2 2 



= 9ti cos a - (6 -+9„^) sin a cos a + 9„„ sin a (6a) 



11 11 



12 21^ 



22 



2 2 



„ = (0 -0 ) sin a cos a + 0,„ cos a - 0„^ sin a (6b) 



2 2 



0„^ = (0^^-0„„) sin a cos a + 0„^ cos a - 0^„ sin a 



(6c) 



2 2 



0^^ = 0^, sin a + (0 „+0„ ) sin a cos a + 0„„ cos a 



22 11 



12 21' 



22 



(6d) 



A, = 6^ cos a - 6„ sin a 



(6e) 



A„ = 6^ sin a + 6„ cos a 



(6f) 



The inverses of Equations (6a-6f) that relate the lower case Greek symbols 



and 6 to their upper case counterparts easily can be derived. 



The two momentum equations, Equations (3a, 3b) are insufficient to 



determine the eight unknowns Q-,-,, ©-i o s '^oi ' ®99' ^i » '^9' ^f ^^^ ^f ' hence, 



(j) 



some other integral equations and empirical information are needed. The 



9 

 calculation method is based on the Cumpsty and Head momentum- integral 



8 7 



method which utilizes the three-dimensional entrainment equation 



u: (%^-"^i) - h (u.^-u^) 



917 (UgS-UA^) - Kg (U06-UA2) 



= F 



(7) 



where F is the three-dimensional rate of entrainment function. It is 

 assumed, in this three-dimensional boundary layer calculation method, that 



