By Holt Ashley

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**Extra resources for Aerodynamics of Wings and Bodies**

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Dz. (4-56) This is called the "displacement thickness," because the effect of the slowing down of the fluid in the boundary layer on the flow outside it is equivalent to that of a body of thickness 6·. 73EVx. (4-57) The equivalence of the limiting value with that occurring in (4-50) is easily seen since f' (00) = 1. A flow that is tangent to a thin body of this thick. --+--,. 73 Re {yl/2}. 73iy 1 / 2 . 111 BOUNDARY LAYER ON A FLAT PLATE (4-53) It is easily verified that the appropriate solution is wi = I ) 4-3] .

143)* (4-46) 'lil = V2x/(Tt), where Tt = z/V2x. This transformation gives an ordinary differential equation for I, namely: It follows directly from (4-36) that the outer flow must be a parallel undisturbed one: (4-38) 'lig = z, Po = P.. (x, 00) = 1. (4-45) (4-36) (4-37) pg = p.. I BOUNDARY LAYER ON A FLAT PLATE 4-3] UO (4-33) I I I 1 (4-40) I'" 1(0) + If" = 1'(0) = 1'(00) = (4-41) • Notice that this efIuation contains only x-derivatives of first order. It is a parabolic differential equation, like the equation of heat conduction (with x replacing time).

Flow problem Expansion in 6 or liVRe I .. 1 c ~ Two-dimensional flow Two-dimensional crossflow Slender-body theory FIG. 3-1. Use of series expansions for obtaining approximate solutions to aerodynamic problems. 1 I I 62 I I 1 SINGULAR PERTURBATION PROBLEMS [CHAP. 3 The second method of approximation that will be considered is the purely numerical one. In the future this will undoubtedly become of increasing importance as the full potentialities of modern computing devices are realized among aerodynamicists.