doubled because a pair of distributions on the body surface has coalesced 

 on the centerplane, as was done in the example of the boundary layer on a 

 flat plate. 



Similarly to (14), the displacement-thickness profile, y = h(x) , may 

 be expressed by 



h(x) ■= f(x) + S-. sec Y 



(19) 



and (17) becomes 



M^(x) = ^^ [u(x,0) h(x); 



(20) 



Comparison with the form of (16) now shows that, to the second order of 

 accuracy, the irrotational flow about the displaced surface satisfies the 

 specified boundary condition (8) at the edge of the boundary layer and wake. 



Solutions for Axisymmetric Flow - First Approximation 



Let r_(s) denote the radius of a body of revolution, where s is arc 

 length along a meridian section of the body, and r the radial distance to an 

 arbitrary point. Let n denote distance from the body along the outward 

 normal to its surface. We shall also employ cylindrical coordinates, (x,r) 

 where the axis of symmetry is taken as the x-axis, and put r„(s) = f (x) 

 and tan y = df/dx. The edge of the boundary layer is defined by the surface 



x' -x=6' siny' 



Figure 4 



