r^(s) = TqCs) + 6 cos y or g(x) = f(x') + 6 (x') cos y (x') (21) 



By a Taylor expansion about x, with dy/ds = - k, where k is the curvature 

 of the meridian profile, and with x' - x = 6(x') cos y(x'), g(x) becomes 



12 2 

 ;(x) = f(x) + 6 sec y + 66' tan y - •;r k6 tan y sec y + ... (22) 



The element of arc along a curve n = constant is h ds = (1+kn) ds . The 

 equation of continuity is then 



^p^+^ [(1+kn) rv] = (23) 



ds on 



where u(s,n) and v(s,n) are the actual velocity components in the directions 

 of increasing values of s and n. We shall also require the velocity com- 

 ponents U(s,n) and V(s,n) of the "equivalent" irrotational flow. 



The boundary-layer thickness of an axisymmetric boundary layer is 

 usually defined as 



h- \ V-, [- sfeff] - 



An alternative definition, in which a higher-order term is retained, is 

 given by 



6* 6 



j r U(s,6) dn = r [U(s,6)-u(s,n) ] 



dn = r„ U 6 



Since r = r + n cos y, this yields the quadratic equation 



Tq 6* + I 6*^ cos Y = r^ 6^ / (25) 



