each -n term. The solution of each set of simultaneous equations gives 

 the exponents of each variable in each tt term, as follows: 



-1 = ^L^'t^r(i^) '^'^^"- ^'"''^ 



For L, 

 For T, 

 For M, 

 Thus, 

 and 

 Similarly, 



and 



For L, 

 For T, 

 For M, 

 Thus, 

 and 



+ y, - 3z, - 1 = 



-y.i 



= . 





^1 



= . 





^1 



= 1, 



y, = 0, zj = , 



'^i 



_ a 

 b • 





'^2 



c ' 





'^S 



_ a 

 d ■ 





7r4 



= (L) 





X4 



+ y4 



- 3Z4 + 1 = . 



-y4 



+ 2 = 



. 



^4 



- 1 = 



. 



X4 



= 0, 



y4 = 2, Z4 = 1 , 



H '■ 



V2p 

 Ap 



V2 

 Ap/p • 



In a similar manner it can be shown that 



V^p V2 



D 



37 



ag 



'^e 



= Xi = 

 y^lp 



Va 



TTj 



_ v\ 



o/p ' 





^8 



V2 



E/p • 





(2-24) 



and 



TT^ is known as the Euler number, which is taken as the dependent vari- 

 able since it contains the essential characteristics of the flow itself. 



34 



