Desai and Lieber 



3r 



a quantity whose order of magnitude cannot be determined in advance. Conse- 

 quently we cannot compare the orders of magnitude of the left-hand sides of 

 Eqs. (1.76a) and (1.76b), although we recognize that these contributions have 

 opposite signs insofar as the term involving ' . ~ 





3v, 



Tc 



is concerned. The result is that we cannot know in advance the orders of mag- 

 nitudes of these contributions to the total pressure field p. Since there is no 

 contribution to pressure from convective terms in Eqs. (1.75c) and (1.76c), the 

 pressure field P3 may be assumed to contribute little to the total pressure field 

 p if we bear in mind that U3 and V3 vanish at both boundaries. As argued be- 

 fore, higher iteration pressure fields p^ will behave essentially as P3, but with 

 decreasing intensity, and this indicates the relative unimportance of iterations 

 higher than the second, which, on the contrary, is very significant. 



A comparison of this case with the case previously considered shows that 

 in both instances the third and higher iterations are relatively unimportant as 

 compared to the first two iterations. In both cases, we may say that at least 

 two iterations are necessary and that they are sufficient to take into account, to 

 a large extent, the significant convective terms which are related to the curva- 

 ture of the streamlines. In this respect both the solutions of Eqs. (1.45) and 

 (1.46) are equally appropriate as base solutions. However, the solution of Eqs. 

 (1.45) is more appropriate than the solution of Eqs. (1.46), because the former 

 allows us to estimate the orders of magnitude of the linear and nonlinear con- 

 vective terms in Uj, Vj and their derivatives in advance, while the latter does 

 not, because of the unknown magnitude of 



Bv, 



It is interesting to note that this comparison tempts us to say that 



3l 



Br 



-2 sin 



i.e., it almost leads us to information which we cannot have in advance without 

 such a comparative study. Whether this information turns out to be correct or 

 not, it is still true that Eqs. (1.45) is the more appropriate solution from the 

 point of view of the a priori information that it provides. 



From both the physical and the mathematical considerations we then see 

 that the irrotational potential flow solution of Eq. (1.17) which satisfies all 



550 



