^21 = ^2 + ^12 (1^> 



This equation can be used to eliminate one of the unknowns from the boundary 

 layer momentum- integral equations. The Mager crossflow model, Equation (17), 

 in conjunction with the approximation 



u V 



.. (H-l)/2 



and Equation (10) for the nominal thickness 6, can be used to express the 

 crossflow boundary layer thicknesses in terms of the streamwise momentum 

 thickness 9^ , the shape parameters G and H, and the crossflow angle 3 by 

 the equations 



2 e (G+H) tan 3 

 ^21 = - H(H+1) (H+2) ^ ^11 ^- P ^l(«) (^^^) 



= - e^^(G+H) tan 3 [^ - 3^ + 3J^ + ^ - ^] ^ e^^ tan 3 f^CH) (21b) 

 = - 9^^(G+H) tan^ 3 [i _ -^ + ^ - ^ + ^] . 9^^^ tan^ 3 f3(H) (21c) 



62 = - 9^,(G+H) tan 3[3^ - ^ + ^] ^ 6^^ tan 3 f,(H) (21d) 



Thus Equations (8) through (11), (13), (17), (19), and (21), together with 

 the transformation Equations (6a-6f ) , can be used to reduce the total 

 number of unknown quantities to three, A convenient set of unknown 

 quantities, that are integrated in the ((j),9) coordinate system by Equations 

 (3) and (7) are the streamwise momentum thickness Q-iij the shape factor H, 

 and the tangent of the wall crossflow angle t = tan 3. The details of the 

 final forms of Equations (3) and (7) in terms of these variables are given 

 in the appendix. 



12 



22 



13 



