It is convenient to define a radius r to the surface of the equivalent body, shown in 

 Figure 2, 



T* = T^ + a cos a [15] 



Then from [12] 



T* =yrj +2 A* cos a [16] 



AXISYMMETRIC LAMINAR BOUNDARY LAYER 



The solution of laminar boundary layers in either two-dimensional or axisymmetric 

 flows has been the subject of numerous mathematical investigations owing to the interesting 

 characteristics of the resulting equations of motion. The considerable literature that has 

 developed contains methods of various degrees of complexity and precision which are given in 

 the summaries by Goldstein^ and more recently in the AVA Monographs^ and by Schlichting.^ 

 For many drag calculations very precise solutions of the boundary layer, requiring extensive 

 numerical work, are usually not warranted, especially where the laminar boundary layer con- 

 stitutes a small part of the whole boundary layer. A simple approximate formula, well adapted 

 to drag calculations, will be devised by an extension to axisymmetric flow of a method of suc- 

 cessive approximiation introduced by Shvets^ for two-dimensional flows. 



Owing to the thinness of the laminar boundary layer on the forward part of the body, 

 5 « r , the equations of motion for steady axisymmetric boundary- layer flow past a body of 

 revolution with negligible longitudinal curvature (Reference 5) reduce to 



[17] 



dx dy p dx 



dp 



dy 



and the equation of contm.'j+y reduces to 



du , dv 



dr. 



^ ^ -if- ^=0 [18] 



dx dy ^ui "'^ 



Here u and v are the x- and y-components of the boundary-layer velocity respectively parallel 

 and normal to the surface of the body in the meridian plane, p is the pressure in the boundary 

 layer, v is the kinematic viscosity of the fluid, and 8 is the thickness of the boundary layer 

 in the y-direction. These equations have been shown^ to remain applicable at the forward 

 stagnation point for bodies with blunt noses even though both 5, r^^ -► 0. The following 

 boundary conditions are to be satisfied by the boundary-layer equations: 



