e R o l e of C o o r d i n a t e S y s t e m s in B o u n d a r y - L a y e r T h e o r y 135 [6] P.

However, to obtain the local distribution of skin friction and pressure at the sphere, the full term u x must be used. Explicit Expression for h for the Sphere. By a straightforward calculation x one finds that the solution of Eqs. 30a, b with conditions (31a, b) is hi = h lp+ h lc + A h 0, where + m b$ ~ I * ( v logr * + S )] + ΐ ο ΐ ϊ έ ( * %^) 1 x v and h is given by Eq. 24. The corresponding pressure is 0 μϋ 2 ~ 128r* L \ r* 2 2 Ί 2r* \ r* + 2 V 2 4r* \ r* 2 1_4(Sx*2 Λ+ 1 _ V 9 χ*3 x (όόΌ) 32r* \r* /J 128 r* ' Here the last term on the right corresponds to ^ h o in (33a).